research article iterative mimo detection and channel...

Research ArticleIterative MIMO Detection and Channel Estimation UsingJoint Superimposed and Pilot-Aided Training

Omar Longoria-Gandara1 Ramon Parra-Michel2

Roberto Carrasco-Alvarez3 and Eduardo Romero-Aguirre4

1Department of Electronics Systems and IT ITESO Jesuit University 45604 Tlaquepaque JAL Mexico2Department of Electrical Engineering CINVESTAV-IPN 45015 Zapopan JAL Mexico3Department of Electronics and Communication CUCEI-Guadalajara University 44430 Guadalajara JAL Mexico4Department of Electrical and Electronic Engineering ITSON 85130 Ciudad Obregon SON Mexico

Correspondence should be addressed to Omar Longoria-Gandara olongoriaitesomx

Received 10 September 2015 Revised 19 January 2016 Accepted 25 February 2016

Academic Editor Yuh-Shyan Chen

Copyright copy 2016 Omar Longoria-Gandara et al This is an open access article distributed under the Creative CommonsAttribution License which permits unrestricted use distribution and reproduction in any medium provided the original work isproperly cited

This paper presents a novel iterative detection and channel estimation scheme that combines the effort of superimposed training(ST) and pilot-aided training (PAT) for multiple-input multiple-output (MIMO) flat fading channels The proposed methodhereafter known as joint mean removal ST and PAT (MRST-PAT) implements an iterative detection and channel estimation thatachieves the performance of data-dependent ST (DDST) algorithm with the difference that the data arithmetic cyclic mean isestimated and removed from data at the receiverrsquos end It is demonstrated that this iterative and cooperative detection and channelestimator algorithm surpasses the effects of data detection identifiability condition that DDST has shown when higher orders ofmodulation are used Theoretical performance of the MRST-PAT scheme is provided and corroborated by numerical simulationsIn addition the performance comparison between the proposed method and different MIMO channel estimation techniquesis analyzed The joint effort between ST and PAT shows that MRST-PAT is a solid candidate in communications systems formultiamplitude constellations in Rayleigh fading channels while achieving high-throughput data rates withmanageable complexityand bit-error rate (BER) as a figure of merit

1 Introduction

Estimation theory deals with the basic problem of inferring aset of required statistical parameters of a random experimentbased on the observation of its outcome It is assumed that itis possible to produce an effect in the experiment by meansof a controlled excitation signal This approach is normallyadopted in practical communications systems where channelestimation is an essential part of standard receiver designs [1]and carried out by transmitting training symbols commonlyknown as pilot symbols [2] In this case the random experi-ment can be seen as an unknown system that is identified byobserving how the system reacts to the applied excitation ortraining signal

Traditionally the most widely used channel estimationtechnique is pilot-assisted training where the pilots are

multiplexed in time or frequency This is widely known inthe literature as pilot symbol assistedmodulation (PSAM) [2]and is denominated as pilot-assisted transmission (PAT) [3]This scheme employs a nonrandom training pilot sequenceknown a priori by the transmitter and the receiverThe train-ing pilots are periodically inserted into certain positions inthe time (frequency) with the information-bearing symbolsbefore modulation and transmission Using the knowledge ofthe training symbols and the corresponding received signalthe channel estimation block at the receiver is able to makean estimate of the channel impulse response (CIR) Con-ventional PAT-based channel estimation methods use pilotsymbols in time-division multiplexing (TDM) schemes thusdecreasing the effective data transmission rate

Recently an alternative channel estimation strategy thatcircumvents the unwanted effect of data rate reduction has

Hindawi Publishing CorporationMobile Information SystemsVolume 2016 Article ID 3723862 11 pageshttpdxdoiorg10115520163723862

2 Mobile Information Systems

emerged called implicit training (IT) [4] Two outstanding ITapproaches known as superimposed training (ST) [5 6] anddata-dependent ST (DDST) [7 8] achieve higher effectivedata rates with manageable complexity [9] These techniquesare based on a training sequence added (superimposed) to theinformation-bearing symbols Both schemes provide a simple(unsophisticated) channel estimation process [10 11] anddiffer only in that the arithmeticmean of the transmitted dataof the DDST scheme is superimposed onto the transmittedsequence Both techniques have been successfully applied tosingle-input single-output (SISO) as well as multiple-inputmultiple-output (MIMO) systems [11ndash17] combined withorthogonal frequency division multiplexing (OFDM) modu-lations [18ndash20] and time-varying channels [21ndash23] Likewisethere are interesting alternatives to OFDM in [24 25] wherethe single-carrier modulation approach is employed using ajoint frequency domain equalization and channel estimation

Although DDST outperforms ST [12] in terms of channelestimation error it is worth mentioning that the data decod-ing underDDST is of an iterative nature as it needs to removethe data-dependent distortion Furthermore DDST [8] per-forms similarly to TDM-based channel estimation while sav-ing the overhead in TDM data rate due to pilot transmissionThere are however some drawbacks that must be takeninto consideration when DDST is used First this techniqueintroduces a delay in the transmitted data when it calculatesthe data-dependent signal second it assigns less transmis-sion power to the data signal hence the symbol demappingoperation is not suitable for higher orders of modulation dueto identifiability problems as was highlighted in [26] This isan important issue because recent communication standardsconsider this type ofmodulation for exampleWiMAX (IEEE80216e-2005 standard) uses 64-QAM digital modulationthat DDST cannot support In addition DDST presents twomore drawbacks its performance is highly sensitive to thedata block length used as well as the increased peak-powerand peak-to-average ratio (PAPR) in the transmitted signalas shown in [27]

This paper proposes an iterative detection and channelestimation structure for MIMO systems which is capableof dealing with the data identifiability problem previouslydescribed The novel algorithm is based on the use of joint(fusion of both techniques) implicit and explicit trainingfor the channel estimation and symbol detection processesPrevious results of the authors related to implicit trainingfor MIMO systems were presented in [28] which introducedthe mean removal ST (MRST) technique devoted to estimatethe arithmetic cycling mean of the data block signal at thereceiver side (instead of at the transmitter side like DDSTdoes) However later on it was recognized that MRST isnot able to deal with the identifiability problem just likeDDST when the MIMO system employs high-order digitalmodulation schemes

The proposal of an iterative detection and channelestimation scheme is hereafter referred to as joint meanremoval ST and PAT (MRST-PAT)Themethod is based on areliable preliminary channel estimate using PAT with a smallnumber of dedicated pilot symbols Subsequently it uses thetime-average estimator with the ST signal added to each

transmitted data block achieving an improvement in systemthroughputThusMRST-PATmerges the best qualities of thetwo techniques achieving a better BER performance than ifemployed separately In addition the proposedmethod elim-inates the data identifiability difficulties that DDST exhibitswhen higher orders of modulation are used [26]

This paper is organized as follows Section 2 presents thespace-time MIMO signal model Section 3 summarizes thefundamental theory and performance of PAT (TDM) STand DDST channel estimation techniques Section 4 detailsthe structure of the iterative MIMO detection and channelestimation joint MRST-PAT and its theoretical performanceanalysis Section 5 depicts the application of the iterative jointMRST-PATusing aG2-OSTBCcoder Section 6 considers thenumerical simulation results and performance analysis forthe training-based frequency-flat block-fading MIMO chan-nel estimation using TDM DDST and MRST-PAT Finallysome concluding remarks in Section 7 close this paper

Notation Bold letters in lower (upper) case are used to denotevector (matrices)C stands for the complex number field (sdot)119879

and (sdot)119867 represent transpose and conjugate transpose respec-

tively I119899119879denotes 119899

119879times119899119879identity matrix sdot and sdot

119865repre-

sent Euclidean norm and Frobenius norm respectively Trsdotdenotes trace of a matrix otimes stands for Kronecker productandCN(aΣ) denotes amultidimensional complex Gaussiandistribution with mean a and covariance matrix Σ

2 Space-Time Signal Model

This section describes the space-time signal model applicableto most existing space-time coding designs such as VerticalBell Labs Layered Space-Time (VBLAST) [29] and the gen-eralized schemes referred to as space-time block codes fromorthogonal designs [30]

With reference to Figure 1 this paper considers a MIMOsingle-carrier system operating over frequency-flat qua-sistatic block-fading channel model with 119899

119879transmit and 119899

119877

receive antennas described by

r = Hx + n (1)

where x isin C119899119879 is the transmitted vector comprising 119899119879

elements denoted as [1199091 1199092 119909

119899119879]119879 and r isin C119899119877 is the

received vectorWe use a random matrix H isin C119899119877times119899119879 that represents the

flat fading channel in a baseband equivalent model whereeach element is generated as an independent and identicallydistributed (iid) circularly symmetric complex Gaussianrandom variableCN(0 1) In addition n isin C119899119877 is an additivewhite circularly symmetric complex Gaussian noise vectorwith zero mean and variance 1205902

119899= 119873

02 per real and

imaginary dimensionLet us assume the block transmission scheme where a

ldquoblockrdquo is defined as a single transmission burst The channelmatrix H is assumed to be constant for 119873 channel uses andthen changes to an independent realization for the next block[31] Here 119873 denotes the block length For any 119899

119879times 119873

Mobile Information Systems 3

CIR

Channelestimator

Data

Pilot

Spac

e

Time

Decoder

PAT transmitter

HX

N

R

1

2

N

nT

X H

Figure 1 A generalized PAT transceiver

transmitted signal matrix X = (119909119894119895) the expression in (1) can

be written as

R = HX + N (2)

where

R ≜ [r (1) r (2) sdot sdot sdot r (119873)]

X ≜ [x (1) x (2) sdot sdot sdot x (119873)]

N ≜ [n (1) n (2) sdot sdot sdot n (119873)]

(3)

are the matrices of the received signals transmitted signalsand noise respectively

The transmit symbol vector prior to space-time codingof size119873

119878is denoted by

s ≜ [1199041 1199042

sdot sdot sdot 119904119873119878

]119879

(4)

where 119904119894isin S and S denotes a normalized (average symbol

energy of S is assumed to be one) signal constellation towhich information symbols belong

The vector s of119873119878information symbols is fed into a space-

time encoder which maps (one-to-one mapping) this vectorto 119899119879times 119873119866code matrix

G = (

11989211

sdot sdot sdot 1198921119873119866

d

1198921198991198791

sdot sdot sdot 119892119899119879119873119866

) isin C119899119879times119873119866 (5)

associated with the space-time scheme in use Therefore thespace-time code data rate in symbols per channel use isgiven by 120578 = 119873

119878119873119866 Additionally the transmitted signal X

is formed by using Δ = 119873119873119866concatenated code matrices

where the block length119873 is a positive integer multiple of119873119866

Particularly 119899119879

times 119873119866complex matrix-valued function

G(s) is called anOSTBC if it satisfies the following conditions[30]

(a) All entries ofG(s) are linear functions of119873119878complex

random variables 1199041 1199042 119904

119873119878and their complex

conjugates(b) For any arbitrary s in C119873119878times1

G (s)G119867 (s) = s2 I119899119879 (6)

3 Channel Estimation Techniques

Consider the PAT diagram in Figure 1 During the trans-mission of one block of information the data and pilotsymbols depicted by white and dark boxes respectively canbe transmitted separately or combined in different ways Forthe purpose of channel estimation the key to unifying variousschemes is to view the problem of training design as one ofpower allocation [3]

Conventionally a PAT scheme where some knownsymbols (pilots) are time-multiplexed (TDM) with theinformation-bearing data is known as a conventional pilot-(CP-) based MIMO system [32] This transmission scheme isshown in Figure 2 and analyzed in the following subsectionIn this case pilot symbols are known at the receiver and canbe used for channel estimation Since pilot symbols carry nodata information the time and the power spent on pilot sym-bols degrade the throughput of the system If more frequentpilot symbols are transmitted then a better channel estima-tion is achieved However the PAT transceiver shown in Fig-ure 1 suggests another scheme for solving the problem wherea training sequence is superimposed onto the dataThis tech-nique known as superimposed pilots (SIP) in [32] was intro-duced in [5] and has been developed extensively under differ-ent modalities such as ST in [33] implicit training in [4 6]and DDST in [7]

It should be emphasized that in the following calcula-tions H is assumed to be random The estimation processhowever will obtain estimates of the parameters of a par-ticular realization of H that corresponds to the current datablockWe consider the channel estimation procedure appliedto TDM ST DDST and MRST-PAT schemes starting fromthe least squares (LS) analysis proposed in [34]

31 PAT (TDM) Case With reference to Figure 2 let usconsider a PAT transceiver under TDM modality with 119873 =

119879+119871 In this scenario119879 is the number of pilot symbols trans-mitted in a given transmission interval (block) 119899

119879times119879matrix

C = (119888119894119895) represents the training signal transmitted at the

beginning of each block of information (preamble) and 119899119879times119871

matrix B = (119887119894119895) represents the information-bearing data of

length 119871 per transmit antenna In this scheme the data andtraining symbols have the same average power defined as119875

119887=

119864|119887119894119895| and 119875

119888= 119864|119888

119894119895| that is 119875

119887= 119875119888 It is clear that during

the training stage the transmission power is allocated to thepilot symbols that is 119875

119888= 119875119909 where 119875

119909= 119864|119909

119894119895| denotes

the average power of the transmitted symbolIt is important to note that the TDM-based channel

estimation algorithm employs only the pilot signals It followsthat the noise contribution and the received signal spanduring 119879 channel uses In this caseR andN have dimensions119899119877times 119879


CIR

Channelestimator

Spac

e

Time

Decoder

TDM transmitter

HX

N

R

1

2

nT

XH

C pilot

B data

Figure 2 Block diagram of PAT transceiver using TDM transmitter

Assuming thatC has full row-rank knowing the receivedsignalR and using the LS approach as is developed in [34 35]then the realization of channel matrixH can be estimated as

HTDM = RC119867 (CC119867)minus1

= RCdagger (7)

where Cdagger = C119867(CC119867)minus1 is the pseudoinverse of C Con-straining the transmitted power during the training intervalthe following is obtained

C2

119865= 119899119879119879119875119909= P (8)

Let us findC that minimizes the channel estimation errorand satisfies condition (8) This is equivalent to the followingoptimization problem

minC

119864 10038171003817100381710038171003817H minus HTDM

10038171003817100381710038171003817

2

119865 (9)

Using (2) and (7) we have H minus HTDM = NCdagger and thereforethe objective function can be written as

JTDM = 119864 10038171003817100381710038171003817H minus HTDM

10038171003817100381710038171003817

2

119865 (10)

Using EN119867N = 1205902119899119899119877I119879with 1205902

119899representing the receiver

noise power then (10) can be rewritten as

JTDM = 119864 10038171003817100381710038171003817NCdagger100381710038171003817100381710038172

119865 = 1205902

119899119899119877Tr Cdagger119867Cdagger

= 1205902

119899119899119877Tr (CC119867)

minus1

(11)

From (11) the optimization problem shown by (9) can beequivalently reformulated as

minC

Tr (CC119867)minus1

(12)

The choice ofCmust be such thatCC119867 is nonsingular whichimplies that 119879 ge 119899

119879 Furthermore any training matrix is

optimal in the sense of (12) if it satisfies

CC119867 =P

119899119879

I119899119879 (13)

In other words any matrix C with orthogonal rows of thesame normradicP119899

119879is optimal [35]

For optimal training that satisfies (13) the LS channelestimate (7) yields

HTDM = (119899119879

P)RC119867 = H + (

119899119879

P)NC119867 (14)

that is the estimation error is (119899119879P)NC119867

From (11) and (13) it follows that the channel estimationerror under the MSE criterion and optimal training is givenby

MSETDM (H) =12059021198991198992119879119899119877

P (15)

Finally using the constraint indicated in (8) for the TDM-based estimate the channel estimation error can be expressedas

MSETDM (H) =1205902119899119899119879119899119877

119879119875119909

(16)

32 Superimposed Training Case Let us consider Figure 1with an ST-based channel estimation algorithm In compari-son with TDM-based channel estimation the ST scheme has119875119887

= 0 throughout the transmission and the training matrixC is 119899119879times119873matrix that is119879 equiv 0 For this reason this scheme is

called overlay pilot in [32] It follows that (2) can be describedas

R = H (B + C) + N (17)

Accordingly the least square (LS) channel estimate canbe obtained by treating HB as an extra additive noise termfor channel estimation purposes Even though there are aninfinite number of matrices C that satisfy the optimum con-dition of (12) the goal is to select a trainingmatrix that makesthe ST technique computationally attractive

Under frequency-flat fading conditions the optimallength of the training interval is 119899

119879[36] Hence the training

matrix C may be a block column matrix that can be con-structed by 119876 concatenated replicas of C

119887matrix where 119876 =

119873119899119879 and the block length119873 is chosen to be an integermulti-

ple of the number of transmit antennas 119899119879Then the training

matrix C can be written as

C = u otimes C119887 (18)

where u is the unit 1times119876 vector and the block training patternC119887is 119899119879times 119899119879matrix where their rows are orthogonal to each

other and it satisfies the constraint C119887C119867119887

= 119899119879119875119888I119899119879

The training sequence at ℓth transmit antenna is given by

119888 (ℓ 119899) = radic119875119888exp(

1198952120587119899 (ℓ minus 1)

119899119879

) (19)

with ℓ = 1 119899119879and 119899 = 0 119873minus1 Another way to build

the training sequence is by shaping C119887matrix as a circulant

matrix whose first row entries are given by

119888119887 (1 V) = radic119875

119888(exp(

119895120587

119899119879

))

(V(V+120572))

(20)


where V = 0 119899119879minus 1 with 120572 = 2 when 119899

119879is even and

120572 = 1 if 119899119879is odd [6] The Walsh-Hadamard matrices are

other attractive optionsThe benefit of using any of these training patterns is that a

time-domain estimator based on the synchronized averagingof the received signal R can be implemented as in the SISOcase described in [12]

Let R be 119899119877times 119899119879matrix which defines the time-average

of the received signal R We assume that the channel remainsconstant over the entire block length of time 119873 Specifically(119894 119895)th entry of R is given by

R119894119895

= (1

119876)

119876

sum119896=1

R119894119895+119899119879(119896minus1)

(21)

where 119894 = 1 2 119899119877and 119895 = 1 2 119899

119879

It follows that R can be written as

R = (1

119876)RU (22)

where U is 119873 times 119899119879matrix constructed by 119876 concatenated

replicas of identity matrix I119899119879

and is given by

U = u119879 otimes I119899119879 (23)

From (17) and (22) R can be reformulated as

R = H [(1

119876) (BU + CU)] + (

1

119876)NU

= H (B + C119887) + N

(24)

where B is 119899119879times119899119879matrix and N is 119899

119877times119899119879matrix that represent

the time-average of the data B and noise N respectively forevery block transmitted Moreover C

119887= (1119876)CU Since

the training matrix C119887is known at the receiver the channel

matrix realization can be estimated as

HST = RCminus1119887 (25)

From (24) and (25) the channel estimation error is given by

HST minusH = HBCminus1119887

+ NCminus1119887 (26)

Since C119887is an orthogonal matrix that satisfies C

119887C119867119887

=

119899119879119875119888I119899119879

then Cminus1119887

= (1119899119879119875119888)C119867119887 Therefore using this

result in (26) the channel estimate (for the ST case) can beexpressed as

HST =1

119899119879119875119888

[H (B + C119887) + N]C119867

119887

= H +1

119899119879119875119888

(HB + N)C119867119887

(27)

The MSE of the ST case can be found in [11] It may beinferred from (27) that B represents an extra term for thechannel estimate This time-average term is exploited by thefollowing method

33 Data-Dependent ST Case In DDST the signal B =

(1119876)BU is used to define the perturbation matrix

E = minus (u otimes B) (28)

which will be arithmetically added to the data signal Bin every transmitted block Hence the transmitted signal isdetermined byX = B+E+C and the corresponding receivedsignal is given by

R = H (B + E + C) + N (29)

It is important to stress that the term Bwill be nonexistentat the receiver end because it was removed at the transmitterside when the signal Ewas added Hence using (25) and (27)the LS time-domain channel estimator based on the synchro-nized averaging of the received signal R is given by

HDDST = H + (1

119899119879119875119888

) NC119867119887 (30)

Subsequently the mean-square channel estimation errorunder optimal training with C

119887C119867119887

= 119899119879119875119888I119899119879

is given by

MSEDDST (H) = 119864 10038171003817100381710038171003817HLS minusH10038171003817100381710038171003817

2

119865 = 119864

10038171003817100381710038171003817NCminus1119887

10038171003817100381710038171003817

2

119865 (31)

Using N = (1119876)NU the DDST mean-square estimationerror may be expressed as

MSEDDST (H) = 11986410038171003817100381710038171003817100381710038171003817

1

119876(NU)Cminus1

119887

10038171003817100381710038171003817100381710038171003817

2

119865

(32)

by replacing the inverse of C119887 A2

119865= TrA119867A and

119864N119867N = 1198991198771205902119899I then

MSEDDST (H) =1198991198771205902119899

(119899119879119875119888119876)2Tr C119887U119867UC119867

119887 (33)

which is finally reduced to

MSEDDST (H) =1198991198771205902

119899

(119899119879119875119888119876)2119876 (119899119879119899119879119875119888) =

1198991198791198991198771205902

119899

119873119875119888

(34)

In order to have the same estimation error performancebetween the DDSTmethod and the TDM-based estimate wecompare (16) and (34) and the resulting relation is given by

119875119888

119875119909

=119879

119873 (35)

Similar expressions for (34) and (35) are obtained usinganother procedure in [11]

In DDST the data-dependent term has the purposeof removing the dependency on data therefore certainfrequency components are removed at the transmitter anddata symbolsmay be distortedThis data distortion becomes aproblem at the receiver when its value is commensurable withthe Euclidean distance between the symbols of the constella-tion used It is more significant as the order of modulation


increases at fixed transmission power In this case thereceiver would not be able to identify the signals from theconstellation This problem was highlighted and designatedthe data identifiability problem in [26] In preliminary DDSTworks such as [7 8] the data distortion is removed in thereceiver using an iterative method that performs effectivelyfor low orders of modulations Recently in [26] another iter-ative removal scheme is proposed for high orders of modula-tions In what follows we will show a hybrid trainingmethodthat overcomes this impairment by combining ST and PAT

4 Iterative Joint MRST-PAT

Even though the DDST channel estimate is better (accordingto the LS criterion) than the ST estimate theDDST techniquepresents several disadvantages compared to ST as mentionedin the Introduction Here we want to stress only its maindrawbacks it cannot work with high-order constellationsand it is highly sensitive to block length For these mainreasons it is desirable to find ST improvements that do notpresent these disadvantages

The MRST scheme in [28 37] was developed from thefollowing two points (i) the fact that the difference betweenST (27) and DDST (30) channel estimation techniques is thefactor HB and (ii) the hypothesis that if we could obtain anestimate of the signal E at the receiver end we would achievethe performance of DDST in terms of channel estimate MSEHowever as more power is allocated to data signals BERperformance should increase

Assuming this hypothesis the signalE can be approachedas E ≃ minus(u otimes

B) with B = (1119876)BU where B represents thedata estimate computed at the receiver Then using (24) and(25) the MRST-PAT channel estimate is given by

HMRST-PAT = RCminus1119887

= (H (B + C119887) minus H B + N)Cminus1

119887

= H +1

119899119879119875119888

[(HB minus H B) + N]C119867119887

(36)

it follows that if H B = HB then HMRST-PAT = HDDST andsubsequently MSEMRST-PAT(H) = MSEDDST(H)

As its name indicates theMRST algorithm has the goal ofremoving the mean of the data-bearing signal at the receiverin an iterative way The structure of this algorithm offersanother benefit

The initial channel estimation may be performed in oneof several ways employing the ST scheme designating afew pilots according to [36] at the beginning of each blocktransmitted in the TDM scheme or using the expectationmaximization (EM) algorithm with iterative decoding strate-gies [38]

In order to make a reliable estimate ( B) of B we considerthe joint effort of PAT (TDM) and ST techniques This isillustrated in Figure 3 where P represents 119899

119879times 119879 matrix of

pilot symbolsThe pilots are considered to have a preliminarychannel estimate and consequently an initial estimate Bof B then the superimposed training signal is used in the

CIR

Channelestimator

Spac

e

Time

Decoder

TDM and ST transmitter

X

H

N

R

1

2

nT

X

H

B dataC ST signal

P pilot

B

Figure 3 Block diagram of a transceiver with MRST-PAT

refinement phase to improve upon the initial estimate Thefollowing steps describe the iterative detection and channelestimation procedure of the joint MRST-PAT technique

(1) Set 119873119879 and compute 119871 = 119873 minus 119879 In this case 119876 =

119871119899119879

(2) Set the number of iterations denoted by numIterSTfor the ST phase

(3) Use (14) to obtain a preliminary channel estimateusing the pilots in the TDM case

(4) Use the channel estimated to obtain B which repre-sents an estimate of the transmitted symbols

(5) If numIterST gt 0 compute the signal B with B =

(1119876)BU else end(6) Compute the time-average of the received signal R

and make Rold= R

(7) Remove B from the received signal to obtain new Rnew

according to

Rnew= Rold

minus H B (37)

(8) Use (36) with R = Rnew to obtain the channel estimateHMRSTminusPAT

(9) Decrease the value of numIterST(10) Go to step (4)

5 MRST-PAT for AlamoutiSpace-Time Coding

In this section we will show the use of the proposed MRST-PAT channel estimation method with G2-OSTBC system(Alamouti scheme) using 119899

119879= 2 and 119899

119877= 2 This

implementation assumes 119873 and 119879 to be even so 2 times 119873


transmitted matrix is given by X = [G1 G2

sdot sdot sdot GΔ] In

extended form

X =[[[

[

1199041

minus119904lowast2

1199043

minus119904lowast4

sdot sdot sdot 119904119873minus1

minus119904lowast119873

1199042

119904lowast1⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟

G1

1199044

119904lowast3⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟

G2

119904119873

119904lowast119873minus1⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟

GΔ

]]]

]

(38)

Thematrixrsquos rows and columns indicate the transmit antennaand the time slot (channel use) respectively

2 times 119879 pilot matrix P is given by

P = [1199011

minus119901lowast2

1199013

minus119901lowast4



1199012

119901lowast1

1199014

119901lowast3

sdot sdot sdot 119901119879

119901lowast119879minus1

] (39)

The entries of the pilot matrix are given by the Walsh-Hadamard bipolar spreading sequences [39] The Walsh-Hadamard sequences of length119872 with119872 = 2

119898 and119898 isin Nare often defined using Hadamard matricesW

119872[2] with

W2= [

1 1

1 minus1]

W2119872

= [W119872

W119872

W119872

minusW119872

]

(40)

The resulting matrices W119872

are orthogonal matrices that isfor every119872 we have

W119872W119879119872

= 119872I119872 (41)

where I119872is the119872-dimensional identitymatrix Additionally

the structure of W2assures that the rows (or columns) of a

Hadamard matrix are mutually orthogonal2 times 119871 data-bearing matrix B is given by

B = [1198871

minus119887lowast2

1198873

minus119887lowast4



1198872

119887lowast1

1198874

119887lowast3



] (42)

In this case the matrix U has a dimension of 119871 times 2 andtherefore B = (1119876)BU is a 2 times 2matrix

Assuming a frequency-flat fading scenario [36] C119887

matrix can be composed of two symbols 1198881 1198882and two other

symbols generated through the Alamouti scheme exploitingthe property of orthogonality In this way

C119887= [

1198881

minus119888lowast2

1198882

119888lowast1

] (43)

Likewise 2 times 119871 ST matrix C is given by

C =[[

[

1198881

minus119888lowast2

1198881

minus119888lowast2


minus119888lowast2

1198882

119888lowast1⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟

C119887

1198882

119888lowast1⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟

C119887


119888lowast1⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟

C119887

]]

]

(44)

and therefore the two row vectors of matrixC are orthogonalThe initial channel estimate (step (3) of the iterative

algorithm) is performed using the symbol pilot matrix P

with the TDM scheme An improved estimate of the channelmatrix H will be made using the ST time-domain estimatorpursuant to the iterative algorithm described in Section 4

Let us estimate the channel matrix H For the sake ofsimplicity we restricted the analysis to a noise-free scenarioFrom (24) the time-average of the received signal is given by

vec R =

[[[[[[[

[

ℎ11

(1+ 1198881) + ℎ12

(1198872+ 1198882)

ℎ21

(1+ 1198881) + ℎ22

(1198872+ 1198882)

minusℎ11

(2+ 1198882)lowast

+ ℎ12

(1198871+ 1198881)lowast

minusℎ21

(2+ 1198882)lowast

+ ℎ22

(1198871+ 1198881)lowast

]]]]]]]

]

(45)

where vecsdot is the column-wise vectorization operator Sub-sequently the expression in (45) can be reformulated as

vec R = A vec H119879 (46)

with A = [

[

(1+1198881) (2+1198882) 0 0

0 0 (1+1198881) (2+1198882)

minus(2+1198882)lowast(1+1198881)

lowast0 0

0 0 minus(2+1198882)lowast(1+1198881)

lowast

]

]

An estimate of A can be used for the purpose of avoidingthe computational complexity of H B in step (7) therefore

A

=

[[[[[[[[[

[

(1198871+ 1198881) (

1198872+ 1198882) 0 0

0 0 (1198871+ 1198881) (

1198872+ 1198882)

minus(1198872+ 1198882)lowast

(1198871+ 1198881)lowast

0 0

0 0 minus (1198872+ 1198882)lowast

(1198871+ 1198881)lowast

]]]]]]]]]

]

(47)

It is important to note that A is an orthogonal matrixConsequently the channel estimate matrix is given by

vec H119879 = Aminus1vec R (48)

and finally

H = [(vec I119899119877119879

otimes I119899119879) (I119899119877

otimes vec H119879)]119879

(49)

where I119899119879

and I119899119877

are 119899119879times 119899119879and 119899

119877times 119899119877identity matrices

respectively Matrix H represents a new MIMO channelestimate which is used in the iterative procedure to obtaina new estimate of the arithmetic mean of the data-bearing

The key idea of this procedure is the removal of the meanat the receiver Instead of subtracting themean from the time-average received matrix R this MRST-PAT implementationincorporates the estimated mean B in the matrix A to obtainan estimate of the channel

6 Simulation Results

The following section presents the performance of the pro-posed channel estimation scheme in a frequency-flat fading


5 10 15 200SNR (dB)

10minus3

10minus2

10minus1

100

MSE

of c

hann

el es

timat

e

DDST Pc = 017 theoretical resultMRST-PAT iter 1 Pc = 017 Oh = 4256

DDST Pc = 017

Figure 4MSE of channel estimate exhibited by theG2-OSTBC 2times2

system employing QPSK

scenario A G2-OSTBC system with 119899119879

= 119899119877

= 2 antennaswas usedThis simulation scenario was also employed in [28]The block length was fixed to 119873 = 256 symbols unlessanother value is indicated and all simulations were run until1000 block errors were found The BER is represented as afunction of the average SNR where119873

0= 119864119904119899119879SNR and119864

119904is

the average symbol energy QPSK and 119872-ary QAM (119872 gt 4)constellations were used with Gray-coded symbols and thetransmitted power level for each antenna was normalized toone for example 119875

119909= 1 (Watt)

To test the channel estimation techniques we use as a fig-ure of merit the MSE of channel estimate Figure 4 plots thismetric for DDST and MRST-PAT using QPSK Both of theseuse 119875119888= 17 of the transmitted power 119875

119909 This power level

was chosen using the values of previous works such as [6 1528]

The initial channel estimation for theMRST-PAT schemewas implemented using 119879 = 4 pilots per block transmitted(remember that an Alamouti space-time coding scheme isconsidered) hence the overhead associated with the pilots is119874ℎ= 119879119873 = 4256 which is 156 For the ST stage 119871 = 252

symbols are usedThrough an analysis of this performance it can be noted

that the proposed scheme approaches DDST for SNR valueshigher than 10 dB as was anticipated However it is worthhighlighting that although the MSE channel estimate inMRST-PAT is not close to DDST at low SNR levels it is goodenough to provide a close BER performance which is theultimate metric for system comparison

Before considering the BER performance let us discussFigure 5 which shows the MSE versus power fraction fortraining signal with the SNR fixed at 15 dB andQPSK signalsThree different channel estimation schemes (TDM DDSTandMRST-PAT) were compared If 119875

119888119875119909= 119879119873 with 119879 = 4

and119873 = 256 then the three schemes have the sameMSE per-formance It can be observed that the proposed MRST-PATscheme follows DDST for all power levels of 119875

119888 The selected

SNR value is based on [11] because it allows a suitable BER

DDSTTDM Oh = 4256

MRST-PAT iter 1 Oh = 4256

10minus3

10minus2

10minus1

MSE

of c

hann

el es

timat

e

05042032022012002Pc

Figure 5 MSE of channel estimate versus power fraction fortraining exhibited by theG2-OSTBC 2times2 at SNR= 15 dB employingQPSK

TDM 17 overhead

15 201050SNR (dB)

BER

10minus6

10minus4

10minus2

MRST-PAT iter 1 Pc = 17Oh = 4256

DDST iter 1 Pc = 17

Figure 6 BER performance exhibited by the G2-OSTBC 2 times 2


TheBERperformance of thisMIMOsystemworkingwithQPSK signals is shown in Figure 6 It can be seen that theTDM scheme achieves the best BER performance at the costof 17 of data rate overhead due to pilot transmission whileMRST-PATwith 156of overhead for example119874

ℎ= 4256

achieves very close to DDST BER performanceIn this scenario DDST matches the relation described in

(35) for the purpose of having the same MSE performance asTDM the parameters forMRST-PATwere chosen to have thesame training power119875

119888as DDST and 4 pilots although under

frequency-flat fading conditions the minimum length is 119899119879

[36]According to [26] when119872-ary QAM constellations with

119872 ge 16 are used there is evidence of DDST performancedegradation due to the data identifiability problem which isdiscussed in the following paragraph

In some block realizations the data-dependent signaldistortion can have more power than the difference betweentwo symbols consequently the data-bearing signal will be


10minus3

10minus2

10minus1

100

BLER

20 251510SNR (dB)

MRST-PAT iter 1Pc = 925 Oh = 4256

DDST iter 1 Pc = 925


TDM Oh = 32256

Figure 7 BLER performance exhibited by the G2-OSTBC 2 times 2

system employing 16 QAM

3020 251510SNR (dB)

10minus6

10minus4

10minus2

100

BER

MRST-PAT iter 1 Pc = 925

Oh = 4256


Oh = 2256


TDM Oh = 32256 TDM Oh = 8256



modified to such a degree that it is not possible to correctlyrecover it

Figure 7 shows the block error rate (BLER) performanceusing 16 QAM signals In this case BLER performanceis used because it is a relevant measurement used for 3GPP performance testing requirements which determine thequality of the radio link It corresponds to the ratio of thenumber of blocks received with at least one symbol error tothe total number of blocks transmitted

It can be observed that at fixed BLER of 10minus2 an advantageclose to 1 dB was accomplished by MRST-PAT over DDSTboth using one iteration and 119875

119888= 925 of the transmitted

powerFigure 8 plots the BER performance for 64 QAM signals

Here the advantage of the proposed MRST-PAT algorithmis more evident An interesting analysis is that MRST-PAT(119874ℎ= 4256 and one iteration) shows the same performance

as TDM with 119874ℎ= 8256 MRST-PAT (119874

ℎ= 2256 and two

DDST iter 2TDM 2 pilotsTDM 4 pilotsTDM 8 pilots

TDM 32 pilotsMRST-PAT 2 pilots iter 2MRST-PAT 2 pilots iter 1

10minus6

10minus4

10minus2

100

BER

103

104

102

Block length (symbols)

Figure 9 BER versus block length of G2-OSTBC 2 times 2 system atSNR = 30 dB and 119875

119888= 75 for 64 QAM

iterations) approaches TDM with 119874ℎ= 8256 in 05 dB for

SNR levels above 20 dBFigure 9 plots the performance of 64 QAM G2-OSTBC

versus the block length for the SNR fixed at 30 dB and 119875119888=

75 forDDST andMRST-PAT It can be seen from the figurethat DDST for short block length yields poor results and forlarge block length (119873 = 8192 symbols) approachesTDMwitheight pilots while MRST-PAT for short block length yieldsgood results and the performance increases proportionally as119873 increases

It is important to note that DDSTrsquos BER performanceis highly sensitive to block length In this scenario we canappreciate the benefits and flexibility of theMRST-PAT struc-ture which exploits the presence of the known training sym-bols and the fact that the ST algorithm achieves a better chan-nel estimate when the block length of the data transmittedis increased Hence the system user can change the param-eters according to the requirements of block length or lessrate loss for example fewer dedicated pilots or BER perfor-mance

Finally it is important to analyze the BER performanceversus the power fraction for the training signal with theSNR fixed at 34 dB and 256 QAM signals This SNR value iscommonly required for this order of modulation Figure 10shows that DDST exhibits a poor BER performance for everyvalue of power fraction allocated to the training signal How-ever the BER performance exhibited by the MRST-PAT con-firms that the proposed method overcomes the identifiabilityproblem andmakes the superimposed technique an attractivechoice for multiamplitude QAM constellations The samebehavior is found at other SNR levels

For future research purposes the proposed approach willbe used with more sophisticated equalizers such as thatdeveloped in [24 25 28] as well as with channel coders Theresults obtained in this future researchwill allow determiningthe scenarios under which this new technique represents thebest practical solution to be employed


DDST iter 2

04 050302010Pc

10minus6

10minus4

10minus2

100

BER


Figure 10 BER performance versus power fraction for trainingexhibited by theG2-OSTBC 2times2 system at SNR = 34 dB employing256 QAM

7 Conclusion

The iterative joint MRST-PAT MIMO detection and channelestimation technique introduced in this contribution dealseffectively with DDSTrsquos identifiability problem when higher-order modulation schemes are used This leads to commu-nication systems that achieve near-DDST performance forlow-order symbols such as BPSK and QPSK and attainPAT (TDM) performance for higher-order symbols such as16 QAM or beyond with minimal reduction in throughputand using a computationally efficient implementation SinceMRST-PAT is an iterative joint scheme it can take advantageof both efforts that is using pilots by means of explicit train-ing (PAT) and taking the benefit of the implicit training usingthe ST training signal in the transmitted block Consequentlymore flexible communication systemsmay be built accordingto different requirements and constraints Similar results areexpected for MIMO frequency-selective channels

Competing Interests

The authors declare that they have no competing interests

References

[1] H Arslan and G E Bottomley ldquoChannel estimation in narrow-band wireless communication systemsrdquo Wireless Communica-tions and Mobile Computing vol 1 no 2 pp 201ndash219 2001

[2] J K Cavers ldquoAn analysis of pilot symbol assistedmodulation forRayleigh fading channels [mobile radio]rdquo IEEE Transactions onVehicular Technology vol 40 no 4 pp 686ndash693 1991

[3] L Tong B M Sadler and M Dong ldquoPilot-assisted wirelesstransmissions general model design criteria and signal pro-cessingrdquo IEEE Signal Processing Magazine vol 21 no 6 pp 12ndash25 2004

[4] S Haykin and K J R Liu Handbook on Array Processing andSensor Networks Wiley-Blackwell Hoboken NJ USA 2010

[5] B Farhang-Boroujeny ldquoPilot-based channel identification pro-posal for semi-blind identification of communication channelsrdquoElectronics Letters vol 31 no 13 pp 1044ndash1046 1995

[6] A G Orozco-LugoMM Lara andD CMcLernon ldquoChannelestimation using implicit trainingrdquo IEEE Transactions on SignalProcessing vol 52 no 1 pp 240ndash254 2004

[7] M Ghogho D McLernon E Alameda-Hernandez and ASwami ldquoChannel estimation and symbol detection for blocktransmission using data-dependent superimposed trainingrdquoIEEE Signal Processing Letters vol 12 no 3 pp 226ndash229 2005

[8] E Alameda-Hernandez D C McLernon A G Orozco-Lugo M M Lara and M Ghogho ldquoFrametraining sequencesynchronization and DC-offset removal for (data-dependent)superimposed training based channel estimationrdquo IEEE Trans-actions on Signal Processing vol 55 no 6 pp 2557ndash2569 2007

[9] E Romero-Aguirre R Carrasco-Alvarez R Parra-Michel AG Orozco-Lugo and A F Mondragon-Torres ldquoFull-hardwarearchitectures for data-dependent superimposed training chan-nel estimationrdquo Journal of Signal Processing Systems vol 70 no2 pp 105ndash123 2013

[10] F Martın del R Campo R Perez-Andrade and A G Orozco-Lugo ldquoA system on a programmable chip architecture fordata-dependent superimposed training channel estimationrdquoInternational Journal of Reconfigurable Computing vol 2009Article ID 912301 10 pages 2009

[11] M Ghogho and A Swami ldquoChannel estimation for MIMO sys-tems using data-dependent superimposed trainingrdquo in Proceed-ings of the 42nd Annual Allerton Conference on CommunicationControl and Computing Urbana Champaigh Ill USA 2004

[12] M Ghogho D McLernon E Alameda-Hernandez and ASwami ldquoSISO and MIMO channel estimation and symboldetection using data-dependent superimposed trainingrdquo inProceedings of the IEEE International Conference on AcousticsSpeech and Signal Processing (ICASSP rsquo05) vol 3 pp ii461ndashiii464 IEEE March 2005

[13] S M A Moosvi D C McLernon E Alameda-HernandezA G Orozco-Lugo and M M Lara ldquoA low complexityiterative channel estimation and equalisation scheme for (data-dependent) superimposed trainingrdquo in Proceedings of the 14thEuropean Signal Processing Conference (EUSIPCO rsquo06) pp 1ndash5Florence Italy September 2006

[14] X Meng and J K Tugnait ldquoSemi-blind channel estimationand detection using superimposed trainingrdquo in Proceedings ofthe IEEE International Conference on Acoustics Speech andSignal Processing (ICASSP rsquo04) vol 4 pp iv-417ndashiv-420 IEEEMontreal Canada May 2004

[15] R Carrasco-Alvarez R Parra-Michel A G Orozco-Lugo andJ K Tugnait ldquoEnhanced channel estimation using superim-posed training based on universal basis expansionrdquo IEEE Trans-actions on Signal Processing vol 57 no 3 pp 1217ndash1222 2009

[16] S He J K Tugnait and X Meng ldquoOn superimposed trainingfor MIMO channel estimation and symbol detectionrdquo IEEETransactions on Signal Processing vol 55 no 6 pp 3007ndash30212007

[17] X Meng J K Tugnait and S He ldquoIterative joint channelestimation and data detection using superimposed trainingalgorithms and performance analysisrdquo IEEE Transactions onVehicular Technology vol 56 no 4 pp 1873ndash1880 2007

[18] R Dinis N Souto J Silva A Kumar and A Correia ldquoOnthe use of implicit pilots for channel estimation with OFDMmodulationsrdquo inProceedings of the IEEE 66thVehicular Technol-ogy Conference (VTC rsquo07) pp 1077ndash1081 Baltimore Md USAOctober 2007


[19] N Chen and G T Zhou ldquoSuperimposed training for OFDMa peak-to-average power ratio analysisrdquo IEEE Transactions onSignal Processing vol 54 no 6 pp 2277ndash2287 2006

[20] A Goljahani N Benvenuto S Tomasin and L VangelistaldquoSuperimposed sequence versus pilot aided channel estimationsfor next generation DVB-T systemsrdquo IEEE Transactions onBroadcasting vol 55 no 1 pp 140ndash144 2009

[21] H Zhang X Dai D Li and S Ye ldquoLinearly time-varying chan-nel estimation and symbol detection for OFDMA uplink usingsuperimposed trainingrdquo EURASIP Journal onWireless Commu-nications and Networking vol 2009 no 1 Article ID 3073752009

[22] R Carrasco-Alvarez R Parra-Michel A G Orozco-Lugoand J K Tugnait ldquoTime-varying channel estimation usingtwo-dimensional channel orthogonalization and superimposedtrainingrdquo IEEE Transactions on Signal Processing vol 60 no 8pp 4439ndash4443 2012

[23] X Dai H Zhang and D Li ldquoLinearly time-varying channelestimation for MIMOOFDM systems using superimposedtrainingrdquo IEEE Transactions on Communications vol 58 no 2pp 681ndash693 2010

[24] R Dinis C-T Lam and D Falconer ldquoJoint frequency-domain equalization and channel estimation using superim-posed pilotsrdquo in Proceedings of the IEEE Wireless Communi-cations and Networking Conference (WCNC rsquo08) pp 447ndash452IEEE Las Vegas Nev USA 2008

[25] N Benvenuto R Dinis D Falconer and S Tomasin ldquoSinglecarrier modulation with nonlinear frequency domain equaliza-tion an idea whose time has comemdashagainrdquo Proceedings of theIEEE vol 98 no 1 pp 69ndash96 2010

[26] TWhitworth M Ghogho and D CMcLernon ldquoData identifi-ability for data-dependent superimposed trainingrdquo in Proceed-ings of the IEEE International Conference on Communications(ICC rsquo07) pp 2545ndash2550 IEEE Glasgow Scotland June 2007

[27] T Levanen J Talvitie andM Renfors ldquoPerformance evaluationof time-multiplexed and data-dependent superimposed train-ing based transmission with practical power amplifier modelrdquoEURASIP Journal onWireless Communications and Networkingvol 2012 no 1 article 49 2012

[28] O Longoria-Gandara R Parra-MichelM Bazdresch andAGOrozco-Lugo ldquoIterative mean removal superimposed trainingfor SISO and MIMO channel estimationrdquo International Journalof DigitalMultimedia Broadcasting vol 2008 Article ID 5352699 pages 2008

[29] PWWolniansky G J Foschini G D Golden and R A Valen-zuela ldquoV-BLAST an architecture for realizing very high datarates over the rich-scattering wireless channelrdquo in Proceedingsof the URSI International Symposium on Signals Systems andElectronics (ISSSE rsquo98) pp 295ndash300 October 1998

[30] V Tarokh H Jafarkhani and A R Calderbank ldquoSpace-timeblock codes from orthogonal designsrdquo IEEE Transactions onInformation Theory vol 45 no 5 pp 1456ndash1467 1999

[31] A Gershman and N Sidiropoulos Space-Time Processing forMIMO Communications John Wiley amp Sons New York NYUSA 2005

[32] M Coldrey and P Bohlin ldquoTraining-based MIMO systemsmdashpart I performance comparisonrdquo IEEE Transactions on SignalProcessing vol 55 no 11 pp 5464ndash5476 2007

[33] J K Tugnait and W Luo ldquoOn channel estimation usingsuperimposed training and first-order statisticsrdquo IEEE Commu-nications Letters vol 7 no 9 pp 413ndash415 2003

[34] S M Kay Fundamentals of Statistical Signal Processing VolumeI EstimationTheory Prentice-Hall Englewood Cliffs NJ USA1st edition 1993

[35] M Biguesh and A B Gershman ldquoTraining-based MIMOchannel estimation a study of estimator tradeoffs and optimaltraining signalsrdquo IEEE Transactions on Signal Processing vol 54no 3 pp 884ndash893 2006

[36] B Hassibi and B M Hochwald ldquoHow much training is neededin multiple-antenna wireless linksrdquo IEEE Transactions onInformation Theory vol 49 no 4 pp 951ndash963 2003

[37] O Longoria-Gandara R Parra-MichelM Bazdresch andAGOrozco-Lugo ldquoIterative mean removal superimposed trainingfor frequency selective channel estimationrdquo in Proceedingsof the International Conference on Wireless CommunicationsNetworking and Mobile Computing (WiCOM rsquo08) pp 1ndash5Dalian China October 2008

[38] S Y Ronen S I Bross S S Shitz and T M Duman ldquoIterativechannel estimation and decoding in turbo coded space-timesystemsrdquo European Transactions on Telecommunications vol 18no 7 pp 719ndash734 2007

[39] X Huang ldquoComplementary properties of hadamard matricesrdquoin Proceedings of the International Conference on Communica-tions Circuits and Systems (ICCCAS rsquo06) vol 1 pp 588ndash592Guilin China June 2006

Submit your manuscripts athttpwwwhindawicom

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Distributed Sensor Networks


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ReconfigurableComputing

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014


Applied Computational Intelligence and Soft Computing

thinspAdvancesthinspinthinsp

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HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014

Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014


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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Human-ComputerInteraction

Advances in

Computer EngineeringAdvances in



emerged called implicit training (IT) [4] Two outstanding ITapproaches known as superimposed training (ST) [5 6] anddata-dependent ST (DDST) [7 8] achieve higher effectivedata rates with manageable complexity [9] These techniquesare based on a training sequence added (superimposed) to theinformation-bearing symbols Both schemes provide a simple(unsophisticated) channel estimation process [10 11] anddiffer only in that the arithmeticmean of the transmitted dataof the DDST scheme is superimposed onto the transmittedsequence Both techniques have been successfully applied tosingle-input single-output (SISO) as well as multiple-inputmultiple-output (MIMO) systems [11ndash17] combined withorthogonal frequency division multiplexing (OFDM) modu-lations [18ndash20] and time-varying channels [21ndash23] Likewisethere are interesting alternatives to OFDM in [24 25] wherethe single-carrier modulation approach is employed using ajoint frequency domain equalization and channel estimation

Although DDST outperforms ST [12] in terms of channelestimation error it is worth mentioning that the data decod-ing underDDST is of an iterative nature as it needs to removethe data-dependent distortion Furthermore DDST [8] per-forms similarly to TDM-based channel estimation while sav-ing the overhead in TDM data rate due to pilot transmissionThere are however some drawbacks that must be takeninto consideration when DDST is used First this techniqueintroduces a delay in the transmitted data when it calculatesthe data-dependent signal second it assigns less transmis-sion power to the data signal hence the symbol demappingoperation is not suitable for higher orders of modulation dueto identifiability problems as was highlighted in [26] This isan important issue because recent communication standardsconsider this type ofmodulation for exampleWiMAX (IEEE80216e-2005 standard) uses 64-QAM digital modulationthat DDST cannot support In addition DDST presents twomore drawbacks its performance is highly sensitive to thedata block length used as well as the increased peak-powerand peak-to-average ratio (PAPR) in the transmitted signalas shown in [27]

This paper proposes an iterative detection and channelestimation structure for MIMO systems which is capableof dealing with the data identifiability problem previouslydescribed The novel algorithm is based on the use of joint(fusion of both techniques) implicit and explicit trainingfor the channel estimation and symbol detection processesPrevious results of the authors related to implicit trainingfor MIMO systems were presented in [28] which introducedthe mean removal ST (MRST) technique devoted to estimatethe arithmetic cycling mean of the data block signal at thereceiver side (instead of at the transmitter side like DDSTdoes) However later on it was recognized that MRST isnot able to deal with the identifiability problem just likeDDST when the MIMO system employs high-order digitalmodulation schemes

The proposal of an iterative detection and channelestimation scheme is hereafter referred to as joint meanremoval ST and PAT (MRST-PAT)Themethod is based on areliable preliminary channel estimate using PAT with a smallnumber of dedicated pilot symbols Subsequently it uses thetime-average estimator with the ST signal added to each

transmitted data block achieving an improvement in systemthroughputThusMRST-PATmerges the best qualities of thetwo techniques achieving a better BER performance than ifemployed separately In addition the proposedmethod elim-inates the data identifiability difficulties that DDST exhibitswhen higher orders of modulation are used [26]

This paper is organized as follows Section 2 presents thespace-time MIMO signal model Section 3 summarizes thefundamental theory and performance of PAT (TDM) STand DDST channel estimation techniques Section 4 detailsthe structure of the iterative MIMO detection and channelestimation joint MRST-PAT and its theoretical performanceanalysis Section 5 depicts the application of the iterative jointMRST-PATusing aG2-OSTBCcoder Section 6 considers thenumerical simulation results and performance analysis forthe training-based frequency-flat block-fading MIMO chan-nel estimation using TDM DDST and MRST-PAT Finallysome concluding remarks in Section 7 close this paper

Notation Bold letters in lower (upper) case are used to denotevector (matrices)C stands for the complex number field (sdot)119879

and (sdot)119867 represent transpose and conjugate transpose respec-

tively I119899119879denotes 119899

119879times119899119879identity matrix sdot and sdot

119865repre-

sent Euclidean norm and Frobenius norm respectively Trsdotdenotes trace of a matrix otimes stands for Kronecker productandCN(aΣ) denotes amultidimensional complex Gaussiandistribution with mean a and covariance matrix Σ

2 Space-Time Signal Model

This section describes the space-time signal model applicableto most existing space-time coding designs such as VerticalBell Labs Layered Space-Time (VBLAST) [29] and the gen-eralized schemes referred to as space-time block codes fromorthogonal designs [30]

With reference to Figure 1 this paper considers a MIMOsingle-carrier system operating over frequency-flat qua-sistatic block-fading channel model with 119899

119879transmit and 119899

119877

receive antennas described by

r = Hx + n (1)

where x isin C119899119879 is the transmitted vector comprising 119899119879

elements denoted as [1199091 1199092 119909

119899119879]119879 and r isin C119899119877 is the

received vectorWe use a random matrix H isin C119899119877times119899119879 that represents the

flat fading channel in a baseband equivalent model whereeach element is generated as an independent and identicallydistributed (iid) circularly symmetric complex Gaussianrandom variableCN(0 1) In addition n isin C119899119877 is an additivewhite circularly symmetric complex Gaussian noise vectorwith zero mean and variance 1205902

119899= 119873

02 per real and

imaginary dimensionLet us assume the block transmission scheme where a

ldquoblockrdquo is defined as a single transmission burst The channelmatrix H is assumed to be constant for 119873 channel uses andthen changes to an independent realization for the next block[31] Here 119873 denotes the block length For any 119899

119879times 119873


CIR

Channelestimator

Data

Pilot

Spac

e

Time

Decoder

PAT transmitter

HX

N

R

1

2

N

nT

X H



be written as

R = HX + N (2)

where




(3)



119878is denoted by

s ≜ [1199041 1199042

sdot sdot sdot 119904119873119878

]119879

(4)





G = (

11989211

sdot sdot sdot 1198921119873119866

d

1198921198991198791

sdot sdot sdot 119892119899119879119873119866

) isin C119899119879times119873119866 (5)












G (s)G119867 (s) = s2 I119899119879 (6)












119887=

119864|119887119894119895| and 119875

119888= 119864|119888

119894119895| that is 119875



119888= 119875119909 where 119875

119909= 119864|119909

119894119895| denotes




CIR

Channelestimator

Spac

e

Time

Decoder

TDM transmitter

HX

N

R

1

2

nT

XH

C pilot

B data




= RCdagger (7)


C2

119865= 119899119879119879119875119909= P (8)


minC

119864 10038171003817100381710038171003817H minus HTDM

10038171003817100381710038171003817

2

119865 (9)


JTDM = 119864 10038171003817100381710038171003817H minus HTDM

10038171003817100381710038171003817

2

119865 (10)

Using EN119867N = 1205902119899119899119877I119879with 1205902



JTDM = 119864 10038171003817100381710038171003817NCdagger100381710038171003817100381710038172

119865 = 1205902


= 1205902

119899119899119877Tr (CC119867)

minus1

(11)


minC

Tr (CC119867)minus1

(12)




CC119867 =P

119899119879

I119899119879 (13)




HTDM = (119899119879

P)RC119867 = H + (

119899119879

P)NC119867 (14)



MSETDM (H) =12059021198991198992119879119899119877

P (15)


MSETDM (H) =1205902119899119899119879119899119877

119879119875119909

(16)




R = H (B + C) + N (17)









C = u otimes C119887 (18)



= 119899119879119875119888I119899119879


119888 (ℓ 119899) = radic119875119888exp(

1198952120587119899 (ℓ minus 1)

119899119879

) (19)




119888119887 (1 V) = radic119875

119888(exp(

119895120587

119899119879

))

(V(V+120572))

(20)



119879is even and






R119894119895

= (1

119876)

119876

sum119896=1

R119894119895+119899119879(119896minus1)

(21)

where 119894 = 1 2 119899119877and 119895 = 1 2 119899

119879


R = (1

119876)RU (22)



and is given by

U = u119879 otimes I119899119879 (23)


R = H [(1

119876) (BU + CU)] + (

1

119876)NU

= H (B + C119887) + N

(24)




119887= (1119876)CU Since






+ NCminus1119887 (26)


119887C119867119887

=

119899119879119875119888I119899119879

then Cminus1119887



HST =1

119899119879119875119888

[H (B + C119887) + N]C119867

119887

= H +1

119899119879119875119888

(HB + N)C119867119887

(27)






R = H (B + E + C) + N (29)


HDDST = H + (1

119899119879119875119888

) NC119867119887 (30)


119887C119867119887

= 119899119879119875119888I119899119879

is given by


2

119865 = 119864

10038171003817100381710038171003817NCminus1119887

10038171003817100381710038171003817

2

119865 (31)


MSEDDST (H) = 11986410038171003817100381710038171003817100381710038171003817

1

119876(NU)Cminus1

119887

10038171003817100381710038171003817100381710038171003817

2

119865

(32)


119865= TrA119867A and

119864N119867N = 1198991198771205902119899I then

MSEDDST (H) =1198991198771205902119899

(119899119879119875119888119876)2Tr C119887U119867UC119867

119887 (33)


MSEDDST (H) =1198991198771205902

119899

(119899119879119875119888119876)2119876 (119899119879119899119879119875119888) =

1198991198791198991198771205902

119899

119873119875119888

(34)


119875119888

119875119909

=119879

119873 (35)












119887

= H +1

119899119879119875119888

[(HB minus H B) + N]C119867119887

(36)







CIR

Channelestimator

Spac

e

Time

Decoder


X

H

N

R

1

2

nT

X

H

B dataC ST signal

P pilot

B




119871119899119879






and make Rold= R


according to

Rnew= Rold

minus H B (37)





119879= 2 and 119899

119877= 2 This





extended form

X =[[[

[

1199041

minus119904lowast2

1199043

minus119904lowast4



1199042

119904lowast1⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟

G1

1199044

119904lowast3⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟

G2

119904119873

119904lowast119873minus1⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟

GΔ

]]]

]

(38)



P = [1199011

minus119901lowast2

1199013

minus119901lowast4



1199012

119901lowast1

1199014

119901lowast3



] (39)



119872[2] with

W2= [

1 1

1 minus1]

W2119872

= [W119872

W119872

W119872

minusW119872

]

(40)



W119872W119879119872

= 119872I119872 (41)




B = [1198871

minus119887lowast2

1198873

minus119887lowast4



1198872

119887lowast1

1198874

119887lowast3



] (42)





C119887= [

1198881

minus119888lowast2

1198882

119888lowast1

] (43)


C =[[

[

1198881

minus119888lowast2

1198881

minus119888lowast2


minus119888lowast2

1198882

119888lowast1⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟

C119887

1198882

119888lowast1⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟

C119887


119888lowast1⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟

C119887

]]

]

(44)





vec R =

[[[[[[[

[

ℎ11

(1+ 1198881) + ℎ12

(1198872+ 1198882)

ℎ21

(1+ 1198881) + ℎ22

(1198872+ 1198882)

minusℎ11

(2+ 1198882)lowast

+ ℎ12

(1198871+ 1198881)lowast

minusℎ21

(2+ 1198882)lowast

+ ℎ22

(1198871+ 1198881)lowast

]]]]]]]

]

(45)


vec R = A vec H119879 (46)

with A = [

[

(1+1198881) (2+1198882) 0 0

0 0 (1+1198881) (2+1198882)

minus(2+1198882)lowast(1+1198881)

lowast0 0

0 0 minus(2+1198882)lowast(1+1198881)

lowast

]

]


A

=

[[[[[[[[[

[

(1198871+ 1198881) (

1198872+ 1198882) 0 0

0 0 (1198871+ 1198881) (

1198872+ 1198882)

minus(1198872+ 1198882)lowast

(1198871+ 1198881)lowast

0 0

0 0 minus (1198872+ 1198882)lowast

(1198871+ 1198881)lowast

]]]]]]]]]

]

(47)



and finally

H = [(vec I119899119877119879

otimes I119899119879) (I119899119877

otimes vec H119879)]119879

(49)

where I119899119879

and I119899119877

are 119899119879times 119899119879and 119899







5 10 15 200SNR (dB)

10minus3

10minus2

10minus1

100

MSE

of c

hann

el es

timat

e


DDST Pc = 017




= 119899119877


0= 119864119904119899119879SNR and119864

119904is


119909= 1 (Watt)








119888119875119909= 119879119873 with 119879 = 4


119888 The selected


DDSTTDM Oh = 4256


10minus3

10minus2

10minus1

MSE

of c

hann

el es

timat

e

05042032022012002Pc


TDM 17 overhead

15 201050SNR (dB)

BER

10minus6

10minus4

10minus2


DDST iter 1 Pc = 17




ℎ= 4256









10minus3

10minus2

10minus1

100

BLER

20 251510SNR (dB)




TDM Oh = 32256



3020 251510SNR (dB)

10minus6

10minus4

10minus2

100

BER


Oh = 4256


Oh = 2256


TDM Oh = 32256 TDM Oh = 8256










ℎ= 2256 and two



10minus6

10minus4

10minus2

100

BER

103

104

102



119888= 75 for 64 QAM









DDST iter 2

04 050302010Pc

10minus6

10minus4

10minus2

100

BER



7 Conclusion


Competing Interests


References
















































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in




CIR

Channelestimator

Data

Pilot

Spac

e

Time

Decoder

PAT transmitter

HX

N

R

1

2

N

nT

X H



be written as

R = HX + N (2)

where




(3)



119878is denoted by

s ≜ [1199041 1199042

sdot sdot sdot 119904119873119878

]119879

(4)





G = (

11989211

sdot sdot sdot 1198921119873119866

d

1198921198991198791

sdot sdot sdot 119892119899119879119873119866

) isin C119899119879times119873119866 (5)












G (s)G119867 (s) = s2 I119899119879 (6)












119887=

119864|119887119894119895| and 119875

119888= 119864|119888

119894119895| that is 119875



119888= 119875119909 where 119875

119909= 119864|119909

119894119895| denotes




CIR

Channelestimator

Spac

e

Time

Decoder

TDM transmitter

HX

N

R

1

2

nT

XH

C pilot

B data




= RCdagger (7)


C2

119865= 119899119879119879119875119909= P (8)


minC

119864 10038171003817100381710038171003817H minus HTDM

10038171003817100381710038171003817

2

119865 (9)


JTDM = 119864 10038171003817100381710038171003817H minus HTDM

10038171003817100381710038171003817

2

119865 (10)

Using EN119867N = 1205902119899119899119877I119879with 1205902



JTDM = 119864 10038171003817100381710038171003817NCdagger100381710038171003817100381710038172

119865 = 1205902


= 1205902

119899119899119877Tr (CC119867)

minus1

(11)


minC

Tr (CC119867)minus1

(12)




CC119867 =P

119899119879

I119899119879 (13)




HTDM = (119899119879

P)RC119867 = H + (

119899119879

P)NC119867 (14)



MSETDM (H) =12059021198991198992119879119899119877

P (15)


MSETDM (H) =1205902119899119899119879119899119877

119879119875119909

(16)




R = H (B + C) + N (17)









C = u otimes C119887 (18)



= 119899119879119875119888I119899119879


119888 (ℓ 119899) = radic119875119888exp(

1198952120587119899 (ℓ minus 1)

119899119879

) (19)




119888119887 (1 V) = radic119875

119888(exp(

119895120587

119899119879

))

(V(V+120572))

(20)



119879is even and






R119894119895

= (1

119876)

119876

sum119896=1

R119894119895+119899119879(119896minus1)

(21)

where 119894 = 1 2 119899119877and 119895 = 1 2 119899

119879


R = (1

119876)RU (22)



and is given by

U = u119879 otimes I119899119879 (23)


R = H [(1

119876) (BU + CU)] + (

1

119876)NU

= H (B + C119887) + N

(24)




119887= (1119876)CU Since






+ NCminus1119887 (26)


119887C119867119887

=

119899119879119875119888I119899119879

then Cminus1119887



HST =1

119899119879119875119888

[H (B + C119887) + N]C119867

119887

= H +1

119899119879119875119888

(HB + N)C119867119887

(27)






R = H (B + E + C) + N (29)


HDDST = H + (1

119899119879119875119888

) NC119867119887 (30)


119887C119867119887

= 119899119879119875119888I119899119879

is given by


2

119865 = 119864

10038171003817100381710038171003817NCminus1119887

10038171003817100381710038171003817

2

119865 (31)


MSEDDST (H) = 11986410038171003817100381710038171003817100381710038171003817

1

119876(NU)Cminus1

119887

10038171003817100381710038171003817100381710038171003817

2

119865

(32)


119865= TrA119867A and

119864N119867N = 1198991198771205902119899I then

MSEDDST (H) =1198991198771205902119899

(119899119879119875119888119876)2Tr C119887U119867UC119867

119887 (33)


MSEDDST (H) =1198991198771205902

119899

(119899119879119875119888119876)2119876 (119899119879119899119879119875119888) =

1198991198791198991198771205902

119899

119873119875119888

(34)


119875119888

119875119909

=119879

119873 (35)












119887

= H +1

119899119879119875119888

[(HB minus H B) + N]C119867119887

(36)







CIR

Channelestimator

Spac

e

Time

Decoder


X

H

N

R

1

2

nT

X

H

B dataC ST signal

P pilot

B




119871119899119879






and make Rold= R


according to

Rnew= Rold

minus H B (37)





119879= 2 and 119899

119877= 2 This





extended form

X =[[[

[

1199041

minus119904lowast2

1199043

minus119904lowast4



1199042

119904lowast1⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟

G1

1199044

119904lowast3⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟

G2

119904119873

119904lowast119873minus1⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟

GΔ

]]]

]

(38)



P = [1199011

minus119901lowast2

1199013

minus119901lowast4



1199012

119901lowast1

1199014

119901lowast3



] (39)



119872[2] with

W2= [

1 1

1 minus1]

W2119872

= [W119872

W119872

W119872

minusW119872

]

(40)



W119872W119879119872

= 119872I119872 (41)




B = [1198871

minus119887lowast2

1198873

minus119887lowast4



1198872

119887lowast1

1198874

119887lowast3



] (42)





C119887= [

1198881

minus119888lowast2

1198882

119888lowast1

] (43)


C =[[

[

1198881

minus119888lowast2

1198881

minus119888lowast2


minus119888lowast2

1198882

119888lowast1⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟

C119887

1198882

119888lowast1⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟

C119887


119888lowast1⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟

C119887

]]

]

(44)





vec R =

[[[[[[[

[

ℎ11

(1+ 1198881) + ℎ12

(1198872+ 1198882)

ℎ21

(1+ 1198881) + ℎ22

(1198872+ 1198882)

minusℎ11

(2+ 1198882)lowast

+ ℎ12

(1198871+ 1198881)lowast

minusℎ21

(2+ 1198882)lowast

+ ℎ22

(1198871+ 1198881)lowast

]]]]]]]

]

(45)


vec R = A vec H119879 (46)

with A = [

[

(1+1198881) (2+1198882) 0 0

0 0 (1+1198881) (2+1198882)

minus(2+1198882)lowast(1+1198881)

lowast0 0

0 0 minus(2+1198882)lowast(1+1198881)

lowast

]

]


A

=

[[[[[[[[[

[

(1198871+ 1198881) (

1198872+ 1198882) 0 0

0 0 (1198871+ 1198881) (

1198872+ 1198882)

minus(1198872+ 1198882)lowast

(1198871+ 1198881)lowast

0 0

0 0 minus (1198872+ 1198882)lowast

(1198871+ 1198881)lowast

]]]]]]]]]

]

(47)



and finally

H = [(vec I119899119877119879

otimes I119899119879) (I119899119877

otimes vec H119879)]119879

(49)

where I119899119879

and I119899119877

are 119899119879times 119899119879and 119899







5 10 15 200SNR (dB)

10minus3

10minus2

10minus1

100

MSE

of c

hann

el es

timat

e


DDST Pc = 017




= 119899119877


0= 119864119904119899119879SNR and119864

119904is


119909= 1 (Watt)








119888119875119909= 119879119873 with 119879 = 4


119888 The selected


DDSTTDM Oh = 4256


10minus3

10minus2

10minus1

MSE

of c

hann

el es

timat

e

05042032022012002Pc


TDM 17 overhead

15 201050SNR (dB)

BER

10minus6

10minus4

10minus2


DDST iter 1 Pc = 17




ℎ= 4256









10minus3

10minus2

10minus1

100

BLER

20 251510SNR (dB)




TDM Oh = 32256



3020 251510SNR (dB)

10minus6

10minus4

10minus2

100

BER


Oh = 4256


Oh = 2256


TDM Oh = 32256 TDM Oh = 8256










ℎ= 2256 and two



10minus6

10minus4

10minus2

100

BER

103

104

102



119888= 75 for 64 QAM









DDST iter 2

04 050302010Pc

10minus6

10minus4

10minus2

100

BER



7 Conclusion


Competing Interests


References
















































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in




CIR

Channelestimator

Spac

e

Time

Decoder

TDM transmitter

HX

N

R

1

2

nT

XH

C pilot

B data




= RCdagger (7)


C2

119865= 119899119879119879119875119909= P (8)


minC

119864 10038171003817100381710038171003817H minus HTDM

10038171003817100381710038171003817

2

119865 (9)


JTDM = 119864 10038171003817100381710038171003817H minus HTDM

10038171003817100381710038171003817

2

119865 (10)

Using EN119867N = 1205902119899119899119877I119879with 1205902



JTDM = 119864 10038171003817100381710038171003817NCdagger100381710038171003817100381710038172

119865 = 1205902


= 1205902

119899119899119877Tr (CC119867)

minus1

(11)


minC

Tr (CC119867)minus1

(12)




CC119867 =P

119899119879

I119899119879 (13)




HTDM = (119899119879

P)RC119867 = H + (

119899119879

P)NC119867 (14)



MSETDM (H) =12059021198991198992119879119899119877

P (15)


MSETDM (H) =1205902119899119899119879119899119877

119879119875119909

(16)




R = H (B + C) + N (17)









C = u otimes C119887 (18)



= 119899119879119875119888I119899119879


119888 (ℓ 119899) = radic119875119888exp(

1198952120587119899 (ℓ minus 1)

119899119879

) (19)




119888119887 (1 V) = radic119875

119888(exp(

119895120587

119899119879

))

(V(V+120572))

(20)



119879is even and






R119894119895

= (1

119876)

119876

sum119896=1

R119894119895+119899119879(119896minus1)

(21)

where 119894 = 1 2 119899119877and 119895 = 1 2 119899

119879


R = (1

119876)RU (22)



and is given by

U = u119879 otimes I119899119879 (23)


R = H [(1

119876) (BU + CU)] + (

1

119876)NU

= H (B + C119887) + N

(24)




119887= (1119876)CU Since






+ NCminus1119887 (26)


119887C119867119887

=

119899119879119875119888I119899119879

then Cminus1119887



HST =1

119899119879119875119888

[H (B + C119887) + N]C119867

119887

= H +1

119899119879119875119888

(HB + N)C119867119887

(27)






R = H (B + E + C) + N (29)


HDDST = H + (1

119899119879119875119888

) NC119867119887 (30)


119887C119867119887

= 119899119879119875119888I119899119879

is given by


2

119865 = 119864

10038171003817100381710038171003817NCminus1119887

10038171003817100381710038171003817

2

119865 (31)


MSEDDST (H) = 11986410038171003817100381710038171003817100381710038171003817

1

119876(NU)Cminus1

119887

10038171003817100381710038171003817100381710038171003817

2

119865

(32)


119865= TrA119867A and

119864N119867N = 1198991198771205902119899I then

MSEDDST (H) =1198991198771205902119899

(119899119879119875119888119876)2Tr C119887U119867UC119867

119887 (33)


MSEDDST (H) =1198991198771205902

119899

(119899119879119875119888119876)2119876 (119899119879119899119879119875119888) =

1198991198791198991198771205902

119899

119873119875119888

(34)


119875119888

119875119909

=119879

119873 (35)












119887

= H +1

119899119879119875119888

[(HB minus H B) + N]C119867119887

(36)







CIR

Channelestimator

Spac

e

Time

Decoder


X

H

N

R

1

2

nT

X

H

B dataC ST signal

P pilot

B




119871119899119879






and make Rold= R


according to

Rnew= Rold

minus H B (37)





119879= 2 and 119899

119877= 2 This





extended form

X =[[[

[

1199041

minus119904lowast2

1199043

minus119904lowast4



1199042

119904lowast1⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟

G1

1199044

119904lowast3⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟

G2

119904119873

119904lowast119873minus1⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟

GΔ

]]]

]

(38)



P = [1199011

minus119901lowast2

1199013

minus119901lowast4



1199012

119901lowast1

1199014

119901lowast3



] (39)



119872[2] with

W2= [

1 1

1 minus1]

W2119872

= [W119872

W119872

W119872

minusW119872

]

(40)



W119872W119879119872

= 119872I119872 (41)




B = [1198871

minus119887lowast2

1198873

minus119887lowast4



1198872

119887lowast1

1198874

119887lowast3



] (42)





C119887= [

1198881

minus119888lowast2

1198882

119888lowast1

] (43)


C =[[

[

1198881

minus119888lowast2

1198881

minus119888lowast2


minus119888lowast2

1198882

119888lowast1⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟

C119887

1198882

119888lowast1⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟

C119887


119888lowast1⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟

C119887

]]

]

(44)





vec R =

[[[[[[[

[

ℎ11

(1+ 1198881) + ℎ12

(1198872+ 1198882)

ℎ21

(1+ 1198881) + ℎ22

(1198872+ 1198882)

minusℎ11

(2+ 1198882)lowast

+ ℎ12

(1198871+ 1198881)lowast

minusℎ21

(2+ 1198882)lowast

+ ℎ22

(1198871+ 1198881)lowast

]]]]]]]

]

(45)


vec R = A vec H119879 (46)

with A = [

[

(1+1198881) (2+1198882) 0 0

0 0 (1+1198881) (2+1198882)

minus(2+1198882)lowast(1+1198881)

lowast0 0

0 0 minus(2+1198882)lowast(1+1198881)

lowast

]

]


A

=

[[[[[[[[[

[

(1198871+ 1198881) (

1198872+ 1198882) 0 0

0 0 (1198871+ 1198881) (

1198872+ 1198882)

minus(1198872+ 1198882)lowast

(1198871+ 1198881)lowast

0 0

0 0 minus (1198872+ 1198882)lowast

(1198871+ 1198881)lowast

]]]]]]]]]

]

(47)



and finally

H = [(vec I119899119877119879

otimes I119899119879) (I119899119877

otimes vec H119879)]119879

(49)

where I119899119879

and I119899119877

are 119899119879times 119899119879and 119899







5 10 15 200SNR (dB)

10minus3

10minus2

10minus1

100

MSE

of c

hann

el es

timat

e


DDST Pc = 017




= 119899119877


0= 119864119904119899119879SNR and119864

119904is


119909= 1 (Watt)








119888119875119909= 119879119873 with 119879 = 4


119888 The selected


DDSTTDM Oh = 4256


10minus3

10minus2

10minus1

MSE

of c

hann

el es

timat

e

05042032022012002Pc


TDM 17 overhead

15 201050SNR (dB)

BER

10minus6

10minus4

10minus2


DDST iter 1 Pc = 17




ℎ= 4256









10minus3

10minus2

10minus1

100

BLER

20 251510SNR (dB)




TDM Oh = 32256



3020 251510SNR (dB)

10minus6

10minus4

10minus2

100

BER


Oh = 4256


Oh = 2256


TDM Oh = 32256 TDM Oh = 8256










ℎ= 2256 and two



10minus6

10minus4

10minus2

100

BER

103

104

102



119888= 75 for 64 QAM









DDST iter 2

04 050302010Pc

10minus6

10minus4

10minus2

100

BER



7 Conclusion


Competing Interests


References
















































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in





119879is even and






R119894119895

= (1

119876)

119876

sum119896=1

R119894119895+119899119879(119896minus1)

(21)

where 119894 = 1 2 119899119877and 119895 = 1 2 119899

119879


R = (1

119876)RU (22)



and is given by

U = u119879 otimes I119899119879 (23)


R = H [(1

119876) (BU + CU)] + (

1

119876)NU

= H (B + C119887) + N

(24)




119887= (1119876)CU Since






+ NCminus1119887 (26)


119887C119867119887

=

119899119879119875119888I119899119879

then Cminus1119887



HST =1

119899119879119875119888

[H (B + C119887) + N]C119867

119887

= H +1

119899119879119875119888

(HB + N)C119867119887

(27)






R = H (B + E + C) + N (29)


HDDST = H + (1

119899119879119875119888

) NC119867119887 (30)


119887C119867119887

= 119899119879119875119888I119899119879

is given by


2

119865 = 119864

10038171003817100381710038171003817NCminus1119887

10038171003817100381710038171003817

2

119865 (31)


MSEDDST (H) = 11986410038171003817100381710038171003817100381710038171003817

1

119876(NU)Cminus1

119887

10038171003817100381710038171003817100381710038171003817

2

119865

(32)


119865= TrA119867A and

119864N119867N = 1198991198771205902119899I then

MSEDDST (H) =1198991198771205902119899

(119899119879119875119888119876)2Tr C119887U119867UC119867

119887 (33)


MSEDDST (H) =1198991198771205902

119899

(119899119879119875119888119876)2119876 (119899119879119899119879119875119888) =

1198991198791198991198771205902

119899

119873119875119888

(34)


119875119888

119875119909

=119879

119873 (35)












119887

= H +1

119899119879119875119888

[(HB minus H B) + N]C119867119887

(36)







CIR

Channelestimator

Spac

e

Time

Decoder


X

H

N

R

1

2

nT

X

H

B dataC ST signal

P pilot

B




119871119899119879






and make Rold= R


according to

Rnew= Rold

minus H B (37)





119879= 2 and 119899

119877= 2 This





extended form

X =[[[

[

1199041

minus119904lowast2

1199043

minus119904lowast4



1199042

119904lowast1⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟

G1

1199044

119904lowast3⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟

G2

119904119873

119904lowast119873minus1⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟

GΔ

]]]

]

(38)



P = [1199011

minus119901lowast2

1199013

minus119901lowast4



1199012

119901lowast1

1199014

119901lowast3



] (39)



119872[2] with

W2= [

1 1

1 minus1]

W2119872

= [W119872

W119872

W119872

minusW119872

]

(40)



W119872W119879119872

= 119872I119872 (41)




B = [1198871

minus119887lowast2

1198873

minus119887lowast4



1198872

119887lowast1

1198874

119887lowast3



] (42)





C119887= [

1198881

minus119888lowast2

1198882

119888lowast1

] (43)


C =[[

[

1198881

minus119888lowast2

1198881

minus119888lowast2


minus119888lowast2

1198882

119888lowast1⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟

C119887

1198882

119888lowast1⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟

C119887


119888lowast1⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟

C119887

]]

]

(44)





vec R =

[[[[[[[

[

ℎ11

(1+ 1198881) + ℎ12

(1198872+ 1198882)

ℎ21

(1+ 1198881) + ℎ22

(1198872+ 1198882)

minusℎ11

(2+ 1198882)lowast

+ ℎ12

(1198871+ 1198881)lowast

minusℎ21

(2+ 1198882)lowast

+ ℎ22

(1198871+ 1198881)lowast

]]]]]]]

]

(45)


vec R = A vec H119879 (46)

with A = [

[

(1+1198881) (2+1198882) 0 0

0 0 (1+1198881) (2+1198882)

minus(2+1198882)lowast(1+1198881)

lowast0 0

0 0 minus(2+1198882)lowast(1+1198881)

lowast

]

]


A

=

[[[[[[[[[

[

(1198871+ 1198881) (

1198872+ 1198882) 0 0

0 0 (1198871+ 1198881) (

1198872+ 1198882)

minus(1198872+ 1198882)lowast

(1198871+ 1198881)lowast

0 0

0 0 minus (1198872+ 1198882)lowast

(1198871+ 1198881)lowast

]]]]]]]]]

]

(47)



and finally

H = [(vec I119899119877119879

otimes I119899119879) (I119899119877

otimes vec H119879)]119879

(49)

where I119899119879

and I119899119877

are 119899119879times 119899119879and 119899







5 10 15 200SNR (dB)

10minus3

10minus2

10minus1

100

MSE

of c

hann

el es

timat

e


DDST Pc = 017




= 119899119877


0= 119864119904119899119879SNR and119864

119904is


119909= 1 (Watt)








119888119875119909= 119879119873 with 119879 = 4


119888 The selected


DDSTTDM Oh = 4256


10minus3

10minus2

10minus1

MSE

of c

hann

el es

timat

e

05042032022012002Pc


TDM 17 overhead

15 201050SNR (dB)

BER

10minus6

10minus4

10minus2


DDST iter 1 Pc = 17




ℎ= 4256









10minus3

10minus2

10minus1

100

BLER

20 251510SNR (dB)




TDM Oh = 32256



3020 251510SNR (dB)

10minus6

10minus4

10minus2

100

BER


Oh = 4256


Oh = 2256


TDM Oh = 32256 TDM Oh = 8256










ℎ= 2256 and two



10minus6

10minus4

10minus2

100

BER

103

104

102



119888= 75 for 64 QAM









DDST iter 2

04 050302010Pc

10minus6

10minus4

10minus2

100

BER



7 Conclusion


Competing Interests


References
















































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in












119887

= H +1

119899119879119875119888

[(HB minus H B) + N]C119867119887

(36)







CIR

Channelestimator

Spac

e

Time

Decoder


X

H

N

R

1

2

nT

X

H

B dataC ST signal

P pilot

B




119871119899119879






and make Rold= R


according to

Rnew= Rold

minus H B (37)





119879= 2 and 119899

119877= 2 This





extended form

X =[[[

[

1199041

minus119904lowast2

1199043

minus119904lowast4



1199042

119904lowast1⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟

G1

1199044

119904lowast3⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟

G2

119904119873

119904lowast119873minus1⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟

GΔ

]]]

]

(38)



P = [1199011

minus119901lowast2

1199013

minus119901lowast4



1199012

119901lowast1

1199014

119901lowast3



] (39)



119872[2] with

W2= [

1 1

1 minus1]

W2119872

= [W119872

W119872

W119872

minusW119872

]

(40)



W119872W119879119872

= 119872I119872 (41)




B = [1198871

minus119887lowast2

1198873

minus119887lowast4



1198872

119887lowast1

1198874

119887lowast3



] (42)





C119887= [

1198881

minus119888lowast2

1198882

119888lowast1

] (43)


C =[[

[

1198881

minus119888lowast2

1198881

minus119888lowast2


minus119888lowast2

1198882

119888lowast1⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟

C119887

1198882

119888lowast1⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟

C119887


119888lowast1⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟

C119887

]]

]

(44)





vec R =

[[[[[[[

[

ℎ11

(1+ 1198881) + ℎ12

(1198872+ 1198882)

ℎ21

(1+ 1198881) + ℎ22

(1198872+ 1198882)

minusℎ11

(2+ 1198882)lowast

+ ℎ12

(1198871+ 1198881)lowast

minusℎ21

(2+ 1198882)lowast

+ ℎ22

(1198871+ 1198881)lowast

]]]]]]]

]

(45)


vec R = A vec H119879 (46)

with A = [

[

(1+1198881) (2+1198882) 0 0

0 0 (1+1198881) (2+1198882)

minus(2+1198882)lowast(1+1198881)

lowast0 0

0 0 minus(2+1198882)lowast(1+1198881)

lowast

]

]


A

=

[[[[[[[[[

[

(1198871+ 1198881) (

1198872+ 1198882) 0 0

0 0 (1198871+ 1198881) (

1198872+ 1198882)

minus(1198872+ 1198882)lowast

(1198871+ 1198881)lowast

0 0

0 0 minus (1198872+ 1198882)lowast

(1198871+ 1198881)lowast

]]]]]]]]]

]

(47)



and finally

H = [(vec I119899119877119879

otimes I119899119879) (I119899119877

otimes vec H119879)]119879

(49)

where I119899119879

and I119899119877

are 119899119879times 119899119879and 119899







5 10 15 200SNR (dB)

10minus3

10minus2

10minus1

100

MSE

of c

hann

el es

timat

e


DDST Pc = 017




= 119899119877


0= 119864119904119899119879SNR and119864

119904is


119909= 1 (Watt)








119888119875119909= 119879119873 with 119879 = 4


119888 The selected


DDSTTDM Oh = 4256


10minus3

10minus2

10minus1

MSE

of c

hann

el es

timat

e

05042032022012002Pc


TDM 17 overhead

15 201050SNR (dB)

BER

10minus6

10minus4

10minus2


DDST iter 1 Pc = 17




ℎ= 4256









10minus3

10minus2

10minus1

100

BLER

20 251510SNR (dB)




TDM Oh = 32256



3020 251510SNR (dB)

10minus6

10minus4

10minus2

100

BER


Oh = 4256


Oh = 2256


TDM Oh = 32256 TDM Oh = 8256










ℎ= 2256 and two



10minus6

10minus4

10minus2

100

BER

103

104

102



119888= 75 for 64 QAM









DDST iter 2

04 050302010Pc

10minus6

10minus4

10minus2

100

BER



7 Conclusion


Competing Interests


References
















































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in






extended form

X =[[[

[

1199041

minus119904lowast2

1199043

minus119904lowast4



1199042

119904lowast1⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟

G1

1199044

119904lowast3⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟

G2

119904119873

119904lowast119873minus1⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟

GΔ

]]]

]

(38)



P = [1199011

minus119901lowast2

1199013

minus119901lowast4



1199012

119901lowast1

1199014

119901lowast3



] (39)



119872[2] with

W2= [

1 1

1 minus1]

W2119872

= [W119872

W119872

W119872

minusW119872

]

(40)



W119872W119879119872

= 119872I119872 (41)




B = [1198871

minus119887lowast2

1198873

minus119887lowast4



1198872

119887lowast1

1198874

119887lowast3



] (42)





C119887= [

1198881

minus119888lowast2

1198882

119888lowast1

] (43)


C =[[

[

1198881

minus119888lowast2

1198881

minus119888lowast2


minus119888lowast2

1198882

119888lowast1⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟

C119887

1198882

119888lowast1⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟

C119887


119888lowast1⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟

C119887

]]

]

(44)





vec R =

[[[[[[[

[

ℎ11

(1+ 1198881) + ℎ12

(1198872+ 1198882)

ℎ21

(1+ 1198881) + ℎ22

(1198872+ 1198882)

minusℎ11

(2+ 1198882)lowast

+ ℎ12

(1198871+ 1198881)lowast

minusℎ21

(2+ 1198882)lowast

+ ℎ22

(1198871+ 1198881)lowast

]]]]]]]

]

(45)


vec R = A vec H119879 (46)

with A = [

[

(1+1198881) (2+1198882) 0 0

0 0 (1+1198881) (2+1198882)

minus(2+1198882)lowast(1+1198881)

lowast0 0

0 0 minus(2+1198882)lowast(1+1198881)

lowast

]

]


A

=

[[[[[[[[[

[

(1198871+ 1198881) (

1198872+ 1198882) 0 0

0 0 (1198871+ 1198881) (

1198872+ 1198882)

minus(1198872+ 1198882)lowast

(1198871+ 1198881)lowast

0 0

0 0 minus (1198872+ 1198882)lowast

(1198871+ 1198881)lowast

]]]]]]]]]

]

(47)



and finally

H = [(vec I119899119877119879

otimes I119899119879) (I119899119877

otimes vec H119879)]119879

(49)

where I119899119879

and I119899119877

are 119899119879times 119899119879and 119899







5 10 15 200SNR (dB)

10minus3

10minus2

10minus1

100

MSE

of c

hann

el es

timat

e


DDST Pc = 017




= 119899119877


0= 119864119904119899119879SNR and119864

119904is


119909= 1 (Watt)








119888119875119909= 119879119873 with 119879 = 4


119888 The selected


DDSTTDM Oh = 4256


10minus3

10minus2

10minus1

MSE

of c

hann

el es

timat

e

05042032022012002Pc


TDM 17 overhead

15 201050SNR (dB)

BER

10minus6

10minus4

10minus2


DDST iter 1 Pc = 17




ℎ= 4256









10minus3

10minus2

10minus1

100

BLER

20 251510SNR (dB)




TDM Oh = 32256



3020 251510SNR (dB)

10minus6

10minus4

10minus2

100

BER


Oh = 4256


Oh = 2256


TDM Oh = 32256 TDM Oh = 8256










ℎ= 2256 and two



10minus6

10minus4

10minus2

100

BER

103

104

102



119888= 75 for 64 QAM









DDST iter 2

04 050302010Pc

10minus6

10minus4

10minus2

100

BER



7 Conclusion


Competing Interests


References
















































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in




5 10 15 200SNR (dB)

10minus3

10minus2

10minus1

100

MSE

of c

hann

el es

timat

e


DDST Pc = 017




= 119899119877


0= 119864119904119899119879SNR and119864

119904is


119909= 1 (Watt)








119888119875119909= 119879119873 with 119879 = 4


119888 The selected


DDSTTDM Oh = 4256


10minus3

10minus2

10minus1

MSE

of c

hann

el es

timat

e

05042032022012002Pc


TDM 17 overhead

15 201050SNR (dB)

BER

10minus6

10minus4

10minus2


DDST iter 1 Pc = 17




ℎ= 4256









10minus3

10minus2

10minus1

100

BLER

20 251510SNR (dB)




TDM Oh = 32256



3020 251510SNR (dB)

10minus6

10minus4

10minus2

100

BER


Oh = 4256


Oh = 2256


TDM Oh = 32256 TDM Oh = 8256










ℎ= 2256 and two



10minus6

10minus4

10minus2

100

BER

103

104

102



119888= 75 for 64 QAM









DDST iter 2

04 050302010Pc

10minus6

10minus4

10minus2

100

BER



7 Conclusion


Competing Interests


References
















































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in




10minus3

10minus2

10minus1

100

BLER

20 251510SNR (dB)




TDM Oh = 32256



3020 251510SNR (dB)

10minus6

10minus4

10minus2

100

BER


Oh = 4256


Oh = 2256


TDM Oh = 32256 TDM Oh = 8256










ℎ= 2256 and two



10minus6

10minus4

10minus2

100

BER

103

104

102



119888= 75 for 64 QAM









DDST iter 2

04 050302010Pc

10minus6

10minus4

10minus2

100

BER



7 Conclusion


Competing Interests


References
















































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in




DDST iter 2

04 050302010Pc

10minus6

10minus4

10minus2

100

BER



7 Conclusion


Competing Interests


References
















































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in
































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in



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