a null-subcarrier-aided reference symbol

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624 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 61, NO. 2, FEBRUARY 2012

A Null-Subcarrier-Aided Reference SymbolMapping Scheme for 3GPP LTE Downlink in

High-Mobility ScenariosSiva D. Muruganathan, Member, IEEE, Witold A. Krzymien, Senior Member, IEEE, and

Abu B. Sesay, Senior Member, IEEE

AbstractIn this paper, a new reference symbol (RS) mappingscheme for the Third-Generation Partnership Project (3GPP)long-term evolution (LTE) and LTE-Advanced (LTE-A) downlinkis proposed to improve channel estimation performance in high-mobility communication scenarios. The proposed scheme employsnull subcarriers to guard RSs, which helps mitigate the effectof intercarrier interference (ICI) on subcarriers carrying RSs.Additionally, the proposed scheme allows the ICI gain parame-ters to be estimated via a simple frequency-domain estimator.Modified CramerRao bound (MCRB) expressions are derivedfor the proposed scheme, as well as for the conventional RSmapping scheme defined in the 3GPP LTE and LTE-A standardsto compare their performance at high mobile user speeds. Thesebounds, together with mean square errors obtained from sim-ulations, reveal superior performance achieved by the proposedscheme in high-mobility scenarios. Additionally, at high mobileuser speeds, the proposed scheme offers significant bit-error-rate(BER) performance improvement over the standard RS mapping.

Index TermsChannel frequency response estimation, inter-carrier interference (ICI), modified CramerRao bound (MCRB),orthogonal frequency-division multiplexing.

I. INTRODUCTION

S UPPORTING high mobile user speeds is one of the keyrequirements of the Third-Generation Partnership Projects(3GPP) long-term evolution (LTE) and LTE-Advanced

(LTE-A) standards [1]. However, the time-varying nature of the

radio channel in such high-mobility communication scenarios

poses a significant challenge in achieving this goal. In the 3GPP

LTE/LTE-A downlink, the mobile radio channel variations

within the transmit duration of one orthogonal frequency-

division multiplexed (OFDM) symbol lead to the loss of

Manuscript received January 25, 2011; revised June 30, 2011 andOctober 20, 2011; accepted October 30, 2011. Date of publication December 7,2011; date of current version February 21, 2012. This work was supported inpart by the Natural Sciences and Engineering Research Council of Canada, byTRLabs, and by the Rohit Sharma Professorship. This paper was presented inpart at the IEEE VTC-Spring, Taipei, Taiwan, May 2010. The review of thispaper was coordinated by Dr. G. Bauch.

S. D. Muruganathan was with the Department of Electrical and ComputerEngineering, University of Alberta, Edmonton, AB T6G 2V4, Canada. He isnow with Research in Motion Limited, Ottawa, ON K2K 3K2, Canada.

W. A. Krzymien is with the Department of Electrical and Computer Engi-neering, University of Alberta, Edmonton, AB T6G 2V4, Canada, and also withTRLabs, Edmonton, AB T5K 2M5, Canada (e-mail: [email protected]).

A. B. Sesay is with the Department of Electrical and Computer Engineer-ing, University of Calgary, Calgary, AB T2N 1N4, Canada (e-mail: [email protected]).

Digital Object Identifier 10.1109/TVT.2011.2178621

orthogonality between different subcarriers. This will cause in-

tercarrier interference (ICI) at the mobile receiver, which needs

to be mitigated to avoid severe performance degradation [2],

[3]. Furthermore, due to the presence of ICI, channel estimation

at the mobile receiver becomes a formidably challenging task.

Recently, various practical schemes have been studied to

estimate the time-varying channel in OFDM systems. In [4],a time-domain raised-cosine interpolator and a frequency-

domain raised-cosine interpolator with adaptive rolloff fac-

tor are proposed for channel estimation in a mobile digital

video broadcasting handheld (DVB-H) receiver. A reduced-

complexity channel estimator for DVB-H, which exploits the

banded and sparse structures of the channel matrix in the fre-

quency and time domains, respectively, is proposed in [3] and

[5]. In [6], a channel estimation scheme combining minimum

mean-square-error (MMSE) interpolation and time-domain

windowing is proposed to estimate the time-varying channel in

DVB-H systems. More recently, in [7], the medium access con-

trol layer performance of various channel estimation algorithms

has been studied in the context of the 3GPP LTE downlink.In this paper, we propose a new reference symbol (RS)

mapping scheme to improve downlink channel estimation per-

formance in high-mobility scenarios over the standard RS

mapping scheme defined in the 3GPP LTE standard [8]. The

proposed scheme employs null subcarriers to guard RSs, which

helps mitigate the effect of ICI at subcarriers carrying RSs. In

addition, the proposed scheme allows the ICI gain parameters

to be estimated via a simple frequency-domain estimator. A

major contribution of this paper is the derivation of modified

CramerRao bounds (MCRBs) to study the efficiency of the

standard and the proposed RS mapping schemes in estimat-

ing the channel frequency response (CFR) gains. Generally,the MCRB is a looser bound than the standard CramerRao

bound (CRB) [9][11]. However, in the presence of nuisance

or unwanted parameters in the observed signal, the MCRB is

much easier to evaluate than the standard CRB [9][11]. In

this paper, we treat the discrete transmitted symbols as the

nuisance or unwanted parameters and derive the MCRBs cor-

responding to the standard and proposed RS mapping schemes

under different user mobility scenarios. Noting that, for discrete

nuisance parameters, the MCRB asymptotically approaches the

standard CRB at high signal-to-noise ratios [11], we use the

derived MCRBs to analytically demonstrate the performance

gain achieved by the proposed RS mapping scheme over the

0018-9545/$26.00 2011 IEEE


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MURUGANATHAN et al.: NULL-SUBCARRIER-AIDED RS MAPPING SCHEME FOR 3GPP LTE DOWNLINK 625

standard scheme under high-mobility conditions. Additionally,

we compare the simulated mean-square-error (MSE) and bit-

error-rate (BER) performance of the two schemes under differ-

ent mobile user speeds. These comparisons also show excellent

performance improvement achieved by the proposed scheme

over the standard scheme at high mobile user speeds. This paper

is a significantly extended version of our earlier conferencepaper [17]. The additional work presented here includes the

derivation of simplified expressions for CFR and ICI gains us-

ing piecewise linear approximation for channel time variations,

derivation of equivalent real-valued received signal models,

detailed derivation of MCRBs corresponding to the CFR gain

estimates for both the standard and proposed RS mapping

schemes, and verification of the tightness of the MCRBs via

numerical simulations.

We note that the MCRB analysis presented in this paper sig-

nificantly differs from the CRB analyses presented in [18][21]

for channel estimation/prediction in mobile OFDM systems.

In [18], CRBs are derived for channel prediction under a

doubly selective ray-based physical channel model. A major

assumption made in the derivation of the CRBs in [18] is that

the channel parameters remain constant within the estimation/

prediction time window and slowly vary beyond this time

window. As a result, the derivations in [18] do not take into

account the effect of ICI caused by channel variations within

the transmit duration of one OFDM symbol. Similarly, the

derivations in [19] assume a quasi-stationary communication

environment, where the channel impulse response coefficients

do not significantly change within a single OFDM symbol

duration. Hence, the analyses carried out in [19] also do not take

ICI into account. (It should be noted that single-tap equalizers

are utilized on individual subcarriers in [19].) In this paper, weassume that the channel significantly varies within the transmit

duration of one OFDM symbol and thus take into account

the effect of ICI in our MCRB analysis. Unlike in [19], to

mitigate the ICI caused by symbols from adjacent subcarriers,

we employ MMSE equalizers for data symbol detection on

individual subcarriers. Our work differs from [20] and [21]

in the way time variations within an OFDM symbol duration

are modeled. In [20], the Bayesian CRB is analyzed by ap-

proximating time variations of Rayleigh channel gains within

an OFDM symbol by a polynomial model, and in [21], the

time-varying channel is approximated as a superposition of a

number of complex exponential basis functions. In our work,we utilize a piecewise-linear model to approximate the equiv-

alent discrete channel-tap variations within an OFDM symbol

duration.

The rest of this paper is organized as follows: Section II

presents an overview of the system and defines the channel

and signal models assumed. Next, in Section III, the chan-

nel estimation method employed in the standard RS mapping

scheme is briefly discussed. Details of the channel estimation

improvement achieved with the proposed RS mapping scheme

are then provided in Section IV. This is followed in Section V

by the derivation of the MCRBs for both the standard and

proposed RS mapping schemes. Numerical results are then

presented in Section VI. Finally, this paper is concluded inSection VII.

TABLE IDETAILS OF KEY SYSTEM PARAMETERS

Notation: Throughout this paper, the transpose operation is

denoted by ()T. Given a complex element x, we denote its

real and imaginary components by {x} and {x}, respec-tively. Moreover, the (q, s)th element of a given matrix A isrepresented by [A]q,s. The q

th element of a given vector p

is denoted by [p]q. Lastly, the notation f(|{p,k}

X)

used throughout this paper is defined as follows: Let index k

take on values from an arbitrary set A = {A1, A2, . . . , AA},where A denotes the cardinality of the set. Additionally,let {Xp , XA1 , XA2 , . . . , XAA} be a given set of discretetransmitted symbol vectors. (Note that we alternatively rep-

resent this set of discrete transmitted symbol vectors as X,

where {p, k}.) Then, f(|

{p,k}

X) denotesthe conditional probability density function (pdf) of con-

ditioned on all of the discrete transmitted symbols vectorsXp , XA1 , XA2 , . . . , XAA .

II. SYSTEM OVERVIEW AND CHANNEL/S IGNAL MODELS

In this section, we provide an overview of the system param-

eters, the downlink reference signal type, the channel model,

and the signal model assumed throughout this paper.

A. System Parameters

We consider a single-inputsingle-output downlink scenario

where both the base station and the mobile receiver employ

single antennas. The transmission bandwidth is chosen to be

10 MHz, which corresponds to a nominal resource block size

of 50 [12]. Following the definitions in [8], frame structure

type 1 consisting of 20 0.5-ms downlink slots is considered.

Furthermore, the number of OFDM symbols per downlink slot

is assumed to be 7. Details of other key system parameters

assumed throughout this paper are provided in Table I.

B. Reference Signals

To facilitate channel estimation at the mobile receiver,

three types of downlink reference signals are defined in the

3GPP LTE standard [8]. In this paper, we will consideruser-equipment (UE)-specific RS mapping. Fig. 1 shows the


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sample at RS subcarrier p of the mth OFDM symbol can be

expressed as

Rmp = Hmp,p

Xmp +k=p

Hmp,k Xmk + W

mp

. (7)

Generally, the CFR gains at RS subcarriers are first estimated

at the mobile receiver by ignoring the ICI [i.e., the second termon the right-hand side of (7)] [7]. Hence, the CFR gain estimate

corresponding to the pth RS Xmp is given by

Hmp,p =RmpXmp

, p = 1, 2, . . . , P . (8)

Using the estimates in (8), the CFR gains at the remaining

subcarriers of OFDM symbol m are obtained via frequency-domain interpolation. To estimate the CFR gains corresponding

to subcarriers of OFDM symbols not carrying RSs, various

interpolators in the time domain can be employed [13]. In

this paper, two 1-D Wiener filters are separately employed forfrequency and time interpolations [7], [13]. For the sake of

simplicity, the statistical information (i.e., frequency and time

correlations of the channel and the noise variance) required

by the Wiener filters is assumed to be available at the mobile

receiver. In practice, the required statistical information may be

obtained at the mobile receiver using methods described in [23].

It should be noted that the RS subcarrier CFR estimate in

(8) is reasonable for low-mobility environments, where the

ICI gains Hmp,k(k = p) in (7) are relatively insignificant.

However, under propagation conditions with high mobility,

the ICI term in (7) [i.e., the second term on the right-hand

side of (7)] becomes progressively significant with increasingmaximum Doppler frequency fD. As a result, the applicationof (8) results in inaccurate RS subcarrier CFR estimates, which,

in turn, lead to additional channel estimation errors during

interpolation.

IV. IMPROVED CHANNEL ESTIMATION WIT H PROPOSEDREFERENCE SYMBOLS MAPPING SCHEME

To alleviate the problems caused by ICI under communi-

cation scenarios with high mobility, we propose a new RS

mapping scheme different from the standard scheme shown

in Fig. 1. The proposed scheme is based on the concept of

guarding RSs with null subcarriers. The proposed RS mappingscheme is motivated by the observation that most of the ICI

term energy in (7) is caused by symbols (i.e., data or other

overhead symbols) located at subcarriers adjacent to the RS

subcarrier [3]. Hence, to mitigate the ICI at the RS subcarriers,

M adjacent subcarriers around the RS subcarrier are designatedas null subcarriers in the proposed RS mapping scheme. This is

equivalent to setting

Xmk = 0 (9)

for k values satisfying |k p| < M. (Recall that p is theRS subcarrier corresponding to the pth RS Xmp .) The time-

frequency grids corresponding to the proposed RS mappingscheme for M = 1 and M = 2 are shown in Figs. 2 and 3,

Fig. 2. Time-frequency grid illustration of the proposed RS mapping schemefor M= 1.

Fig. 3. Time-frequency grid illustration of the proposed RS mapping schemefor M= 2.

respectively. Comparing Figs. 2 and 3 to Fig. 1, it is

noted that the figures are similar in the sense that the RSs

are mapped to identical RS subcarriers. However, comparedwith Figs. 13 differ in that the RSs are guarded by null


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subcarriers. Now, substituting (9) into (7), the received signal

sample at RS subcarrier p of the mth OFDM symbol isgiven by

Rmp = Hmp,p

Xmp +

|kp|>M

Hmp,k Xmk + W

mp

. (10)

Comparing (10) with (7), it is evident that the proposed RS

mapping scheme removes the deleterious contributions from

the 2M significant ICI gain terms Hmp,k(k = p M , . . . ,

p 1, p + 1, . . . , p + M). Hence, using (10) in (8), moreaccurate CFR gain estimates can be attained at RS subcarriers.

Likewise, due to the placement of nulls on subcarriers ad-

jacent to the RS subcarriers, the ICI gain terms can also be

estimated in the frequency domain. For instance, let us consider

the first adjacent subcarrier (p + 1) of the mth OFDM symbol.

From (3) and (9), the received signal sample corresponding to

this subcarrier is given by

Rmp+1 = Hmp+1,p

Xmp +

|kp|>M

Hmp+1,kXmk + W

mp+1

.

(11)

In (11), the contribution from the dominant CFR gain term

Hmp+1,p+1 is eliminated due to the null placed at subcarrier

(p + 1) [i.e., Xmp+1

= 0]. Now, using the pth RS Xmp and(11), the ICI gain term Hmp+1,p can be estimated as

Hmp+1,p =Rmp+1

Xmp. (12)

The ICI gain terms HmpM,p , . . . , H mp1,p

, Hmp+2,p , . . . ,Hmp+M,p can be similarly estimated. The ICI gain termscorresponding to the remaining subcarriers can be obtained via

frequency and time interpolations.

It should be noted that, since Xmp+1 = 0 in the case of thestandard RS mapping scheme, the contribution of the dominant

CFR gain term Hmp+1,p+1 is not eliminated. As a result, whenused with the simple ICI gain estimator of (12), the standard

RS mapping scheme suffers severe performance degradation

due to the interference caused by the dominant CFR gain term

Hmp+1,p+1.

The key advantage of the proposed RS mapping scheme isthat it enables higher mobile user speeds through improved

downlink channel estimation. The proposed scheme allows the

ICI gain parameters to be estimated via the simple estimator

of (12). However, this advantage is traded off for a slight

reduction in the number of complex data symbols that can be

transmitted during a downlink slot. (This is due to (9), where

the data symbols at subcarriers adjacent to the RS subcarrier

are replaced by nulls.) To assess the effect of this tradeoff,

we draw MSE and BER performance comparisons between

the proposed RS mapping scheme and the standard scheme

of Fig. 1 in Section VI. In the next section, we derive the

MCRBs corresponding to the RS subcarrier CFR gain estimates

Hmp,p(p = 1, 2, . . . , P ) for the cases of the proposed RSmapping scheme and the standard scheme.

V. MODIFIED CRAMERR AO BOUNDS FOR REFERENCE

SYMBOL SUBCARRIER CFR GAI N ESTIMATES

This section is organized as follows: First, in Section V-A, we

simplify the CFR gain and the ICI gain expressions of (4) and

(6) using the piecewise linear approximation for channel time

variations within the transmit duration of one OFDM symbol.

Using the simplified expressions of Section V-A, equivalentreal-valued signal models of (7) and (10) are derived in Sec-

tion V-B to facilitate the derivation of the MCRBs. Next, in

Section V-C, we find the conditional Fisher information matri-

ces corresponding to the standard and proposed RS mapping

schemes. This is followed in Section V-D by the derivation of

the MCRBs corresponding to the standard and proposed RS

mapping schemes for the high-mobility scenario.

A. Simplified CFR Gain and ICI Gain Expressions

The CFR gain Hm

k,k and the ICI gain Hm

k,k

expressed in (4)and (6) depend on the NFFTL random channel taps hm,n( =

0, 1, . . . , L 1; n = 0, 1, . . . , N FFT 1). We now employthe piecewise linear approximation for channel time variations

within one OFDM symbol to simplify the expressions in (4) and

(6). This results in simplified expressions for Hmk,k and Hmk,k ,

which only depend on the 2L random channel taps hm,n(; n =0, NFFT 1). It should be noted that, for normalized Dopplervalues of up to 20% (fDT 0. 20), the piecewise linear modelis a good approximation for channel time variations within one

OFDM symbol [2], [3].

Using the piecewise linear approximation, hm,n(; n =1, 2, . . . , N FFT 2) can be approximated as a function of h

m,0

and hm,NFFT1 as [2]

hm,n = hm,0 + n

hm,NFFT1 h

m,0

NFFT

=

1

n

NFFT

hm,0 +

n

NFFThm,NFFT1. (13)

In the preceding equation, n represents the time-variationindex within one OFDM symbol corresponding to a given

channel tap. A substitution of (13) into (4) yields

Hmk,k =1

NFFT

NFFT1n=0

L1=0

1

n

NFFT

hm,0

+n

NFFThm,NFFT1

exp

j2k

NFFTTS

=

1

NFFT

NFFT1n=0

1

n

NFFT

L1=0

hm,0 exp

j2kNFFTTS


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+

1

NFFT

NFFT1n=0

n

NFFT

L1=0

hm,NFFT1 exp

j2k

NFFTTS

. (14)

Now, using the facts

1

NFFT

NFFT1n=0

1

n

NFFT

=

1

2+

1

2NFFT(15)

1

NFFT

NFFT1n=0

n

NFFT=

1

2

1

2NFFT(16)

in (14), the expression for Hmk,k can be further simplified as

Hmk,k =

1

2+

1

2NFFT

L1=0

hm,0 exp

j2k

NFFTTS

+

1

2

1

2NFFT

L1=0

hm,NFFT1 exp

j2k

NFFTTS

. (17)

Having derived a simplified expression for Hmk,k , we nextproceed toward simplifying the expression for Hmk,k given in(6). First, we substitute (13) in (6) to obtain

Hmk,k =1

NFFT

NFFT1n=0

L1=0

1

n

NFFT

hm,0

+n

NFFT

hm,NFFT1 exp

j2k

NFFTTS

exp

j2n[k k]

NFFT

=

1

NFFT

NFFT1n=0

1

n

NFFT

exp

j2n[k k]

NFFT

L1=0

hm,0 exp

j2k

NFFTTS

+

1

NFFT

NFFT1n=0

n

NFFT

exp

j2n[k k]

NFFT

L1=0

hm,NFFT1 exp

j2k

NFFTTS

. (18)

Now, as shown in Appendix A, the partial sums involving

index n in the second equality of (18) can be expressed as

1

NFFT

NFFT1n=0

1

n

NFFT

exp

j2n[k k]

NFFT

= 1NFFT

1 exp

j2[k k]

NFFT

1

(19)

1

NFFT

NFFT1n=0

n

NFFT

exp

j2n[k k]

NFFT

=1

NFFT

1 exp

j2 [k k]

NFFT

1. (20)

Substituting (19) and (20) in (18), the simplified expressionfor Hmk,k is obtained as

Hmk,k =1

NFFT

1 exp

j2 [k k]

NFFT

1

L1=0

hm,0 exp

j2k

NFFTTS

L1=0

hm,NFFT1 exp

j2k

NFFTTS

. (21)

B. Equivalent Real-Valued Signal Models

In this section, we derive equivalent real-valued signal mod-

els of (7) and (10) using the simplified expressions found in

Section V-A. The need for the equivalent real-valued models

arises since it is more convenient to evaluate MCRBs involv-

ing real-valued quantities than those involving complex-valued

quantities [11].

First, using (17) and (21) with k = p, we can alternativelyexpress (7) as

Rmp =NFFT + 1

2NFFTL1=0

hm,0

exp

j2pNFFTTS

+

NFFT 1

2NFFT

L1=0

hm,NFFT1 exp

j2pNFFTTS

Xmp

+1

NFFT

L1=0

hm,0 exp

j2pNFFTTS

L1=0

hm

,NFFT1 expj2p

NFFTTS

k=p

1 exp

j2[p k

]

NFFT

1Xmk

+ Wmp .

(22)

Let us next denote the matrix representations of hm,n(n =

0, NFFT 1) and exp(j2 p/NFFTTS) by hm,n and ,p ,

respectively. Then, hm,n and ,p can be defined as

hm,n =hm,n hm,n

hm,n

hm,n

(23)


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,p =

expj2pNFFTTS

expj2pNFFTTS

expj2pNFFTTS

expj2pNFFTTS

=

cos

2pNFFTTS

sin

2pNFFTTS

sin 2pNFFTTS cos 2pNFFTTS

. (24)

Likewise, noting that

1 exp

j2[p k

]

NFFT

1

=1

2+j

1

2

1 cos

2[p k

]

NFFT

1sin

2[p k

]

NFFT

(25)

we can define the matrix representation p,k of [1 exp(2[p k

]/NFFT)]1 as (26), shown at the bottom of the

page.Now, using the definitions (23)(26) in (22), the equivalent

real-valued signal model of (7) can be derived as

Rmp =

NFFT + 1

2NFFT

L1=0

T

,phm,0

+

NFFT 1

2NFFT

L1=0

T

,phm,NFFT1

Xmp

+1

NFFT L1

=0

T

,phm,0

L1

=0

T

,phm,NFFT1

k=p

T

p,kXmk

+ Wmp (27)

where

Rmp =

Rmp

Rmp

T(28)

Xm = [ {Xm } {X

m } ]T , {p, k

} (29)

Wmp = Wmp W

mpT

. (30)

Lastly, following a procedure similar to (22)(27) and using

the notations established in (23)(30), the equivalent real-

valued signal model of (10) can be obtained as follows:

Rmp =

NFFT + 1

2NFFT

L1=0

T

,phm,0

+NFFT 12NFFT

L1

=0

T

,phm,NFFT1 Xmp

+1

NFFT

L1=0

T

,phm,0

L1=0

T

,phm,NFFT1

|kp|>M

T

p,kXmk

+ Wmp . (31)

C. Conditional Fisher Information Matrices

In this section, we derive the conditional Fisher information

matrices, corresponding to the standard and proposed RS map-

ping schemes, given the discrete transmitted symbol vectors

Xm ( {p, k}). (Recall from (29) that Xm is a real vector

composed of the real and imaginary parts of transmitted symbol

Xm .)1 For notational convenience, we first define the following

4L 1 real vector, which consists of the real and imagi-nary components of random channel taps hm,n( = 0, 1, . . . ,L 1; n = 0, NFFT 1):

=

hm0,0

,

hm0,0

, . . . ,

hmL1,0

,

hmL1,0

,

hm0,NFFT1

,

hm0,NFFT1

, . . . ,

hmL1,NFFT1 , hmL1,NFFT1T . (32)Furthermore, from the assumptions made in Section II-C, the

(q, s)th element of the correlation matrix C = E[T] of is

defined in (33), shown at the bottom of the next page, wherein

the channel-tap variance 2h, is as defined in Section II-C, and = J0 (2fDNFFTTS).

Now, given the conditional joint pdf f(Rmp ,|{p,k}

Xm )2, the (q, s)th element of the conditional Fisher

1Note that the Fisher information matrices are conditioned on the transmittedsymbol vectors Xm

( {p, k}) since these symbol vectors represent the

nuisance or unwanted parameters in the equivalent real-valued signal models of(27) and (31).

2Here, f(Rmp ,|{p,k} Xm ) denotes the conditional joint pdf

of Rmp and , given the discrete transmitted symbol vectors Xm

for

{p, k}.

p,k =

1 exp

j2[pk

]NFFT

1

1 exp

j2[pk

]NFFT

1

1 exp

j2[pk

]NFFT

1

1 exp

j2[pk

]NFFT

1

= 12 12 1 cos2[pk

]NFFT

1sin 2[pk

]NFFT

12

1 cos

2[pk

]NFFT

1sin2[pk

]NFFT

12

(26)


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information matrix JR,|X can generally be expressed as [10],

[11], [14][16]

[JR,|X]q,s

= ER,|X

2 lnfR

mp

, {p,k} Xm

[]q[]s (34)

where ER,|X[] represents expectation with respect to the

conditional joint pdf f(Rmp , |{p,k}

Xm ). Since thechannel-tap vector is statistically independent of the transmit-

ted symbol vectors Xm ( {p, k}), the conditional joint

pdff(Rmp ,|{p,k}

Xm ) can be factorized as

f

Rmp ,

{p,k}

Xm

= fRmp ,

{p,k}

Xm

f(). (35)Substituting (35) in (34), we next rewrite the (q, s)th element

ofJR,|X as a sum of the following two parts:JR,|X

q,s

= ER |,X

2 ln

fRmp

,{p,k} Xm

[]q[]s

E

2

ln {f()}[]q[]s

(36)

where ER|,X[] and E[] denote expectations with respect to

the pdfs f(Rmp |,{p,k}

Xm ) and f(), respectively.Let us now consider the derivation of the conditional

Fisher information matrix for the standard RS mapping

scheme. Under the assumptions made in Section II, it can be

shown (see Appendix B) that, for the standard RS mapping

scheme

2 ln

fRmp

,{p,k}

Xm

[]q[]s

= 2

2w

mp,Standard

[]q

T mp,Standard[]s

(37)

where

mp,Standard =

NFFT + 1

2NFFT

L1=0

T

,phm,0

+

NFFT 1

2NFFT

L1=0

T

,phm,NFFT1

Xmp

+1

NFFT

L1=0

T

,phm,0

L1=0

T

,phm,NFFT1

k=p

T

p,kXmk

. (38)

Furthermore, in Appendix C, we show (39), shown at the

bottom of the page, where

amp,Standard

=

NFFT + 1

2NFFT

Xmp +

1

NFFT

k=p

T

p,kXmk

(40)

[C]q,s =

12

2h,q/21, 1 q 2L, s = q1

22h,q/2L1

, (2L + 1) q 4L, s = q12

2h,q/21, 1 q 2L, s = q+ 2L12

2h,q/2L1, (2L + 1) q 4L, s = q 2L0, otherwise

(33)

mp,Standard

[]=

T

/21,pamp,Standard

, = 1, 3, . . . , (2L 1)

T

/21,p

0 11 0

amp,Standard, = 2, 4, . . . , (2L)

T

/2L1,pbmp,Standard

, = (2L + 1), (2L + 3), . . . , (4L 1)

T/2L1,p

0 11 0

bmp,Standard, = (2L + 2), (2L + 4), . . . , (4L)

(39)


9/15


bmp,Standard

=

NFFT 1

2NFFT

Xmp

1

NFFT

k=p

T

p,kXmk

(41)

holds.

Hence, using (39) in (37) and noting that the resulting

expression in (37) is independent ofRmp , we have the first term

on the right-hand side of (36) as

ER|,X

2 ln

fRmp

,{p,k} Xm

[]q[]s

=2

2w

mp,Standard

[]q

T mp,Standard[]s

(42)

where mp,Standard/[]( {q, s}) is as defined in (39).

To evaluate the second term on the right-hand side of(36), we first note that the channel-tap vector is zero-mean

Gaussian distributed (recall the assumptions from Section II-C)

with correlation matrix C, as defined in (33). Then,

we have

ln {f()} = 2L ln(2) ln

det 1/2[C]

1

2T (C)

1. (43)

Now, taking the second derivative of (43) with respect to the

elements of yields

2 ln {f()}

[]q[]s= eT4L,q (C)

1e4L,s (44)

where e4L,( {q, s}) denotes a 4L 1 vector of allzeros, except the th entry, which equals 1. Since the right-hand side of (44) is independent of the channel-tap vector , the

second term on the right-hand side of (36) can be expressed as

E

2 ln {f()}

[]q[]s

= eT4L,q (C)

1e4L,s. (45)

Hence, from (42), (45), and (36), the (q, s)th element ofthe conditional Fisher information matrix JStandard

R,|Xfor the

standard RS mapping scheme is derived as

JStandardR,|X

q,s

=2

2w

mp,Standard

[]q

T mp,Standard[]s

+ eT4L,q (C)1e4L,s. (46)

The conditional Fisher information matrix JProposed

R,|Xfor

the proposed RS mapping scheme can be derived, following

a procedure similar to that outlined in (37)(46). Following

such a procedure, it can be shown that the (q, s)th element

of the conditional Fisher information matrix JProposedR,|X

is

given by

JProposed

R,|X

q,s

=2

2w

mp,Proposed

[]q

T mp,Proposed[]s

+ eT4L,q (C)1e4L,s (47)

where (48), shown at the bottom of the page, holds.

In (48), vectors amp,Proposed and bmp,Proposed

are defined as

amp,Proposed =

NFFT + 1

2NFFT

Xmp

+1

NFFT

|kp|>M

T

p,kXmk

(49)

bmp,Proposed =

NFFT 1

2NFFT

Xmp

1NFFT

|kp|>M

Tp,k

Xmk . (50)

It should be noted that, due to the dependence ofamp,Proposedand bmp,Proposed on the number M of null subcarriersguarding each RS, the conditional Fisher information matrix

JProposed

R,|Xfor the proposed RS mapping scheme also depends

on M.

D. MCRB Expressions for the High-Mobility Scenario

First, we note that the CFR gainH

m

p,pis the desired

parameter to be estimated in both (7) and (10). Hence, to

find the MCRB expressions for the standard and proposed RS

mp,Proposed

[]=

T

/21,pamp,Proposed, = 1, 3, . . . , (2L 1)

T

/21,p

0 1

1 0

amp,Proposed, = 2, 4, . . . , (2L)

T

/2L1,pbmp,Proposed, = (2L + 1), (2L + 3), . . . , (4L 1)

T/2L1,p

0 11 0

bmp,Proposed, = (2L + 2), (2L + 4), . . . , (4L)

(48)


10/15


mapping schemes, we next define the following 2 1 vectorcomposed of the real and imaginary parts ofHmp,p :

Hmp,p =

Hmp,p

Hmp,p

=

NFFT + 12NFFT

L1=0

T,p

hm,0

hm,0

+

NFFT 1

2NFFT

L1=0

T

,p

hm,NFFT1

hm,NFFT1

(51)

where ,p is as defined in (24). Then, taking the derivative

ofHmp,p with respect to the th element of, it can be easily

shown that (52), shown at the bottom of the page, holds.

We now define the following 2 2 conditional matrix corre-

sponding to the estimation ofHm

p,p :

Hmp,p |X

=Hmp,p

JR,|X

1Hmp,p

T(53)

where the 2 4L Jacobin matrix is

Hmp,p

=

Hmp,p

[]1

Hmp,p[]2

Hmp,p

[](4L1)

Hmp,p[](4L)

.

(54)

From (53), the 2 2 conditional matrices correspondingto the standard and proposed RS mapping schemes can be

obtained by replacing JR,|X with J

StandardR,|X

and JProposed

R,|X,

respectively. [Recall that JStandardR,|X

and JProposed

R,|Xwere de-

rived earlier in (46) and (47), respectively.] Next, we average

(Hmp,p |X) over the joint pdf of the discrete transmitted

symbol vectors Xm ( {p, k}) as

Hmp,p

= EX

Hmp,p |X

. (55)

A closed-form expression for (Hmp,p) appears to be dif-

ficult to obtain since (Hmp,p | X) requires the inversion

ofJR,|X, which, in turn, depends on the discrete transmitted

symbol vectors Xm ( {p, k}). Hence, in this paper, the

averaging in (55) is performed via the Monte Carlo method.

Lastly, from (55) and using (51), the MCRB for the estimation

ofHmp,p is given by

MCRB

Hmp,p

=1

2

Hmp,p

1,1

+1

2

Hmp,p

2,2

. (56)

As a final remark, we note that only the MCRB analysis

corresponding to the RS subcarrier CFR gain estimates is

presented in this paper. MCRB analysis corresponding to non-

RS subcarriers and theoretical BER analysis are not considered

since these require taking into account the errors introduced

during interpolation (which is beyond the scope of this paper).

VI. NUMERICAL RESULTS

In this section, we compare the averages (over all RS subcar-

riers) of the MCRB expressions derived in Section V to MSE

values obtained from simulations for cases involving the stan-

dard and proposed RS mapping schemes. To obtain the MCRB

values, the averaging in (55) is performed via the Monte Carlo

method with 5000 downlink slots. The MCRB and simulated

MSE values are also used to demonstrate the CFR gain estimate

improvements achieved by the proposed RS mapping scheme

over the standard scheme at RS subcarriers. Additionally, we

also compare the uncoded BERs corresponding to the standard

and proposed RS mapping schemes. To take into account the

slight rate loss suffered by the proposed scheme due to theinsertion of null subcarriers, the MCRB, MSE, and BER per-

formances are compared over the per-bit signal-to-noise ratio

(SNR) Eb/2w. Here, Eb denotes the average energy expendedto transmit one data bit. Throughout this section, an MMSE

equalizer [6] is utilized for data symbol detection.

We first compare the simulated MSE performance and the

MCRB obtained from (56) corresponding to two different

high-mobility scenarios. The results for mobile user speeds

v = 150 km/h and v = 300 km/h are shown in Figs. 47,respectively. These two mobile user speeds are used, so that

the errors caused by the ICI term k=p Hmp,k

Xmk in (7)

on RS subcarrier CFR gain estimates are significant. Notethat the number of null subcarriers guarding each RS for the

proposed scheme is set to M = 1 (in Figs. 4 and 6) and M = 2

Hmp,p[]

=

NFFT+12NFFT

T

/21,p

1

0

, = 1, 3, . . . , (2L 1)

NFFT+12NFFT

T

/21,p

0

1

, = 2, 4, . . . , (2L)

NFFT12NFFT

T

/2L1,p 1

0 , = (2L + 1), (2L + 3), . . . , (4L 1)

NFFT12NFFT

T/2L1,p

01

, = (2L + 2), (2L + 4), . . . , (4L)

(52)


11/15


Fig. 4. Simulated MSE and MCRB comparisons between the standard andproposed (M= 1) RS mapping schemes for the case with mobile user speedv = 150 km/h and normalized Doppler value fDT 0. 0185. Also includedare the simulated MSE results for the case with no mobility (i.e., v = 0 km/h).


(in Figs. 5 and 7). The corresponding simulated MSE results

for the case with no mobility (i.e., mobile user speed v =0 km/h) are also shown in Figs. 47. From the figures, we

note that the proposed RS mapping scheme performs similar

to the standard scheme when v = 0 km/h. This is because, forv = 0 km/h, the ICI term

k=p

Hmp,kXmk in (7) vanishes,

and guarding RSs by null subcarriers does not yield any per-

formance improvement over the standard scheme. However, as

shown in Figs. 47, the proposed RS mapping scheme offersnotable performance improvements over the standard scheme

in the high-mobility scenarios. It should be noted that, with

increasing mobile user speeds, the ICI termk=p

Hmp,kXmk

in (7) becomes proportionally more significant. Due to the

presence of the null subcarriers, the proposed RS mapping

scheme removes the ICI caused by 2M adjacent subcarriers ateach RS subcarrier [see (10)]. As a result, the proposed scheme

offers better CFR gain estimates at the RS subcarriers over

the standard scheme. For v = 150 km/h, the proposed schemeattains MSE improvements of 4.9 dB (when M = 1) and 8.0 dB(when M = 2) over the standard scheme at a per-bit SNRof Eb/2w = 32 dB. The corresponding improvements for the

case of v = 300 km/h are 5.7 dB (when M = 1) and 11.3 dB(when M = 2).


Fig. 7. Simulated MSE and MCRB comparisons between the standard and

proposed (M= 2) RS mapping schemes for the case with mobile user speedv = 300 km/h and normalized Doppler value fDT 0. 0370. Also includedare the simulated MSE results for the case with no mobility (i.e., v = 0 km/h).

Furthermore, it is shown in Figs. 47 that the simulated MSE

values for both the proposed and standard RS mapping schemes

approach the MCRB at high per-bit SNRs (i.e., Eb/2w 0 dB). It should be emphasized here that, when the nuisance

parameters are discrete (which is the case in this paper since the

transmitted symbol vectors Xm ( {p, k}) are discrete),

the MCRB asymptotically approaches the standard CRB at

high per-bit SNRs [11]. Hence, we can infer from Figs. 47

that the least-squares-type CFR estimator of (8) approaches thestandard CRB at high per-bit SNRs, even in the presence of

ICI. However, it should be emphasized that the MCRB values

corresponding to the proposed scheme and those associated

with the standard scheme are significantly different in the

high-per-bit-SNR region. This is because the MCRB analysis

presented in Section V-D takes into account the effect of the

ICI terms in (7) and (10). Once again, the performance gain

achieved by the proposed scheme over the standard RS mapping

scheme in the high-per-bit-SNR region is confirmed by the

MCRB curves in Figs. 47. Next, we note from Figs. 47 that

the MCRB curves deviate away from the simulated MSE curves

at low per-bit SNRs (i.e., for Eb/2w 0 dB). This is because

the MCRB is generally much looser than the standard CRB atlow per-bit SNRs [11].


12/15


Fig. 8. BER performance comparisons between the proposed and standardRS mapping schemes for the cases with v = 0 km/h (fDT = 0) and v =150 km/h (fDT 0. 0185).

Fig. 9. BER performance comparisons between the proposed and standardRS mapping schemes for the cases with v = 0 km/h (fDT = 0) and v =300 km/h (fDT 0. 0370).

Finally, we compare the BER performance of the proposed

scheme to that of the standard scheme. Figs. 8 and 9 show

the BER results corresponding to the cases of v = 150 km/hand v = 300 km/h, respectively. Also shown in Figs. 8 and 9is the BER performance achieved when v = 0 km/h. First, wenote that, when v = 0 km/h, the proposed RS mapping scheme

incurs per-bit SNR penalties of approximately 0.3 dB (for M =1) and 0.5 dB (for M = 2) with respect to the standard scheme.These penalties are due to the relative rate loss suffered by

the proposed scheme from guarding RSs with null subcarriers.

However, despite the rate loss, the proposed scheme offers

significant BER performance improvements over the standard

RS mapping scheme at mobile user speeds of v = 150 km/hand v = 300 km/h. As shown in Fig. 8, when v = 150 km/h,the proposed RS mapping scheme reduces the error floor of

the standard scheme by factors of 4.8 (for M = 1) and 5.6 (forM = 2). From Fig. 9, the corresponding error floor reductionfactors for the case of v = 300 km/h are observed to be 2.4(when M = 1) and 3.1 (when M = 2). These BER perfor-

mance improvements achieved by the proposed RS mappingscheme are due to better CFR and ICI gain estimates obtained

by guarding RSs with null subcarriers. Lastly, we note that, for

the system parameters defined in Section II, the proposed RS

mapping scheme suffers raw bit rate losses of approximately

20.1% (for the case M = 1) and 30.1% (for the case M = 2)when compared with the standard RS mapping scheme. How-

ever, given that decreasing bit rates with increasing mobility

are commonly accepted in practice3

, these losses are acceptablein high-mobility scenarios and are traded off for the improved

performance yielded by the proposed scheme over the standard

RS mapping method.

VII. CONCLUSION

In this paper, we have proposed a new RS mapping scheme

for 3GPP LTE/LTE-A downlink to improve channel estima-

tion performance in high-mobility scenarios. The proposed

scheme employs null subcarriers to guard RSs, which helps

mitigate the effect of ICI at RS subcarriers. In addition, the

proposed scheme allows the ICI gain parameters to be estimated

via a simple frequency-domain estimator. We derive MCRB

expressions to analytically demonstrate the performance gain

attained by the proposed scheme over the standard one at high

mobile user speeds. Furthermore, comparisons of simulated

MSE performance at RS subcarriers have been presented to

reveal reduced MSEs achieved by the proposed scheme in

high-mobility communication scenarios. Additionally, at high

mobile user speeds, the proposed scheme offers significant

BER performance improvements over the standard RS mapping

scheme.

APPENDIX A

DERIVATIONS OF (19) AN D (20)

First, we rewrite the left-hand side of (19) as

1

NFFT

NFFT1n=0

1

n

NFFT

exp

j2n[k k]

NFFT

=1

NFFT

NFFT1n=0

exp

j2[k k]

NFFT

n

1

N2FFT

NFFT1

n=0n

exp

j2[k k]

NFFT

n. (57)

Next, from the geometric series, we know that

NFFT1n=0

n =1 NFFT

(1 )(58)

NFFT1n=0

nn = NFFT+1

(1 )2

NFFTNFFT

(1 )(59)

for = 1. Recalling that k = k from the initial definition ofHmk,k in (6) [note that k

= k ensures the condition = 1 is

3

Note that the target downlink peak data rates defined by IMT-Advancedfor 4G are 1 Gb/s for low-mobility scenarios and 100 Mb/s for high-mobilityscenarios [1].


13/15


met], (58) and (59) can be utilized to evaluate the partial sums

in the right-hand side of (57) as

NFFT1n=0

exp

j2[k k]

NFFT

n

=

1 exp(j2[k k])

1 exp

j2[kk]NFFT

(60)

NFFT1n=0

n

exp

j2[k k]

NFFT

n

=exp

j2[kk]NFFT

exp

j2[kk][NFFT+1]NFFT

1 exp

j2[kk]NFFT

2

NFFT exp(j2[k k])

1 exp

j2[kk]NFFT

. (61)

Now, noting that

exp(j2[k k]) = 1 (62)

exp

j2[k k][NFFT + 1]

NFFT

= exp

j2[k k]

NFFT

(63)

the expressions in (60) and (61) can be further simplified as

NFFT1n=0

exp

j2[k k]

NFFT

n= 0 (64)

NFFT1n=0

n

expj2[k k]

NFFTn

=

NFFT

1 exp

j2[kk]NFFT

.

(65)

Thereupon, substituting (64) and (65) in (57), we have

1

NFFT

NFFT1n=0

1

n

NFFT

exp

j2n[k k]

NFFT

=1

NFFT

1 exp

j2[k k]

NFFT

1. (66)

This completes the derivation of (19).

To derive (20), we first rewrite the left-hand side of (20) as

1

NFFT

NFFT1n=0

n

NFFT

exp

j2n[k k]

NFFT

=1

N2FFT

NFFT1n=0

n

exp

j2[k k]

NFFT

n. (67)

Then, substituting (65) in (67) yields

1

NFFT

NFFT1n=0

n

NFFT

exp

j2n[k k]

NFFT

= 1NFFT

1 exp

j2[k k]

NFFT

1

. (68)


APPENDIX B

DERIVATION OF (37)

Given channel-tap vector and discrete transmitted sym-

bol vectors Xm ( {p, k

}), vector Rmp is conditionally

Gaussian with mean mp,Standard , as defined in (38), and

correlation matrix 12

2w 0

0 12

2w

.

Hence, we have

ln

fRmp

,{p,k}

Xm

= ln 2w 12wRmp mp,Standard

T

Rmp

mp,Standard

. (69)

Then, taking the second derivative of (69) with respect to the

elements of and noting that

2 mp,Standard

[]q[]s= 0, (q, s)

yield

2 ln

f

Rmp

,

{p,k} Xm

[]q[]s

= 2

2w

mp,Standard

[]q

T mp,Standard[]s

. (70)


APPENDIX C

DERIVATION OF (39)

To prove (39), we first rewrite (38) in the following form:

m

p,Standard

= L1

=0

T

,phm

,0amp,Standard

+

L1=0

T

,phm,NFFT1

bmp,Standard (71)

where amp,Standard and bmp,Standard

are as defined in (40) and

(41). Taking the derivative of (71), with respect to [], thenyields

mp,Standard

[]=

L1=0

T

,p

hm,0[]

amp,Standard

+L1=0

T,p hm

,NFFT1

[]

bmp,Standard. (72)


14/15


hm,0[]

=

1 0

0 1

/21,, = 1, 3, . . . , (2L 1)

0 1

1 0

/21,, = 2, 4, . . . , (2L)

0 0

0 0 , = (2L + 1), (2L + 2), . . . , (4L)(73)

hm,NFFT1[]

=

0 0

0 0

, = 1, 2, . . . , (2L)

1 0

0 1

/2L1,, = (2L + 1), (2L + 3), . . . , (4L 1)

0 11 0

/2L1,, = (2L + 2), (2L + 4), . . . , (4L)

(74)

mp,Standard

[]=

T

/21,pamp,Standard, = 1, 3, . . . , (2L 1)

T

/21,p 0

1

1 0amp,Standard, = 2, 4, . . . , (2L)

T

/2L1,pbmp,Standard, = (2L + 1), (2L + 3), . . . , (4L 1)

T

/2L1,p

0 11 0

bmp,Standard, = (2L + 2), (2L + 4), . . . , (4L)

(75)

Next, recalling the definitions in (23) and (32), the derivatives

hm,0/[] and hm,NFFT1

/[] can be computed as (73)and (74), shown at the top of the page, where ,(

{/2 1, /2 L 1}) denote the Kronecker deltafunction. Finally, substituting (73) and (74) in (72) yields (75),shown at the top of the page.


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Siva D. Muruganathan (S02M04) received theB.Sc., M.Sc., and Ph.D. degrees in electrical engi-neering from the University of Calgary, Calgary, AB,Canada, in 2003, 2005, and 2008, respectively.

From 2009 to 2010, he was a Postdoctoral Fellowwith the University of Alberta, Edmonton. He isnow with Research in Motion Limited, Ottawa, ON,Canada.

Witold A. Krzymien (M79SM93) received theM.Sc. (Eng.) and Ph.D. degrees in electrical engi-neering from Poznan University of Technology,Poznan, Poland, in 1970 and 1978, respectively.

Since April 1986, he hasbeen with theDepartmentof Electrical and Computer Engineering, Univer-sity of Alberta, Edmonton, AB, Canada, where hecurrently holds the endowed Rohit Sharma Profes-sorship in Communications and Signal Processing.In 1986, he was one of the key research programarchitects of the newly launched TRLabs, Edmonton,

which is Canadas largest industry-university-government precompetitive re-

search consortium in the Information and Communication Technology area.His research activity has been closely tied to the consortium ever since. Overthe years, he has also done collaborative research work with Nortel Net-works; Ericsson Wireless Communications; German Aerospace Centre (DLR),Oberpfaffenhofen, Germany; TELUS Communications; Huawei Technologies;and the University of Padova, Padova, Italy. He held visiting research appoint-ments with the Twente University of Technology, Enschede, The Netherlands,from 1980 to 1982; Bell-Northern Research, Montral, QC, Canada, from1993 to 1994; Ericsson Wireless Communications, San Diego, CA, in 2000;Nortel Networks Harlow Laboratories, Harlow, U.K., in 2001; and the De-partment of Information Engineering, University of Padova, in 2005. His re-search interests include multiuser multiple-inputmultiple-output (MIMO) andMIMO-OFDM systems, as well as multihop relaying and network coordinationfor broadband cellular applications.

Dr. Krzymien is a Fellow of the Engineering Institute of Canada anda licensed Professional Engineer in the Provinces of Alberta and Ontario.He is an Associate Editor for the IEEE TRANSACTIONS ON VEHICULARTECHNOLOGY and a member of the Editorial Board of Wireless PersonalCommunications (Springer). From 1999 to 2005, he was the Chairman ofCommission C (Radio Communication Systems and Signal Processing) ofthe Canadian National Committee of Union Radio Scientifique Internationale(URSI), and from 2000 to 2003, he was the Editor for Spread Spectrum andMulti-Carrier Systems of the I EEE TRANSACTIONS ON COMMUNICATIONS.He was the recipient of a Polish national award of excellence for his Ph.D.thesis, the1991/1992 A.H. Reeves Premium Award from theInstitutionof Elec-trical Engineers (U.K.) for a paper published in the IEE ProceedingsPart I,and the Best Paper Award at the IEEE Wireless Communications and Network-ing Conference in April 2008.

Abu B. Sesay (S84M89SM01) received thePh.D.degreein electricalengineeringfrom McMasterUniversity, Hamilton, ON, Canada, in 1988

From 1986 to 1989, he was a Research Asso-ciate with McMaster University. From 1979 to 1984,he worked on various International Telecommunica-tions Union projects. In 1989, he joined the Univer-sity of Calgary, Calgary, AB, where he is currently

a Full Professor with the Department of Electricaland Computer Engineering and was the DepartmentHead from 2005 to 2011. Since 1989, he has been

involved with TRLabs, Edmonton, AB, where he is currently a TRLabs AdjunctScientist. His current research interests include space-time coding, multicarrierand code-division multiple access, multiuser detection, equalization, error cor-rection coding, multiple-inputmultiple-output systems, optical fiber/wirelesscommunications, and adaptive signal processing.

Dr. Sesay was the recipient of the IEEE 1996 Neal Shepherd Memorial BestPropagation Paper Award, the Departmental Research Excellence Award for2002, and the 2005 Schulich School of Engineering Graduate Education AwardHis students have also received three IEEE conference Best Paper Awards.

a null-subcarrier-aided reference symbol

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