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Design of High Performance MIMO Receivers for

LTE/LTE-A Uplink

Meilong JiangBroadband and Mobile Networks

NEC Labs America, Inc.

Email: [email protected]

Narayan PrasadBroadband and Mobile Networks

NEC Labs America, Inc.


Xiaodong WangElectrical Engineering Department

Columbia University


AbstractIn this paper we design high performance multiple-input-multiple-output (MIMO) receivers for the DFT-Spread-OFDM based long term evolution (LTE) cellular uplink. In theLTE uplink multiple single-antenna users can be scheduled on thesame time-frequency resource block via space division multipleaccess. The designed receivers are also applicable to the LTE-Advanced cellular uplink wherein simultaneous transmission ofmultiple streams by a single user will be possible. Two typesof advanced non-linear receivers are considered and optimized,

namely, a receiver based on a two-symbol max-log soft-outputdemodulator (two-symbol MLD) and a turbo minimum meansquared error successive interference cancelation (turbo MMSE-SIC) receiver. Based on extensive simulations, it is shown thatboth the two-symbol MLD and the turbo MMSE-SIC receiversexhibit superior performance compared to the conventional linearMMSE (LMMSE) receiver. In general, the turbo MMSE-SIC re-ceiver is robust to timing offsets and offers the best performancebut also introduces larger latency and higher computationalcomplexity. Upon employing a proposed new pairing method,the two-symbol MLD based receiver is also found to yield a goodperformance that is robust to timing offsets and which entails amoderate complexity and latency.

I. INTRODUCTION

DFT-Spread-OFDM (DFT-S-OFDM) based multiple access

technique has been adopted as the uplink access scheme in

emerging cellular systems such as the 3GPP long term evolu-

tion (3GPP-LTE) [1], [2]. Due to the DFT-spreading operation,

the received sufficient statistics can be modeled as the channel

output of a large MIMO system. The large dimension of this

equivalent MIMO model makes it a challenge to design a

MIMO receiver with good performance, low complexity as

well as a low latency. The conventional linear MIMO receiver

such as the linear MMSE receiver has a low complexity and

a low latency but results in a poor performance.

In this paper, we shall investigate two types of advanced

non-linear receivers for the DFT-S-OFDM uplink when multi-ple singe antenna users are co-scheduled on an identical time-

frequency resource block. This scenario, henceforth referred

to as the DFT-S-OFDM-SDMA uplink, is expected to be im-

portant in the LTE cellular uplink. In particular, we consider a

two-symbol MLD based receiver employing a proposed novel

pairing rule and the turbo MMSE-SIC receiver. Such advanced

MIMO receivers are needed to meet the high throughput

requirements of both LTE and LTE-Advanced cellular systems.

The two symbol MLD based receiver (albeit with a fixed

pairing) was initially proposed in [3] and shown to strike a

judicious performance-complexity tradeoff compared to other

non-iterative receivers. However, when there are timing offsets

between the signals received from the co-scheduled users

(UEs), which is quite likely in practise, the receiver was found

to yield a degraded performance. As a remedy, we propose a

new pairing method that results in a robust performance in

the presence of timing offsets. The turbo iterative receiverusing linear filtering and successive interference cancelation

has attracted extensive attention [4], [5]. We present an imple-

mentation friendly turbo-SIC receiver design and evaluate its

performance over the LTE/LTE-A uplink.

The remainder of this paper is organized as follows. Section

II introduces the DFT-S-OFDM-SDMA uplink system model.

The receiver algorithms, including the two-symbol MLD based

one with an improved paring and the turbo MMSE-SIC

are presented in Section III. Section IV presents the BLER

performance results for the proposed receivers. Finally, the

concluding remarks are made in Section V.

Notation: (

) is reserved for complex conjugate; (

)T for

matrix transpose; () for matrix Hermitian (i.e., transposeand conjugate); ()1 for matrix inverse. diag (B1, . . . ,BM)denotes a block diagonal matrix with Bm as its m-th diagonalblock; E{} is the expectation operator; 0 is a zero matrix; Idenotes the identity matrix; and denotes the Frobeniusnorm and C denotes the set of complex numbers.

I I . SYSTEM MODEL FOR THE DFT-S-OFDM-SDMA

UPLINK

In this section, we introduce the system model for the DFT-

S-OFDM-SDMA uplink which consists of one base station

with nR receive antennas and multiple co-scheduled UEs witha single antenna each. The same model also applies to a single

user MIMO DFT-S-OFDM uplink. All UEs are scheduled onthe same subset of time-frequency resource blocks for data

transmission. Without loss of generality, we assume that the

UEs are assigned tones 1 through M out of the N totalavailable subcarriers.

For convenience we consider an SDMA system with two

UEs but the receiver designs given in the sequel can be ex-

tended to more than two UEs. For the m-th tone, the effective(frequency domain) channel response vector corresponding

the k-th user is h(k)m CnR and the DFT-spread symbol is


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Fig. 1. Receiver structures for DFT-S-OFDM-SDMA system

x(k)m C, k = 1, 2. The received signal vector on the m-thtone is now given by

ym = Hmxm + nm, (1)

where Hm

= [h(1)m ,h(2)m ] and xm

= [x(1)m , x

(2)m ]T. We assume

uncorrelated noise vectors i.e. E{nmnm} = I.Let F be the M M DFT matrix with its (k, n)th

element given by Fk,n =1M

ej2(k1)(n1)

M . With s(k) =

[s(k)1 , s

(k)2 , , s(k)M ]T denoting the vector of (unit average

energy) QAM symbols and x(k) = [x(k)1 , x

(k)2 , , x(k)M ]T =

Fs(k), we can collect the received signals over all the M tones

and obtain

y = [H(1),H(2)]

x(1)

x(2)

+n

= [H(1)F,H(2)F]

s(1)

s(2)

+ n, (2)

where y

= [yT1 ,yT2 , ,yTM]T CnRM, and H(k) =

diag(h(k)1 , . . . ,h

(k)M ) CnRMM.

In what follows we discuss the design of two-symbol MLD

(with a new pairing method) and turbo MMSE-SIC receivers

based on the system model obtained in (2).

III. MIMO RECEIVER DESIGNS FOR DFT-S-OFDM

SYSTEMS

A. Conventional linear MMSE (LMMSE) Receiver

For comparison, we first derive a linear MMSE receiver.

The linear MMSE estimate of x(k)m , k = 1, 2, based on ym in

(1) is given by [6]

x(k)m = h(k)m

j=k h(j)m h

(j)m + I

1ym

1 + h(k)m

j=k h(j)m h

(j)m + I

1h(k)m

,

= h(k)mI+ HmH

m

1ym, m = 1, . . . , M .(3)

Defining x(k) = [x(k)1 , ,x(k)M ]T and applying the inverseDFT on x(k), we obtain

s(k) = Fx(k) = FD(k)Fs(k) + n(k), (4)where D(k) = diag

d(k)1 , . . . , d

(k)M

and d

(k)m =

[I+ HmHm

1HmHm]k,k , k = 1, 2. It can be verified

that (4) can be simplified as

s(k)i = (k)s(k)i + v(k)i , i = 1, . . . , M , (5)with (k) =

1

M

M

m=1d(k)m , (6)

where v(k)i contains the residual interference and noise, with

variance

E{|v(k)i |2} = (k)(1 (k)). (7)With (5), we can then calculate the LLR of each bit associated

with the QAM symbol s(k)i .

B. Two-Symbol MLD Receiver with a new pairing method

We now consider the two-symbol MLD based receiver,

that was originally presented in [3]. We now introduce a

new pairing method for the two-symbol MLD scheme, whichensures a robust performance against timing offsets unlike the

simple fixed pairing [7]. The basic idea is to divide the symbol

vectors s(k), k = 1, 2 into M pairs, each with two symbols.Each pair is demodulated using a two-symbol demodulator and

the pairing rule determines the composition of the M pairs.

All operations up-to equation (4) are same as the con-

ventional LMMSE receiver. We thus obtain s(1) = Fx(1)and s(2) = Fx(2). Let us expand s(1) = [s(1)1 , ,s(1)M ]Tand s(2) = [s(2)1 , ,s(2)M ]T. We first derive the two-symbolMLD receiver with fixed pairing by forming the pairs

sm =

[

s(1)m ,

s(2)m ]T for 1 m M. The QAM symbols in each

one of the M pairs shall be demodulated using a two-symbolmax-log demodulator. Before that we need to do a noise-

whitening operation on each one of the M pairs. To do this,we determine C = 1

M

Mm=1(I + H

mHm)

1. Note thatthe terms (I+ HmHm)

1, 1 m M are computed inthe LMMSE filter so they need not be re-computed. Next,

we compute the 2 2 matrix Q C22 using the Choleskydecomposition

QQ = (IC)C (8)and then determine zm

= Q1sm, 1 m M. zm C21


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permits the expansion

zm = Q1(IC)

T

sm + nm, 1 m M, (9)

with T C22, sm = [s(1)m , s(2)m ]T and E[nmnm] = I. Thetwo symbols in sm can now be jointly demodulated using the

two-symbol max-log demodulator on zm for 1

m

M [3].

Notice that the choice of fixed pairing in the two-symbolMLD receiver was made for simplicity but a resulting draw-

back is that the receiver can be sensitive to the timing offset be-

tween the streams transmitted by the two users. An improved

pairing rule is proposed next to achieve robust performance in

the presence of timing offset between the two UEs.

Suppose we form the pairs sm,q = [s(1)m ,s(2)[m+q]]T for 1 m M and any given q : 0 q M 1 and where[m + q] = (m + q 1)mod(M) + 1. Then we determinethe matrix X(q) using (10) where where Rk = I+ HkH

k.

Please note that the pairing used in (9) always uses q = 0.Next, we compute the 2 2 matrix Q(q) C22 using theCholesky decomposition

Q(q)Q(q) = (IX(q))X(q) (11)and then determine zm,q

= Q(q)1sm,q, 1 m M.zm,q C21 permits the expansionzm,q = Q(q)

1(IX(q)) T(q)

sm,q+nm,q, 1 m M, (12)

with T(q) C22, sm,q = [s(1)m , s(2)[m+q]]T andE[nm,qn

m,q] = I. The two symbols in sm,q can now be

jointly demodulated using the two-symbol max-log demodu-

lator on zm,q for 1 m M [3].A way to determine an optimal choice of q is introduced in

Appendix 1.

In order to implement the two-symbol MLD with the

new pairing, we can first determine the optimal q as de-scribed in Appendix 1. Next, we can form the pairs sm,q =[s(1)m ,s(2)[m+q]]T for 1 m M. Further, note that allthe terms needed to determine X(q) are available since1M

Mk=1 h

(1) k R

1k h

(2)k exp(j2q(k1)/M) is the (q+1)-

th element of the vector r computed to determine the optimal

pairing.

C. Turbo MMSE-SIC Receiver

Fig. 2 illustrates the structure of turbo MMSE-SIC receiver

which uses the received signal vector y CMnR given in(2), representing the (frequency domain) received observations

over the M tones of interest. The turbo MMSE-SIC receiver

consists of the per-tone LMMSE prefiltering, stream order-

ing, replica regeneration (symbol and variance estimator) and

interference cancelation blocks.

1) Two Stream MMSE-SIC filter: Let k be the index ofthe stream or codeword currently under detection and k theinterfering stream or codeword index to be subtracted, where

k = k {1, 2}. Each codeword spans one DFT block (M

tones per block) and multiple OFDM symbols. For each DFT

block and OFDM symbol, the received signal ym CnR atm-th tone after canceling the interference data stream at i-thiteration is given by

ym = h(k)m x(k)m + h(k)m (x(k)m x(k,i)m ) + nm,= h(k)m x

(k)m +

(k,i)h(k)m x(k,i)

m +nm n, m = 1,...,M, (1

where the subtracted interfering stream x(k,i) =[x(k,i)1 , ...,x(k,i)M ] is reconstructed based on the mostrecent available estimates of the interfering symbols,x(k,i) = Fs(k,i). s(k,i) = [s(k,i)1 , ...,s(k,i)M ] are the estimatedQAM symbols for the k-th stream. Let x(k,i)m = (x(k)m x(k,i)m )

(k,i)

be the normalized residual interference from stream k atiteration i, with (k,i) = E[|x(k)m x(k,i)m |2] denoting theresidual error variance of the interfering codeword, which

turns out to be invariant to m. Thus

x(k,i)

m can be modeled

as a Gaussian variable with zero mean and unit variance. For

the sake of notional simplicity, the iteration index is omitted

in the sequel except where it is necessary.

We can now apply the conventional LMMSE filter on the

received signal model in (13) .

The MMSE estimate of k-th stream x(k)m after canceling the

interfering stream is given by

x(k)m = h(k)m

(k)h(k)m h(k)m + I

1ym

1 + h(k)m

(k)h(k)m h(k)m + I

1h(k)m

,

= h(k)m I+

Hm

Hm

1

ym, m = 1, . . . , M .(14)

where Hm = [h(k)m ,(k)h(k)m ].Notice that when (k) = 1, the MMSE filter (14) reduces

to the conventional MMSE without SIC given in (3).

With the MMSE estimate of k-th stream, the LLRs ofthe k-th stream can be calculated and fed into a soft outputchannel decoder to perform turbo decoding. Defining x(k) =[x(k)1 , ,x(k)M ]T and applying the inverse DFT on x(k), weobtain

s(k) = Fx(k) = F D(k)Fs(k) + n(k), (15)where

D

(k)= diag

d(k)1 , . . . ,

d(k)M

and

d(k)m =

I+ HmHm1 HmHm1,1

.

It can be verified that (15) can be simplified as narrowband

SISO (single input single output) transmit model

s(k)i = (k)s(k)i + v(k)i , i = 1, . . . , M , (16)with (k) =

1

M

Mm=1

d(k)m , (17)where v

(k)i contains the residual interference and noise, with


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IX(q) = 1M

Mk=1 h

(1) k R

1k h

(1)k

Mk=1 h

(1) k R

1k h

(2)k exp(j2q(k 1)/M)M

k=1 h(2) k R

1k h

(1)k exp(j2q(k 1)/M)

Mk=1 h

(2) k R

1k h

(2)k

, (10)

variance

E{|v(k)i |2} = (k)(1 (k)). (18)Thus the effective SINR for the turbo SIC receiver can be

obtained as

SINR(k)eff =

(k)((k))

1 (k)((k)) . (19)

where (k) denotes the residual error variance of the interfer-ing stream/codeword.

The LLRs for the decoder input corresponding to the sym-

bols s(k)i of k-th stream can be calculated using the effective

SINR and post-IDFT filtered signal (16) [8]. As shown in Fig.

2, the soft output of the Turbo channel decoder LLEis fed intoa symbol replica and variance estimator to obtain the replica

of k-th stream at i-th iteration x(k,i) = [x(k,i)1 ,..., x(k,i)M ] andvariance (k,i), which are used to derive the LMMSE filtersfor the next detection of codeword k as given in (13) and (14).

2) Symbol regeneration and variance estimation: Now we

describe the computation of the symbol replica x(k), k {1, 2} and its residual error variance (k). Assuming {i}are the turbo decoder soft outputs after a specified number

of inner iterations and {bi} are the corresponding codedbits, the a-posteriori i-th bit probability can be obtained as

P r{bi = 0} = 1(1+ei ) and P r(bi = 1) = ei

(1+ei ),

respectively. The first and second statistical moments of the

transmitted QAM symbols can then be obtained as

sm = siA s

iP r(sm = si); (20)

and s2m = siA

|si|2P r(sm = si); (21)

where A represents the QAM constellation set (QPSK,16QAM or 64QAM). The symbol probability P r(sm = si)can be derived as the product of the associated bit probabilities.

Letting s = [ s1, , sM]T, we can computex = Fs. (22)and

= E[|x(k)m x(k,i)m |2] = fmTfm = 1M Mm=1

tj (23)

where fm is the m-th row of DFT matrix F. The matrixT = diag{t1,..., tM} is diagonal with tm = E[|smsm|2] =(s2m |sm|2).

3) Turbo MMSE-SIC algorithm: The iterative MMSE-SIC

receiver involves the following steps:

Step 1:Stream ordering.The stream ordering determines the demodulation / de-

coding sequence of the two codewords at each subframe

based on instantaneous channel state information. The

index of the codeword to be decoded first, denoted byo, can be chosen as the stream index with a higherequivalent SISO channel gain out of the conventional

LMMSE pre-filtering.

o = arg maxk=1,2

(k) (24)

where (k) is the equivalent SISO channel gain given in(16) (with (k) = 1).

Step 2: Decoding the 1st stream in the given order.LMMSE equalization ((14) with (o) = 1) for the streamindex determined in Step 1 (the 1st stream demodulated

in the 1st iteration), followed by a symbol replica and

error variance (o)

estimation for the decoded stream. Step 3: Decoding the 2nd stream in the given order.MMSE-SIC equalization (14) for the stream demodulated

second in the 1st iteration (with soft cancelation of the

other interfering stream), followed by a symbol and error

variance estimation for the 2nd decoded stream. Step 4: MMSE-SIC equalization (14) for both streams

in the remaining iterations (according to the determined

order with soft cancelation of the other interfering stream

using the latest available symbol and variance estimates)

until the maximum number of outer iterations is reached.

In the LTE uplink channel coding scheme, a 24-bit CRC

is attached to each codeblock. It is worth noting that the

per codeblock CRC attachment can be utilized to deviserules for early termination of the turbo MMSE-SIC iterations

to reduce processing complexity in practical implementation.

Specifically, the channel decoder is designed to output the

soft information of the whole coded sequence as well as the

hard decision of systematic bits at each turbo SIC iteration.

Thus, when the CRC check gets passed for a code block,

the decoding of the current code word is completed and the

symbol estimation and error variance of the current code block

can be saved for the other code words decoding.

IV. PERFORMANCE ANALYSIS

A. Simulation resultsWe now compare the block error rate (BLER) performance

of the three types of receivers. Specifically, the required SNRs

for BLER=0.1 are plotted for different schemes. The simula-

tion parameters are summarized in Table I. The descriptions

of the urban macro channel model can be found in [9]. In the

figure legend, MMSE-n denotes conventional MMSE with ninner iterations (within the turbo decoder); MLD-n denotestwo-symbol MLD receiver with n inner iterations and whichemploys the new pairing unless otherwise specified; TM-mn


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Fig. 2. Turbo receiver structure

Parameter Assumption

Bandwidth 10.0 MHz

FFT size 1024

Sub-carrier spacing 15.0 kHz

Sampling frequency 15.36 MHz

Number of occupied sub-carriers 600

Tone mapping method Localized

Number of antennas at Node-B 2 & 4Number of antennas at UE 1 & 2

Number of UEs 1 & 2

Channel model urban macro

Modulation QPSK,16QAM,64QAM

Channel coding rates 1/3,1/2,2/3,3/4

Channel estimation Ideal

TABLE ISIMULATION PARAMETERS

denotes the turbo MMSE-SIC with m outer iterations and n

inner iterations.Fig. 3 illustrates the performance of the two-symbol MLD

(with new pairing and fixed pairing) in an SDMA scenario

when there is an offset of 18 time domain samples betweenthe two UEs over the urban macro channel. Also plotted is

the performance of the two-symbol MLD (with new pairing

and fixed pairing) without any offset. Notice that the two-

symbol MLD with new pairing achieves a much more robust

performance compared to its counterpart with the fixed paring.

Fig. 4 and Fig. 5 compare the receivers performance with

and without timing offset, respectively. It can be seen that

turbo MMSE-SIC has the best performance at the cost of

higher complexity and larger delay. In addition, the proposed

two-symbol MLD exhibits reasonably good performance espe-cially for smaller constellation and higher coding rate regimes.

Similar to the two-symbol MLD with new pairing, MMSE

and MMSE-SIC receivers are quite robust with respect to the

timing offset.

V. CONCLUSIONS

In this paper, we have presented the design and performance

analysis of the two-symbol MLD (with an improved symbol

pairing), turbo MMSE-SIC and LMMSE receivers for the

0.3333 0.5 0.6667 0.755

10

15

20

25

30

35

40

Coding Rate

SNRperreceiveantenna(dB)@B

LER=0.1

Rx2, SCM (urban macro), MLD fixed and new pairing

64QAM, fixed pairing, offset=18


64QAM, new pairing, offset=18






QPSK, fixed pairing, offset=18

QPSK, fixed pairing, offset=0

QPSK, new pairing, offset=18

QPSK, new pairing, offset=0

Fig. 3. Performance comparison of two-symbol MLD with new pairing andfixed pairing; SCM urban macro SDMA; nR = 2.

0.3333 0.5 0.6667 0.755

10

15

20

25

30

35

40

Coding Rate

SNR(dB)@B

LER=0.1

Rx2, SCM (urban macro), offset=18

MMSE8, QPSK

MLD8, QPSK

TM24, QPSK

TM44, QPSK

MMSE8, 16QAM

MLD8, 16QAM

TM24, 16QAM

TM44, 16QAM

MMSE8, 64QAM

MLD8, 64QAM

TM24, 64QAM

TM44, 64QAM

Fig. 4. Performance of receivers for DFT-S-OFDM-SDMA; SCM (urbanmacro SDMA); nR = 2; offset=18.


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0.3333 0.5 0.6667 0.755

10

15

20

25

30

35

40

Coding Rate

SNR(dB)@B

LER=0.1

Rx2, SCM (urban macro), offset=0

MMSE8, QPSK

MLD8, QPSK

TM24, QPSK

TM44, QPSK

MMSE8, 16QAM

MLD8, 16QAM

TM24, 16QAM

TM44, 16QAM

MMSE8, 64QAM

MLD8, 64QAM

TM24, 64QAM

TM44, 64QAM

Fig. 5. Performance of receivers for DFT-S-OFDM-SDMA; SCM (urbanmacro SDMA); nR = 2; offset=0.

DFT-S-OFDM (MIMO or SDMA) uplink. Both the two-

symbol MLD and turbo MMSE-SIC receivers exhibit supe-

rior performance compared to the LMMSE receiver. Turbo

MMSE-SIC receiver in general offers the best performance

but can also introduce larger latency and higher computational

complexity. The two-symbol MLD receiver yields a good

performance at a moderate complexity and latency. On the

other hand, the conventional MMSE receiver is good enoughwhen enough receiver diversity is available. All the three

receivers: MMSE, turbo MMSE-SIC and two-symbol MLD

with new pairing, are robust with respect to the timing offsets

in an SDMA scenario.

APPENDIX 1: BEST PAIRING SELECTION

To determine an optimal q (or equivalently an optimal pair(m, [m + q])) we can use the capacity metric on the model in(12) and determine a suitable q as

arg max0qM1

det(I+ T(q)T(q)) = (25)

arg max0qM1

det(X(q)1) = arg min0qM1

det(X(q)).

Thus, we can equivalently first determine the vector

r = F[h(1) 1 R

11 h

(2)1 , ,h(1) M R1Mh(2)M ]T (24)

and expanding r as r = [r1, , rM], we can compute q asq = arg max

1kM{|rk|} 1. (24)

Note that the terms h(1) m R1m h

(2)m = [(I +

HmHm)1HmHm]1,2, 1 m M are already

available after computing the LMMSE filters so determining

the optimal pairing requires one additional DFT.

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