ExploitingSpatialandFrequencyDiversityinSpatiallyCorrelated ...Correspondence should be addressed to Rosdiadee Nordin, [email protected] Received 23 April 2012; Revised 9 November 2012;

Hindawi Publishing CorporationJournal of Computer Networks and CommunicationsVolume 2012, Article ID 414796, 10 pagesdoi:10.1155/2012/414796

Research Article

Exploiting Spatial and Frequency Diversity in Spatially CorrelatedMU-MIMO Downlink Channels

Rosdiadee Nordin

Department of Electrical, Electronics and System Engineering, Faculty of Engineering and Built Environment, Universiti KebangsaanMalaysia, 43600 Bangi, Selangor, Malaysia

Correspondence should be addressed to Rosdiadee Nordin, [email protected]

Received 23 April 2012; Revised 9 November 2012; Accepted 10 November 2012

Academic Editor: Rui Zhang

Copyright © 2012 Rosdiadee Nordin. This is an open access article distributed under the Creative Commons Attribution License,which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

The effect of self-interference due to the increase of spatial correlation in a MIMO channel has become one of the limiting factorstowards the implementation of future network downlink transmissions. This paper aims to reduce the effect of self-interferencein a downlink multiuser- (MU-) MIMO transmission by exploiting the available spatial and frequency diversity. The subcarrierallocation scheme can exploit the frequency diversity to determine the self-interference from the ESINR metric, while the spatialdiversity can be exploited by introducing the partial feedback scheme, which offers knowledge of the channel condition to the basestation and further reduces the effect before the allocation process takes place. The results have shown that the proposed downlinktransmission scheme offers robust bit error rate (BER) performance, even when simulated in a fully correlated channel, withoutimposing higher feedback requirements on the base controller.

1. Introduction

Dynamic resource assignment from the Orthogonal Fre-quency Division Multiple Access (OFDMA) in combinationwith multiplicative increase in throughput from Multiple-Input Multiple-Output (MIMO) technology offers improvedspectral diversity in a wireless downlink transmission. Theresult of this combination is able to provide a highly efficientand low latency with enhanced spectrum flexibility radiointerface, as can be seen from the downlink implementationof a Long Term Evolution (LTE) network [1]. In addition,the LTE network benefits from MU-MIMO, a multiuserdiversity technique that exploits the spatial diversity fromthe channel knowledge at the transmitter, that is, channelstate information (CSI), to improve the performance gain.However, accurate CSI is obtained at the expense of massivefeedback overhead. A partial feedback scheme, which isbased on a quantized discrete Fourier transform (DFT), isconsidered in this paper. Instead of feeding back the full CSI,mobile users update the E-UTRAN Node B (eNodeB) withthe preferred precoding matrix based on the channel qualityindicator (CQI).

The implementation of the full feedback scheme comesat the expense of CSI; therefore, it requires an enormousamount of feedback to the eNodeB. This scenario is notpractical for the downlink implementation because eNodeBrequires a higher level of computational overhead to com-pute the channel matrix. This situation worsens when thechannel is severely impaired by channel imperfection, suchas spatial correlation, which is also described by Gesbert etal. [2] as an effect of self-interference. This is because MIMOsystem capacity mostly depends on the spatial correlationproperties of the radio channel. An obvious way to achievedecorrelation between a set of antenna elements is to placethem far away from each other. However, in most cases, thenature of the equipment will limit the antenna spacing.

The core novelty of this paper lies in the fact that itconsiders the effective exploitation of both the frequencyand spatial diversity. The spatial diversity is exploited fromthe MU-MIMO feedback scheme, while the frequencydiversity is implemented by means of dynamic subcarrierallocation. Both of the diversity schemes, spatial diversity(from MU-MIMO feedback scheme) and frequency diversity(dynamic subcarrier allocation), are combined in order to

2 Journal of Computer Networks and Communications

reduce the effect of self-interference at the user equip-ment (UE) and/or eNodeB (base station). In addition, twofeedback schemes are considered: (i) full feedback, whichhas full information of the channel’s CQI and (ii) partialfeedback, which represents the channel’s CQI in a quantizedform. The partial feedback scheme aims to reduce theuplink overhead requirement. The proposed combinationof diversity schemes is analyzed against different MIMO-correlated channel environments and codebook sizes toachieve varying degrees of multiuser diversity.

The rest of this paper is organized as follows. Section 2describes the fundamentals of MU-MIMO, Section 3presents different types of feedback schemes, Section 4presents the subcarrier allocation scheme, Section 5describes the system setup and simulation parameters for therepresentation of the LTE downlink transmission, Section 6discusses and analyses the significance of the results from thesimulation, and Section 7 concludes the paper with a briefdiscussion.

2. Spatial Diversity: Multiuser- (MU-) MIMOScheme

MIMO operation can be classified into two modes: Single-user- (SU-) MIMO and Multiuser- (MU-) MIMO. SU-MIMO only considers access to multiple antennas that areconnected to a single UE. However, this configuration doesnot achieve ideal channel capacity when the channel ishighly correlated and thus requires decorrelation between thespatial signatures of the antennas. In an Line-of-Sight LOSsituation, a strong correlation between spatial signatures isexpected. This correlation limits the use of spatial multiplex-ing and degrades the overall system throughput.

By scheduling different UEs on different spatial streamsover the same time-frequency resource, additional diversitycan be exploited in the spatial domain. This spatial diversityscheme is called MU-MIMO. MU-MIMO allows the simulta-neous allocation of different spatial subchannels to differentUEs in the same time-frequency resource. The earlier workin MU-MIMO can be traced back in 2006, published byWeingarten et al. [3].

In MU-MIMO, the burden of spatially separating the UEslies at the eNodeB, thus offering reduced complexity at theUE compared to SU-MIMO. MU-MIMO benefits from theknowledge of channel state information (CSI) to properlyserve the spatially multiplexed users. CSI, while not essentialto SU-MIMO, is of critical importance to downlink MU-MIMO precoding techniques.

3. Feedback Schemes in MU-MIMO

Precoding uses a linear transformation of the symbols at thetransmitter to improve the resilience of spatial multiplexing.In a precoded system, CSI allows a transmitter to senddata along the strongest eigenmodes of a channel andeffectively cope with fading by appropriate weighting fromthe beamforming.

However, the use of precoding comes at the expenseof channel knowledge. Precoding requires an enormousamount of feedback on the uplink to benefit most fromthe full channel information. Therefore, full and accurateCSI feedback may not be available in a severely impairedchannel, reducing the overall spectral efficiency as a resultof the quantization error. These challenges have motivatedresearch into the partial feedback scheme.

3.1. Partial Feedback versus Full Feedback. In the full feedbackscheme, a UE feeds back a channel quality indicator (CQI)value for every matrix in the codebook, as is illustrated inFigure 1. When a precoding matrix for the RB is chosen,the corresponding SINR can be fed into the scheduler,which provides accurate CQI information. The user withthe highest SINR for each spatial subchannel is selected, andthe selected users are then precoded to share the same time-frequency resource grid.

While in a partial feedback scheme, the transmitteris provided with quantized information, and most of thegains of a precoded spatial multiplexing system can beachieved at the cost of a few bits of feedback. For example,Sanayei and Nosratinia [4] have shown that a single bitquantized feedback can preserve the multiuser diversity gain.A user selects one or more preferred beamforming matricesout of the codebook by evaluating the SINRs of differentbeamforming combinations. Thus, each user must signal oneor several indices of the preferred vectors. The UE only feedsback a single CQI value for the preferred precoding matrixfor each RB, by selecting the highest average SINR perceivedby the user. Based on the feedback, the scheduler at theeNodeB chooses the precoding matrix with the highest sumof the average SINR values of all spatial subchannels andapplies it to the RB.

In the full feedback scheme, the corresponding SINRis known to the scheduler because the eNodeB has theinformation from all users. While in the partial feedbackscheme, only the users who declare the same preferred matrixare eligible for selection. For MU-MIMO, feedback schemesmust be jointly designed with appropriate scheduling andmultiple access methods to minimize the CSI inaccuracy andretain the feedback efficiency.

3.2. Unitary Precoding. In unitary precoding (UP), UEsprovide accurate and efficient CSI feedback regarding thepreferred precoding matrix to the eNodeB on the uplinkcontrol channel. Ideally, this information is made availableper resource block, thus allowing channel resources to beallocated to different users in an effective manner andallowing the amount of feedback to be greatly reduced.There are several precoding methods (references [5, 6]provide detailed overview of precoding scheme with limitedfeedback) that have been developed, and one of them, knownas the codebook-based precoding method, has recentlyreceived considerable attention in the literature.

A codebook consists of a finite number of possiblebeamforming matrices at both the transmitter and thereceiver. Instead of using the physical antenna, the network

Journal of Computer Networks and Communications 3

FFT

FFT

FFT

FFT

CQI

FrequencyFrequency

UE2UE2

Rx

Tx

beamforming

IFFT

FFT

beamformer

Rxbeamformer

Channelestimation

Channelestimation

Evaluate

CQIEvaluate

AMC

AMC

eNodeB

CQI CQI

CQI1 feedback

CQI1 feedback

UE2

UE1

UE1UE1

Figure 1: MU-MIMO with CQI feedback.

transmits through a codebook-based spatial beam, thusensuring uniform sector coverage across the cell, as shownby Rohling and Grunheid [7].

This paper considers the use of DFT-based codebooksbecause it is shown in [8–10] that the DFT-based codebookis effective against a wide range of propagation scenarios,from the uncorrelated [8, 10] to the fully correlated channel[9]. Other than its excellent protection against the effectsof self-interference, the DFT-based codebook also has lowcomplexity codebook design, as described in [5].

The DFT-based unitary precoder codebook, E, consistsof the unitary matrix set, that is, E = {E(0) · · ·E(l−1)}, where

E(l) = [e(l)0 · · · e(l)

Nt−1] is the lth precoding matrix and e(l)nt is the

Ntth precoding vector in the set. It is defined in the Fourierbasis, as given in [11]:

e(l)nt =

1√Nt

[w(l)

0nt · · ·w(l)(Nt−1)nt

]T,

w(l)nrnt = exp

{j2πnrNt

(nt +

l

L

)},

(1)

where Nt and Nr are the number of receiving and transmit-

ting antennas, respectively; w(l)mn is the codebook index and

L is the codebook size. From (1), the precoder matrices sets

Table 1: Codebook size for unitary precoding, L = 2.

E0 = 1√2

⎡

⎣1 1

1 −1

⎤

⎦

E1 = 1√2

⎡

⎣1 1

j − j

⎤

⎦

(also known as the codebooks) of size 2 and 4 are generated;they are shown in Tables 1 and 2.

In codebook unitary precoding, the codebook size con-tains a set of L = Nq/Nt predefined and fixed unitarybeamforming matrices of size Nt × Nt , where Nq is theallocated subcarriers at spatial subchannel q. The codebookindices are then used by the eNodeB to construct theprecoding matrix. For each beamforming matrix in thecodebook, each UE computes the SINR for each of the Nt

beamforming vectors in the matrix assuming that the otherspatial subchannels defined by the remaining Nt − 1 vectorsare used for interfering transmission to the other UEs.

Overall, the UE computes Nq SINRs and signals thecodebook index corresponding to the best SINR value


Table 2: Codebook size for unitary precoding, L = 4.

E0 = 1√2

⎡

⎣1 1

1 −1

⎤

⎦

E1 = 1√2

⎡

⎢⎣

1 11√2

(1 + j)1√2

(−1− j)

⎤

⎥⎦

E2 = 1√2

⎡

⎣1 1

j − j

⎤

⎦

E3 = 1√2

⎡

⎢⎣

1 11√2

(−1 + j)1√2

(1− j)

⎤

⎥⎦

back to the eNodeB. The eNodeB then makes use of thisinformation to select the beamforming matrix and schedulethe UEs for transmission. In a partial feedback scheme, theeNodeB has a very limited set of unitary precoding matricesfrom which to choose, and the multiplexing gain is at itsmaximum when enough UEs in the cell have orthogonalchannel signatures that match the vectors in one of thecodebook matrices.

For both the MU-MIMO and SU-MIMO cases, theamount of feedback increases with the number of spatialsubchannels, Q. In the full feedback MU-MIMO scheme, theamount of feedback is further increased by the codebook size(an L fold increase), resulting in a further increase in theuplink overhead. Otherwise, the same precoding matrix isshared among all of the subcarriers in an RB. The feedbackoverhead for each RB for the considered MIMO schemeis summarized in Table 3. The reporting scheme for MU-MIMO scheme is based on CQI per layer. A bitmap (e.g., 4bits) is used to signal the MCS levels. The preferred antennasare implied by filling in the appropriate CQI layer field.The number of “1s” in the bitmap indicates the rank forantenna selection, while a NULL CQI field indicates thecorresponding transmit antenna is not preferred. The matrixindex represents the preferred DFT matrix by indicating “1”in the corresponding bit position.

4. Frequency Diversity: Interference-AwareSubcarrier Allocation

4.1. SINR Metric. The mathematical model of a receivedsignal in the considered MIMO-OFDMA system, after FFTand guard removal, is described as follows:

Ysk = Hs

kEskXs

k + Nsk, (2)

where the subscript k denotes the UE index, s denotesthe subcarrier index, Hs

k is a channel matrix containingthe frequency responses of the spatial subchannels betweenNt and Nr antennas at subcarrier s and applied to thesubcarriers of the OFDMA signal on a cluster basis forthe kth UE, Es

k is the precoding matrix, Nsk denotes a

complex circular symmetric colored noise with an invertible

Table 3: Feedback overhead for the considered MIMO schemes forL = 2, Q = 2.

Feedback SchemeMU-MIMO

fullfeedback

MU-MIMOpartial

feedbackSU-MIMO

Preferred layer 1 CQI 4 bits 4 bits 4 bits

Preferred layer 2 CQI 4 bits 4 bits

Alternative layer 1 CQI 4 bits — —

Alternative layer 2 CQI 4 bits — —

Preferred matrix index 1 bit 1 bit 1 bit

Total bits per RB 17 bits 9 bits 5 bits

covariance matrix, and Xsk denotes the Nt × 1 matrix

containing the transmitted signals.At the receiver, the proposed MIMO detection adopts an

MMSE linear receiver:

Gsk =

((Esk

)H(Hs

k

)HHs

kEsk + Q

Nsk

εI

)−1(Esk

)H(Hs

k

)H, (3)

where Q is the number of data streams and ε is the transmitsymbol energy. The number of data streams in this workis assumed to be limited by min(Nr ,Nt). In the case ofSU-MIMO, both spatial streams go to the same UE. TheMMSE filter is chosen because it has the ability to mitigateself-interference without adversely amplifying the receivednoise. The MMSE filter is also able to separate the spatialsubchannel of the MIMO structure, as shown by Jang andLee [12]. The received signal is multiplied by the MMSE filter(3) to obtain the detected data stream, Ds

k:

Dsk = Gs

k ∗ Ysk = Xs

k + Nsk. (4)

For each data stream q at each RB, UE k then computesthe SINR for every subcarrier (the subcarrier index s isomitted for ease of reference):

SINRqk

=∣∣∣(GkEkHk)qq

∣∣∣

2ε

∣∣∣(GkEkHk)q j, j /= q

∣∣∣

2Es +

(|Gk|2qq +

∑j /= q|Gk|2q j, j /= q

)Ns

k

,

(5)

where q is the spatial subchannel at every subcarrier and|X|q j denotes the element located in row q and column jof matrix X . The SINR metric aims to compute the self-interference from the data stream component |Y |qq andthe self-interference component |Y |q j, j /= q from the othertransmitted data streams within the same subchannel. In thiswork, it is proposed that the allocation will be based on thesum of the achievable capacity of both spatial streams.

In an SU-MIMO system, for RB c, denoting the index ofstarting subcarrier by n and the finishing subcarrier by m, theaverage rate of user k is given by

rk,c = 1m− n + 1

m∑

s=n

min(Nt ,Nr )∑

q

log2

(1 + SINR

qk,s

). (6)


The eNodeB allocates each RB to user according to theselected resource allocation algorithm. The scheduler thenuses this feedback information to allocate the RB to theUE with the highest achievable data rate, r

qk . Compared

to SU-MIMO, the scheduling for the decision to choosethe best precoding matrix is slightly complicated in MU-MIMO. To maximize the system capacity of MU-MIMO,the most suitable precoding matrix must be selected fromthe codebook to transmit on each RB. Based on thechosen precoding matrix, a dynamic subcarrier allocation isemployed to select the user with the best channel condition.The selected users are then precoded to share the same timeand frequency resources to maximize the system capacity.

Because each of the spatial streams can be allocated andscheduled independently in MU-MIMO, the UE k calculatesthe data rate of each spatial layer and feeds it back to the BS.The user k calculates the data rate of each spatial layer q on aRB basis.

rqk,s =

1m− n + 1

m∑

s=nlog2

(1 + SINR

qk,s

). (7)

Again, for every RB, the scheduler allocates each spatiallayer to the UE that has the best channel conditions for thecorresponding layer.

4.2. Subcarrier Allocation. The interference-aware subcarrierallocation scheme uses the SINR as the performance metricto determine the allocation. The SINR metric has theknowledge of a particular subcarrier that is affected by self-interference, especially when the correlation is high inside thespatial subchannels.

The allocation ranks users from the lowest to highestSINR metric in each spatial subchannel. Consequently, thenext best subcarriers are allocated to users in rank order,allowing users with the lowest SINR at that particular spatialsubchannel to have the best SINR that is available for thenext transmission. Each MS provides SINR information tothe BS, and the subcarrier allocation algorithm then allocatessubcarriers to the MSs.

The nomenclatures are set first as references. In thefollowing algorithm, q = {1, . . . ,Q} represents the effectivespatial subchannel considered for the allocation algorithm.Σqk represents the average SINR metric for user k in the qth

spatial subchannel, K is the total number of users, and S is aQ by Nq matrix in which each row is a vector containing theindices of the useable subcarriers for the particular spatialsubchannel (i.e., Nq = {1, . . . ,Nsub}, where Nsub is thetotal number of useable subcarriers). SINR

qk,s is the SINR

matrix for user k at subcarrier s and spatial subchannelq, and Cs,k is a matrix that stores the subcarrier indices(subcarrier location) of the allocated subcarriers for user kand subcarrier s.

The following algorithm performs the proposedinterference-aware subcarrier allocation.

(1) After the eNodeB transmits the data matrix Xsk, the

kth UE computes the MMSE filter (3).

(2) The kth mobile station then computes the SINR (5)of the qth spatial subchannel.

(3) With the feedback information from UE, eNodeBallows the user with the lowest data rate to have thenext choice of best subcarrier as follows.

(a) Generate short list of users and start withthe user with the least SINR, Σ (For the firstiteration in the allocation scheme, when no sub-carriers have been allocated, all users assumedto have equal SINR value; thus the list appearsentirely arbitrary). Find user k satisfying

Σqk ≤ Σ

qi ∀i, 1 ≤ i ≤ K. (8)

(b) For the user k in (a), find the subcarrier s satis-fying

SINRqk ≥ SINR

qj ∀ j ∈ N. (9)

(c) Update SINRqk , Nq, and Cs,k with k and s in (b)

according to

Σqk = Σ

qk + SINR

qk,s,

Nq = Nq − s,

Cs,k = s,

(10)

where Nq is the allocated subcarriers at spatialsubchannel q and Cs,k is the allocation matrixto record the allocated subcarrier s for user k.

(d) Go to the next user in the short list in (a) untilall users are allocated another subcarrier, N /= 0in (c).

In this algorithm, users are not allowed to sharesubcarriers, thus reducing the complexity of the algorithm.In the SISO case, Jang and Lee [12] show that the capacitycan be maximized if a subcarrier is only assigned to oneuser because the interference from other users’ signals thatshare the same subcarrier is reduced. This paper extends thetheory presented in [12] into the MIMO case, in which thenumber of users sharing the same subcarrier is limited to thenumber of available spatial subchannels (two subchannels inthis case).

5. Simulation Environment and Parameters

This paper aims to apply the feedback schemes to spatiallycorrelated subchannel environments. In an MU-MIMOdownlink environment, the effect of self-interference must beconsidered because the spatial correlation experienced by theUE in a real channel environment can vary from an ideallyuncorrelated channel to a fully correlated channel.

This study considers an urban microenvironment with a500 m cell radius, outdoor terminals, and 2 GHz frequencyband. This environment is represented by the 3GPP-SCMUrban Micromodel [13], with an RMS delay spread of251 ns, an excess delay of 923 ns, and a Nonline-of-Sight(NLOS) propagation scenario. The total number of availablesubcarriers depends on the overall transmission bandwidth


Table 4: OFDMA parameters.

Parameters Value

Downlink bandwidth 10 MHzTime slot/subframe duration 0.5 ms/1 msSubcarrier spacing 15 kHzPrecoding codebook size, L 2FFT size, NFFT 1024Useable subcarrier, Nsub 600Number of OFDM symbols per time slot(Short/Long CP)

7/6

Table 5: Correlation scenarios.

Correlation modes RMS RBS

Uncorrelated 0.00 0.00Fully correlated 0.99 0.99

of the system. For this simulation, the representations ofthe LTE-OFDMA downlink parameters are summarized inTable 4.

The proposed interference-aware subcarrier allocation issimulated in QPSK, with a 1/2 rate modulation and codingscheme (MCS). This combination is one of the availableMCS, as specified in [1]. QPSK modulation is chosen in thesimulation because of its robustness and its ability to toleratehigher levels of self-interference, which makes it suitable fortransmission in lower SNR region at the expense of lowertransmission bit rate.

The performance of the subcarrier allocation in com-bination with the partial feedback scheme will be simu-lated against different spatial correlation MIMO environ-ment, that is, self-interference effect. Therefore, the UrbanMicrochannel model is further extended into two correlatedchannel environments: (i) an uncorrelated channel thatrepresents ideal channel conditions, in which the effect ofself-interference is minimal and (ii) a “fully” correlatedchannel, which represents a worst case spatial correlationscenario. In a fully correlated channel, the effective MIMOchannel is similar to a SISO system. The spatial correlationmatrix of the MIMO channel, RMIMO, is the Kroneckerproduct of the spatial correlation matrix at the BS and theMS, RMIMO = RMS

⊗RBS, as proposed by Beh et al. [14]. The

proposed correlation scenarios are summarized in Table 5.Three different feedback schemes are considered: (i) full

feedback, (ii) partial feedback (both of these are applied tothe MU-MIMO case) and (iii) SU-MIMO, which representsa case without any form of feedback. A set of 2000 inde-pendent identically distributed (i.i.d.) quasi-static Rayleighdistributed time samples per user are used in the simulation.A single CQI, which is based on the average SINR of the12 grouped subcarriers, is fed back for each resource block(RB), and it is assumed to be perfectly known. The resultis simulated based on 10 users, unless otherwise stated. A2× 2 antenna configuration is considered for the simulation.Because of the increased computational complexity and theinsignificant power control gain in the frequency domain

dynamic allocation, equal power allocation is assumedthroughout the simulations.

6. Error Performance Analysis

6.1. Comparison between Different Feedback Schemes. Theproposed interference-aware subcarrier allocation schemeis compared against another subcarrier allocation scheme,known as the Dynamic Subcarrier Allocation (DSA), asproposed in [15]. In the DSA scheme, the subcarrierallocation at each spatial layer is treated independently, andchannel gain is used as the performance metric to determinethe subcarrier allocation.

Figure 2 illustrates the BER performance in both theuncorrelated and fully correlated channel. MU-MIMOshows significant improvement over SU-MIMO; the marginof difference is approximately 4 dB at BER = 10−3. Thisresult confirms the multiuser benefit that MU-MIMO canoffer. For the SU-MIMO case, the poor performance canbe explained by the spatial correlation coefficient (RMIMO =0.99); in this case, the effective channel in the SU-MIMOsystem is similar to a SISO (i.e., a single data stream).The increase in the BER gain between MU-MIMO andSU-MIMO is significant, especially at higher SNR. TheDSA offers better performance when simulated in theuncorrelated channel; however, it suffers from severe BERloss as the channel achieves full correlation. This loss occursbecause there is no knowledge of the channel condition fromthe subcarrier allocation scheme because channel gain is usedas the performance metric. Consequently, the results fromSU-MIMO are not considered in this paper.

The advantage of the interference aware allocationscheme is significant in a fully correlated channel, as illus-trated in Figure 3. Full feedback MU-MIMO offers higherBER performance than SU-MIMO, for which the margin ofdifference is approximately 2.5 dB at BER = 10−3 in a fullycorrelated channel. In the case of the MU-MIMO feedbackschemes, full feedback offers superior BER improvementto partial feedback, for which the margin of difference isapproximately 2 dB at BER = 10−3.

Nevertheless, MU-MIMO has been shown to achievemore BER gain through the additional dimension of diversityin the spatial domain in both correlation environments byexploiting the spatial subchannel as an additional dimensionfor allocating resources. By utilizing the interference-awareallocation scheme at each spatial dimension, the effect ofself-interference is further reduced. MU-MIMO also has alarge wavelength separation between the UEs, thus allowinga higher degree of decorrelation.

6.2. Performance of Different Codebook Sizes. In this section,four codebook sizes are compared, L = {1, 2, 4, 8}. In afully correlated channel, the advantage of larger codebooksizes over smaller ones is obvious, particularly for the partialfeedback scheme, as shown in Figure 4. However, in anuncorrelated channel, the BER performance for L = 8is only marginally better than that of L = 2. This lackof improvement occurs as a result of the lower multiuser


100

10−1

10−2

10−3

Bit

err

or r

ate

(BE

R)

Signal-to-noise ratio (SNR) (dB)

−10 −5 0 5 10 15 20

Full MU, uncorrelatedPartial MU, uncorrelatedSU, uncorrelated

SU, full correlatedPartial MU, full correlatedFull MU, full correlated

Figure 2: BER performance for DSA, for L = 2 in different types of feedback.

−8 −6 −4 −2 0 2 4 6 8

100

10−1

10−2

10−3

Bit

err

or r

ate

(BE

R)


Full MU, uncorrelatedPartial MU, uncorrelated

SU, uncorrelated SU, full correlatedPartial MU, full correlatedFull MU, full correlated

Figure 3: BER performance for interference-aware allocation, forL = 2 with different types of feedback.

diversity gain that can be achieved by the partial feedbackscheme because the feedback information has been limitedat the scheduler. In the case of the full feedback scheme, ahigher BER gain can be achieved by larger codebook sizes, asshown in Figure 5. As an example, the codebook with a sizeof L = 8 achieved 3 dB gain over a codebook with a size ofL = 2 in a fully correlated channel at BER = 10−3.

From these results, it can be generally stated that a largercodebook size leads to better BER performance in the fullfeedback scheme, which helps to reduce the effect of self-interference. This improvement occurs because of the greaterselection of precoding matrices. A larger codebook containsmore distinct codewords, which increases the possibilitythat each spatial subchannel can find a better codewordmatch during encoding. Thus, larger codebooks are more

−8 −6 −4 −2 0 2 4 6 8

100

10−1

10−2

10−3

Bit

err

or r

ate

(BE

R)


L = 2, ‘‘full”L = 2, ‘‘uncorrelated”

L = 4, ‘‘full”

L = 4, ‘‘uncorrelated”L = 8, ‘‘full”L = 8, ‘‘uncorrelated”

Figure 4: BER performance between different codebook sizes(partial feedback MU-MIMO).

likely to have a lower BER loss, allowing a more accuraterepresentation of the channel condition. Further, the useof DFT-based codebook precoding effectively reduces theimpact of self-interference in a highly correlated channel.

The results published by Ravindran and Jindal [16] alsoconfirm these findings, showing that, in a fully correlatedchannel, the DFT-based codebook can reduce the channelinformation amplitude difference between different trans-mitting antennas, while a constant modulus DFT codebookproduces less quantization error than nonconstant modulusGrassmannian-based codebook precoding. A recent publica-tion by Yang et al. [9] also demonstrated that the DFT-basedcodebook is effective against spatial correlation in an MU-MIMO system.


L = 2, ‘‘full”L = 2, ‘‘uncorrelated”

L = 4, ‘‘full”

L = 4, ‘‘uncorrelated”L = 8, ‘‘full”L = 8, ‘‘uncorrelated”

−8 −6 −4 −2 0 2 4 6

100

10−1

10−2

10−3

Bit

err

or r

ate

(BE

R)


Figure 5: BER performance between different codebook sizes (fullfeedback MU-MIMO).

The BER performance of the MU-MIMO feedbackschemes is expected to increase further with larger codebooksize. However, using a codebook size that is too large can alsopose a few issues. First, a larger codebook size decreases thespectral efficiency of the uplink channel because the feedbackinformation increases considerably. Increasing the codebooksize incurs exponential complexity in quantizing the CQI,as shown by Beh in [17], thus defeating the main purposeof channel feedback, particularly in the partial feedbackscheme. At the time of writing, only a codebook size of L = 2is supported by the 3GPP specification published in [18]because it trades off between performance gain and feedbackoverhead.

It is also shown that in a fully correlated channel, largercodebook sizes (L ≥ 4) offer superior performance tosmall codebook size (L = 2). This result suggests thatthe size of the codebook has implications for the tradeoffbetween the numbers of signaling bits required to indicatea particular matrix in the codebook and the suitability of theresulting transmitted beam direction. It is shown by Tse andViswanath [19] that the codebook size L = 4 has a marginallybetter multiuser diversity gain than L = 2 when simulated inthe partial feedback scheme. This improvement is observedbecause the number of users selecting the same codebookmatrix is reduced for the larger codebook size, causing asmaller number of users to be scheduled on the same time-frequency resource. For these reasons, it is important toselect a suitable codebook size for the MU-MIMO downlinktransmission.

6.3. Performance Comparison between Partial and FullFeedback Schemes. Figures 6 and 7 compares the BERperformance between the partial feedback and full feedbackschemes for different numbers of users in uncorrelated andfully correlated channels, respectively. As the number of usersincreases from 1 to 25, the BER performance significantly

100

10−1

10−2

10−3

Bit

err

or r

ate

(BE

R)


−5 0 5 10 15

1U, ‘‘Full”1U, ‘‘uncorrelated”2U, ‘‘full”2U, ‘‘uncorrelated”

25U, ‘‘full”25U, ‘‘uncorrelated”

5U, ‘‘Full”5U, ‘‘uncorrelated”



Figure 6: BER performance of an MU-MIMO (partial feedback)with different number of users.

1U, ‘‘Full”1U, ‘‘uncorrelated”2U, ‘‘full”2U, ‘‘uncorrelated”





100

10−1

10−2

10−3

Bit

err

or r

ate

(BE

R)


−5 0 5 10 15

Figure 7: BER performance of an MU-MIMO (full feedback) withdifferent number of users.

increases as a result of the richer spectral multiuser diversitygains. When the number of users is increased (e.g., from 10to 50), the gain of multiuser diversity can be observed toincrease slowly, suggesting that the multiuser diversity gainachieves saturation as the number of users increases. Thisresult is consistent with theoretical observations made by Tseand Viswanath [17], in which greater gain can be achievedthrough the additional dimension of diversity in the spatialdomain. MU-MIMO can achieve a similar level of diversitygain, even with fewer users in the system.


7

6

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cy (

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−10 −5 0 5 10 15 20 25


Full MU, uncorrelatedPartial MU, uncorrelatedSU, uncorrelatedFull MU, full correlated

Partial MU, full correlatedSU, full correlatedSISO

Figure 8: Average bandwidth efficiency comparison between theuncorrelated and fully correlated channels in the partial feedbackscheme.

This result also confirms that, in addition to the abilityto mitigate the effect of self-interference, the proposedinterference-aware allocation scheme also considers theeffect of multiple access interference (MAI) when simulatedin MU-MIMO. In MU-MIMO, the resulting multiuserinterference is handled by the multiple antennas, which pro-vide the degrees of freedom necessary for spatial separationof the users, as well as link diversity. For a higher number ofusers in a full feedback scheme, a larger codebook size canfurther improve the result.

6.4. Throughput Analysis. Figure 8 compares the averagebandwidth efficiency in uncorrelated and highly correlatedchannel environments. The bandwidth efficiency of a SISOsystem is plotted as a reference. The simulation resultconsiders 10 users in both correlation cases.

From the figures, MIMO systems in the uncorrelatedchannel have better bandwidth efficiency than those in“fully” correlated channels. With the additional spatialdiversity that can be exploited, MU-MIMO can providealmost double the throughput across the entire SNR range.In the case of “fully” correlated channels, MU-MIMOachieves significant bandwidth efficiency gain over SU-MIMO. The partial feedback scheme is marginally inferior tothe full feedback scheme in both uncorrelated and correlatedchannels.

At lower SNR, the bandwidth efficiency of MU-MIMOis similar to that of uncorrelated MU-MIMO and otherfeedback schemes because the use of QPSK modulation isrobust against the effect of channel imperfection (especiallychannel correlation) in this case. At higher SNR, the higherlevel of MCS is vulnerable to channel degradation. Byemploying an adaptive modulation scheme, the proposedinterference-aware allocation is also able to reduce the self-interference effect across all SNRs.

Considering the correlation environment simulated in afully correlated channel (correlation coefficient of 0.99), theproposed interference-aware allocation scheme is expected tooffer higher throughput gain in practical applications basedon the results presented in this paper.

7. Conclusion

In this paper, it is shown that the proposed interference-aware allocation scheme (frequency diversity), in combi-nation with the feedback schemes from MU-MIMO (spa-tial diversity), can improve the BER performance whensimulated in a rapidly time-varying channel, which suffersfrom severe spatial correlation between the transmitting andreceiving antennas.

There are two types of MU-MIMO feedback: (i) fullfeedback and (ii) partial feedback. Full feedback offerssuperior performance compared to partial feedback, but atthe expense of high uplink overhead, while partial feedbackoffers a tradeoff between multiuser diversity gain and areduced feedback requirement on the uplink.

In general, a larger codebook implies more accurateknowledge of the MIMO channel at the transmitter, whichleads to improved diversity. There is no significant differencein BER performance between codebook sizes when thechannel is uncorrelated and operating under single user (SU-MIMO) transmission. The DFT-based codebook adaptationenables the quantization to exploit the spatial correlationinherent in the channel.

These results show that the combination of a codebooksize of L = 2 with the partial feedback scheme achievesmarginal BER performance compared to higher L sizes withfull feedback scheme. The utilization of dynamic subcarrierallocation helps to reduce the effect of self-interference byexploiting the frequency diversity. A tradeoff between self-interference reduction and performance gain justifies theselection of the codebook size and feedback scheme in LTEdownlink environment.

Acknowledgment

The author would like to thank the National Universityof Malaysia for the financial support of this work, underthe Grant scheme UKM-GGPM-ICT-032-2011. The authoralso would like to thank the anonymous reviewers for theirvaluable feedbacks.

References

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[2] D. Gesbert, M. Shafi, D. S. Shiu, P. J. Smith, and A. Naguib,“From theory to practice: an overview of MIMO space-timecoded wireless systems,” IEEE Journal on Selected Areas inCommunications, vol. 21, no. 3, pp. 281–302, 2003.

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[4] S. Sanayei and A. Nosratinia, “Exploiting multiuser diversitywith only 1-bit feedback,” in Proceedings of the IEEE WirelessCommunications and Networking Conference (WCNC ’05), pp.978–983, March 2005.

[5] D. Gesbert, M. Kountouris, R. W. Heath, C. Chan-ByoungChae, and T. Salzer, “Shifting the MIMO paradigm,” IEEESignal Processing Magazine, vol. 24, no. 5, pp. 36–46, 2007.

[6] D. J. Love, R. W. Heath, V. K. N. Lau, D. Gesbert, B. D. Rao,and M. Andrews, “An overview of limited feedback in wirelesscommunication systems,” IEEE Journal on Selected Areas inCommunications, vol. 26, no. 8, pp. 1341–1365, 2008.

[7] H. Rohling and R. Grunheid, “Cross layer considerations foran adaptive OFDM-based wireless communication system,”Wireless Personal Communications, vol. 32, no. 1, pp. 43–57,2005.

[8] Philip RI-062483, “Comparison between MU-MIMOcodebook-based channel reporting techniques for L TEdownlink,” 3GPP TSG RAN WG I Meeting #46bis, october2006.

[9] D. Yang, L. L. Yang, and L. Hanzo, “DFT-based beamformingweight-vector codebook design for spatially correlated chan-nels in the unitary precoding aided multiuser downlink,” inProceedings of the IEEE International Conference on Communi-cations (ICC ’10), pp. 1–5, May 2010.

[10] B. Mondal and R. W. Heath, “Channel adaptive quantizationfor limited feedback MIMO beamforming systems,” IEEETransactions on Signal Processing, vol. 54, no. 12, pp. 4717–4729, 2006.

[11] S. J. Kim, H. J. Kim, and K. B. Lee, “Multiuser MIMOScheme for Enhanced 3GPP HSDPA,” in Proceedigs of the 11thEuropean Wireless Conference, February 2005.

[12] J. Jang and K. B. Lee, “Transmit power adaptation formultiuser OFDM systems,” IEEE Journal on Selected Areas inCommunications, vol. 21, no. 2, pp. 171–178, 2003.

[13] J. P. Kermoal, L. Schumacher, K. I. Pedersen, P. E. Mogensen,and F. Frederiksen, “A stochastic MIMO radio channel modelwith experimental validation,” IEEE Journal on Selected Areasin Communications, vol. 20, no. 6, pp. 1211–1226, 2002.

[14] K. C. Beh, C. Han, M. Nicolaou, S. Armour, and A. Doufexi,“Power efficient MIMO techniques for 3GPP LTE andbeyond,” in Proceedings of the IEEE 70th Vehicular TechnologyConference Fall (VTC ’09), pp. 1–5, September 2009.

[15] J. Zhu, J. Liu, X. She, and L. Chen, “Investigation on precodingtechniques in E-UTRA and proposed adaptive precodingscheme for MIMO systems,” in Proceedings of the 14th Asia-Pacific Conference on Communications (APCC ’08), pp. 1–5,October 2008.

[16] N. Ravindran and N. Jindal, “Limited feedback-based blockdiagonalization for the MIMO broadcast channel,” IEEEJournal on Selected Areas in Communications, vol. 26, no. 8, pp.1473–1482, 2008.

[17] K. C. Beh, Resource allocation for the long term evolution (LTE)of 3G [Ph.D. thesis], University of Bristol, Bristol, UK, 2009.

[18] E. Y. Kim and J. Chun, “Random beamforming in MIMOsystems exploiting efficient multiuser diversity,” in Proceedingsof the IEEE 61st Vehicular Technology Conference (VTC ’05),vol. 1, pp. 202–205, June 2005.

[19] D. Tse and P. Viswanath, Fundamental of Wireless Communica-tion, Cambridge University Press, New York, NY, USA, 2005.

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ExploitingSpatialandFrequencyDiversityinSpatiallyCorrelated ...Correspondence should be addressed to Rosdiadee Nordin, [email protected] Received 23 April 2012; Revised 9 November 2012;