A fair MU-MIMO scheme for IEEE 802.11ac

Mounir Esslaoui*t, Felip Riera-Palou* and Guillem Femenias* *Mobile Communications Group, University of the Balearic Islands - 07122 Mallorca (Illes Balears), Spain

tInformation and Telecom Systems Lab, Abdelmalek Essaadi University - 93000 Tetouan, Morocco Email: {mounir.esslaoui.felip.riera.guillem.femenias} @uib.es

Abstract-The next generation of wireless local area networks (WLANs), currently standardized within IEEE S02.11ac, will surely adopt multiuser multiple-input multiple-output (MU­MIMO) technology. This paper addresses the design of a mul­tiuser proportional fair scheduling scheme, based on MU-MIMO orthogonal frequency division multiplexing (OFDM), that is able to schedule simultaneous transmissions to various users while providing a high degree of fairness. The proposed scheme is complemented by a fast link adaptation (FLA) strategy that, in light of the available channel state information (CSI), determines the most appropriate transmission parameters for each selected user. Simulation results generated using specifications envisaged for IEEE S02.11ac demonstrate the gains offered by the proposed technique with practical modulation and coding schemes.

I. INTRODUCTION

Increasing demands for high data rate communication sys­tems have driven the push for Wi-Fi technologies with high spectral efficiency. While current IEEE 802.11n-based wireless local area networks (WLANs) reach data rates of up to 600 Mbps, the upcoming IEEE 802.11ac [1] aims to widely surpass the 1 Gbps barrier by using an expanded bandwidth transmission of up to 160 MHz and allowing the simultaneous transmission to various users using multiuser multiple-input multiple-output (MU-MIMO) techniques [2].

Focusing on the downlink scenario, information theoretic results [3] predict that large gains are possible when the spatial dimension is exploited to transmit data in parallel to various users. It is well known that applying dirty paper coding (DPC) at the transmitter [4] is a capacity-achieving strategy for the MIMO broadcast channels, however, its large computational complexity motivates the need for simpler alternatives. In this line, authors in [5] presented a suboptimal technique that selects a subset of users for simultaneous transmission with a selection criterion based on a metric that takes into account the degree of user orthogonality after linear precoding. The proposed algorithm achieves a sum-rate close to the one promised by DPC at a substantially lower computational complexity. Unfortunately, the framework introduced in [5] solely targets single-carrier architectures. Recently, there has been an extension of this work to a multicarrier architecture based on OFDM [6], where the simultaneously transmitting users must share the utilization of all the subcarriers in the system (i.e., frequency is not used for multiple access as in OFDMA systems). This will be the scenario likely encoun­tered when applying MU-MIMO to future WLAN systems, which is rather different from the one found, for instance, in LTE-Advanced. The multiple access scheme proposed in

[6], designed for single-antenna receivers, is made of a mul­ticarrier user selection (MUS) algorithm and a subcarrier­specific precoder designed to minimize inter-user interference. The MUS algorithm selects those users with good channel conditions while satisfying orthogonality conditions across subcarriers, thus guaranteing their spatial separability. One remaining hurdle to exploit multiuser transmission in practical systems consists of determining an appropriate modulation and coding scheme, that is, how to do link adaptation in a MU-MIMO-OFDM architecture. To this end, in [7] the MUS algorithm was complemented with a fast link adaptation (FLA) strategy that effectively implemented an adaptive modulation and coding (AMC) [8] policy to determine the transmission parameters used for each of the selected users. It was shown in that, at high SNR levels, the proposed scheme increases the system throughput by a factor linearly dependent on the number of transmit antennas, while satisfying a predetermined quality of service (QoS) constraint, usually in the form of an outage probability on the target packet error rate (PER). However, the work in [7] was limited to single-antenna re­ceivers and, furthermore, it did not consider any of the fairness issues MU-MIMO brings along. This paper tackles both issues by considering the availability of multi antenna receivers and introducing mechanisms to improve fairness among users. Numerical results show that the proposed scheme can provide a high degree of fairness among users while only resulting in a slight throughput loss in comparison to a system based on a pure throughput maximization strategy.

II. SY STEM MODEL

We consider a single-cell downlink system with NT transmit antennas at the base station (BS) and Nu mobile users each equipped, without loss of generality, with the same number N R :::; NT of receive antennas. The system operates with Nc OFDM subcarriers, Nd of which are used to transmit user data while the rest correspond to pilots and guard bands. As depicted in Fig. 1, the information bits for each user u are encoded using a separate convolutional encoder. The resulting coded bits are then punctured, interleaved and mapped onto modulation symbols from an M-ary modulation alphabet.

Notational remark: Vectors and matrices are denoted by lower- and upper­case bold letters, respectively, while non-bold letters are used for scalars. V(x) is a (block) diagonal matrix with x at its main diagonal, lUI is the cardinality of subset U, (. ) T and (.) H serve to denote transpose and complex transpose respectively, [Ali,j is the (i,j)-element of matrix A, Ip is the p x P identity matrix, lIall denotes the Euclidean norm of a vector a and, ffi. and IC are the set of real and complex numbers respectively.

978-1-4673-0762-8/12/$31.00 ©2012 IEEE 1049

N" NT ,...-----,

L .................................... ........ .... ......................................................................................................................... �.?!

Fig. 1. Block diagram of MU-MIMO-OFDM base station with NT transmit antennas and fast link adaptation.

Transmission mode selection implies picking up a particular combination of puncturing rate and constellation. Beamform­ing, in the form of linear precoding, and power allocation serve to condition the symbols to the current channel state before being processed by a conventional OFDM modulator made of an IFFT stage and the addition of a guard interval (GI). This transmitter scheme conforms to the model currently being discussed within IEEE 802.11 ac standardization activities [1].

Let Hu[q] E CNRXNT represent the channel gain matrix corresponding to the uth user over the qth subcarrier and admitting singular value decomposition (SVD)

(1)

where Uu[q] = [uu,dq] ... UU,NR[q]] E CNRXNR and Vu[q] = [Vu,l[q] ... Vu,NT[q]] E CNTXNT are unitary matri­ces containing the left and right singular vectors of Hu [q] and �u[q] = D ([O"u,dq]· .. 00U,NR[q]]) E jRNRXNT is a (possibly rectangular) diagonal matrix whose nonzero entries are the singular values of Hu[q]. The received signal of each user u, on subcarrier q, is multiplied by a receiver shaping matrix U�[q]. Therefore, after postprocessing, the equivalent channel gain matrix of user u on subcarrier q can be represented as

The availability of channel state information (CSI) at the transmitter allows the exploitation of the properties of the SVD to convert every user's channel, on every subcarrier q, into N R parallel spatial channels. By treating each spatial stream as a separate virtual user, the resulting system can be seen as a multiuser multiple-input single-output (MV-MISO) broadcast system serving NuNR single-antenna users with channel gains hu,n[q] = O"u,n[q]v�n[q] at the nth receive antenna of the uth user on the qth subcarrier. Let k be the index of the virtual user corresponding to the nth receive antenna of the uth original user. Assuming perfect frequency synchronization between transmitter and receiver and a cyclic prefix duration exceeding the channel delay spread, the received signal at the kth virtual user on subcarrier q for an arbitrary OFDM symbol may be written as

where hk[q] E C1xNT is the equivalent channel vector corre­sponding to the kth virtual user, x[q] E CNTX1 is the vector of transmitted symbols from the BS antennas on subcarrier q, and i}k[q] = U�n[q]1]u[q], where 1]u[q] is a zero-mean circularly symmetric complex gaussian vector with covariance matrix R1) = O"�INR" Since Uk[q] is unitary, i}[q] '" CN(O,O"�).

The base station has a total power PT available for trans­mission and, in light of the available CSI, it selects a sub­set U = {U1, . . . , ulul} (lUI ::; NT) of virtual users for simultaneous transmission during a given time slot. Let us define Hu[q] = [h;l [q] ... h;IUI [q]]T as the lUI x NT matrix collecting the channel coefficients for the selected virtual users on subcarrier q. Assuming a linear precoder is used, the transmitted symbol vector x[q] can be written as

x[q] = Wu [q]PU'2 [q]su [q], (4)

where Wu[q] [WUl [q] ... wu1u1 [qJ] represents the NT x lUI precoding matrix on subcarrier q, Pu [q] D([PUl [q] ... PU1U1 [q]]), such that

L Ilwui[q]112Pui[q] = PT, (5) uiEU

and su [q] = [SUl [q] ... sUlul [qJ] T is the lUI x 1 vector

containing the information symbols belonging to the selected virtual users. If zero-forcing beamforming (ZFBF) is used, the precoding matrix is chosen such that Hu[q]Wu[q] = Ilul. One easy choice of Wu[q] that gives zero-interference is the pseudoinverse of Hu[q] leading to a precoding matrix [5]

Wu[q] = Hlf[q] (fIu[q]Hlf[q]) -1 (6)

Plugging (4) and (6) into (3), the received signal for virtual user k E U on subcarrier q can be rewriten as

The combined precoder-channel gain for the kth virtual user on the qth subcarrier is thus given by

1 'Yk[q] = ..,,------�-[ (fIu[q]Hlf[q]) -1]

k,k

(8)

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Algorithm 1 : Multicarrier user selection (MUS). (a) Initialization: i = 1, 7i = {I, . .. ,Nu}. (b) Singular value decomposition:

for Each user u E Ti. do for Each subcarrier q do

Uu [q]Eu [q]V{; [q]=svd(Hu [q]) end for

endfor (e) UpdateT1 = {I, ... , NuNR}, U = (I).

while (17;1 of O)&(IUI < NT) do (d) Orthogonality measure computation:

for Each virtual user kEG do for Each subcarrier q do

hklq] = O'klq]vr [q]

gklq] - hk[q] INT 2:j=l IIg",(j)lq]1I2 end for

end for

_ - ( _ i-1 g�(j) Iq]g",(j) Iql) (e) Choose most orthogonal virtual user: 7r(i) = argmax 2:

N�l IIgklq] II ;U = U U 7r(i) kE'Ti q-(f) Discard poorly orthogonal virtual users_: H

{ . 1 Nd Ihklq]g"'�:fllq]1 } 7;+1 = k E 7;, k of 7r('): ek = Nd 2:q=l IIhklqlll llg;(i)lqlll < e i=i+l

end while

III. MULTIUSER SCHEDULING STRATEGIES

A. Multicarrier user selection This subsection introduces a multicarrier user selection

(MUS) algorithm (Algorithm 1) aiming at the maximization of system throughput. The selection procedure begins by initializing counters and the set To with the Nu active users in the cell (Step (a». The channel matrix Hu[q] of each user U, on each subcarrier q, is decomposed into N R parallel spatial channels by means of SVD (Step (b». Subsequently, the user pool To is updated with the Nu N R virtual users (Step (c». In Step (d), and for each successive iteration, the vector gk[q] is found as the component hk[q] most orthogonal to the subspace spanned by {g7l'(1)[q], ... ,g7l'(i-l)[q]} where {7I'(1), ... ,71' ( i-I)} denote the indexes of the previously selected virtual users. Step (e) selects the virtual user 71'(i) with the largest projected norm Ilgk II averaged across subcarriers and includes it in the subset U of selected virtual users. Finally, poorly orthogonal virtual users, defined as those whose orthogonality coefficient ek exceeds a certain threshold e, are discarded from the total user pool in order to reduce the computational requirements of the MUS algorithm (Step (t)). Note that e (0 ::::: e ::::: 1) is a small positive number that controls the minimum degree of orthogonality between the already selected virtual user(s) {7I'(1), ... ,71' ( in and those that still remain in the pool of potentially selectable virtual users. The (virtual) user selection process stops when the number of virtual users in the active subset equals the number of transmit antennas NT or the list of remaining virtual users is empty.

B. Proportional fairness for MU-MIMO-OFDM The MUS algorithm focuses on maximizing the system

throughput without taking into account the fairness among users. In practical schemes, fairness plays a key role when determining the user(s) who will be allocated all the spectrum and power resources during a given time slot. Proportional fair (PF) scheduling is an algorithm designed to meet fairness among users while exploiting the multiuser diversity gain

inherent in a system with users having independent, fluctuating channel conditions [9]. The potential data rate of a user U can be defined as

(9) 'VkEKu

where Ku is the set of selected virtual users (each with rate Tk(t» associated to user u. Based on (9), the PF algorithm keeps track of the average throughput Tu (t) of each user U over a past window of length tc using an exponentially weighted low-pass filter process defined by

Tu(t + 1) = (1 -�) Tu(t) + �Ru(t) (10) tc tc

where the window size tc must be determined based on the latency time of the considered application [9].

For each time slot t, the BS schedules the virtual user satisfying

Tk(t) argmax T ( )'

'Vu,kEKu u t among all NuN R virtual users in the cell.

(11)

Aiming at a design that is able to exploit multiuser diversity while maintaining user fairness, PF is applied to the MUS technique described in section lILA resulting in the PF-MUS algorithm described next. It is well known that, in conventional PF, Ru (t) can be obtained before the scheduling decision is made. However, in PF-MUS, the users' rate remain unknown until the scheduling decision finishes and the subset U of virtual users is completely defined. To this end, the PF-MUS works as follows. First, MUS (Algorithm 1) is executed with the following modification in step (e)

71'(i) = argmaxT

l(t)

'f, log2 (1 + �T Ilgk[q]112) . kE'T; u q=l T

(12)

Second, the ZFBF is applied to Hu [q] in order to obtain the actual supported data rates Tk (t) of each virtual user k E U.

IV. FLA IN MULTIUSER MIMO-OFDM

The PF-MUS technique introduced in section III is based on a capacity measure. However, in practical systems such as IEEE 802.11ac, only a finite set .c of transmission modes, formed by a combination of modulation alphabet and coding rates, is available. Consequently, once the group of users has been selected, a procedure is needed to determine the most appropriate transmission modes subject to prescribed QoS requirements. Adaptive modulation and coding (AMC) allows rate selection in light of the available CSL Link adaptation (LA) is a general term used to denote the body of algorithms and protocols governing, among other aspects, the behaviour of AMC schemes. Fast link adaptation (FLA) is a particular form of LA that assumes the availability of instantaneous CSL

In MU-MIMO-OFDM networks, FLA aims at exploiting the varying channel state (over time, frequency and space) to select the MCS that maximizes the system throughput while satisfying a predetermined quality of service (QoS) constraint, usually in the form of an outage probability Pout of a target

105 1

packet error rate (PER) PERo [10]. Therefore, the search for the optimum MCS inevitably requires of a PER prediction methodology that can accurately match CSI and PER.

Unequal SNR levels in both the different subcarriers and spatial streams makes the estimation of PER in MIMO­OFDM networks difficult. Typically, the system PER depends on the MCS, the received SNR, the packet length and the channel realization, thus making the derivation and evalua­tion of analytical PER expressions a cumbersome task. The approach usually followed to solve this problem is to map all these parameters onto a single link quality metric (LQM) which can then be associated to a PER value by means of a look-up table constructed during a calibration phase [10], [11], [12]. In [13] a mapping is found between a particular LQM mapping, known as effective SNR, calculated over all subcarriers, and the operating bit error rate (BER), which can then be easily translated to system PER. For a given MCS m,

the effective SNR is defined as the SNR level that would be required on an AWGN channel to obtain the same BER over the frequency selective fading channel realization. Using, for instance, the exponential effective SNR metric (EESM), it can be analytically expressed as

SNR(m) [k] = _ (m) 1 (2.. � ( -SN Rk [q])) eff Ctl n N LexP (m)

, d q=l Ct2

(13) where the parameters Ct�m) and Ct�m) are optimized for each MCS m E .c and obtained following the calibration procedure detailed in [13], and SNRk[q] = Pk[qhk[q]/(T� is the output SNR corresponding to a transmitted symbol on subcarrier q for a given virtual user k. Look-up tables are available from the

calibration phase mapping SN R�7} [k] to the corresponding

BER, namely, p�m) [k]. Moreover, in [13], [7] it is shown how FLA can operate on the basis of packet error rate (PER), rather than BER, a desirable feature since PER is usually the preferred performance metric in real WLAN scenarios.

The search mechanism, closely following the scheme pre­sented in [7], selects the most efficient MCS m E .c for each virtual user k E U that, based on their corresponding precoding-channel gain 'Yk [q], maximizes its corresponding throughput while satisfying the constraint,

SNR(m)[k] > SNR(m) eff - Th' (14)

where SN R�'7,) represents the mode decision thresholds for each MCS m.

V. NUMERICAL RESULTS

In this section results are presented to illustrate the benefits of the PF-MUS-FLA technique when using parameters cur­rently found in the latest WLAN standard IEEE 802.11n and that will also form part of the forthcoming IEEE 802.11ac norm. The system has been configured to operate at 5.25 GHz carrier frequency on a bandwidth of W = 20 MHz with Nc = 64 subcarriers out of which Nd = 52 are used to carry data while the rest correspond to pilots and guard

bands. The base station is equipped with NT = 4 transmit antennas while all mobiles are assumed to operate with either N R = 2 or N R = 1 receive antennas. Channel profiles B (residential) and E (large office) from [14] have been used in the simulation testbed. Optimal values of parameter e have

been obtained from [6]. The value of parameters Ct�m) and

Ct�m) have been obtained from [13]. The target PER value has been fixed to PERo = 0.1 with an outage probability Pout = 0.05. Packet length has been fixed to L = 1664 bits. Multiple antennas at the MSs are treated as independent virtual single-antenna users. Thus, each virtual user will choose one of the eight different MCSs belonging to the single spatial case modes that are available for transmission yielding bit rates between 6.5 Mbps (BPSK, 112) and 65 Mbps (64-QAM, 5/6). For the convolutional encoder, a basic code rate Rc = 1/2 with generator polynomials 9 = [133,171]8 has been used.

Figure 2 compares system throughput for the proposed MUS-FLA algorithm and opportunistic multicarrier TDMA­FLA (MC-TDMA-FLA) as a function of SNR. In this scenario, the Nu active users in the cell are homogeneous (i.e., all users experiment the same average SNR). Different number of users and antenna receivers over Channel profile B are considered. Note that in opportunistic MC-TDMA-FLA [9] networks the BS schedules a single user at a time (the one experiencing the best channel realization) that will receive multiple data streams (up to N R). One can observe that, thanks to the multiuser diversity and the use of multiple antennas at the subscribers, higher throughput is achieved for both schemes. Nonetheless, while the throughput of opportunistic MC-TDMA-FLA saturates at around 65 Mbps and 130 Mbps for single and multiple spatial stream(s), respectively, the throughput of MUS-FLA for both N R = 1 and N R = 2 saturate at around 260 Mbps at high SNR levels.

In Figure 3, the average throughput of each individual user is compared for MUS-FLA, PF-MUS-FLA, opportunistic MC­TDMA-FLA, PF-MC-TDMA-FLA and Round Robin MC­TDMA-FLA (RR-MC-TDMA-FLA). A population of Nu = 20 users is considered in the cell with an average received SNR ranging from 0 dB (User 1) to 20 dB (User 20) over channel profile B. Note that, in RR-MC-TDMA all spectrum and power resources are allocated to a single user in a Round Robin fashion. It is shown in the figure that MUS-FLA and opportunistic MC-TDMA-FLA strongly favor user(s) with high SNR(s) and thus cause starvation to user(s) experiencing poor SNR(s). However PF-MUS-FLA, PF-MC-TDMA-FLA and RR-MC-TDMA-FLA ensure that no users are starved of resources regardless of their average received SNRs. Among the three fair scheduling schemes, PF-MUS-FLA provides the best individual users' throughput performance.

One of the most relevant fairness indicators is the so-called Jain's fairness index (JFI) [15] defined as

[L:�l Ru(t)f JFI= N 2' (15)

Nu Lu�l [Ru(t)] J F I ranges from 1

Nu (only one user is served) to 1 (all

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300rc=====:::;-r---�--�-�--, __ N,=10, NR=1 MUS-FLA

°OL--�--�1�O--�15�-� 2�O--�25�--" 30 SNR [dB[

Fig. 2. MUS-FLA vs Opportunistic MC-TDMA-FLA throughput.

"' �90rc=7=�==�===�=i--�----' 6 -+- PF-MUS-FLA � 80 ___ MUS-FLA � 70 � Opportunistic MC-TDMA-FLA � -e- PF-MC-TDMA-FLA � 60 -+- RR-MC-TDMA-FLA � 50 � 40 � 30 � 20

�1° l���������������� � � 0

0 10 15 20 Users

Fig. 3. Average throughput of individual user comparison for different scheduling schemes. Nu = 20 , N R = 2.

users are served at the same rate). Figure 4 plots the lain's fairness index for MUS-FLA, PF-MUS-FLA and RR-MC­TDMA-FLA as a function of the number of users in the cell for channel profiles B (continuous lines) and E (dashed lines). We assume that users are heterogeneous (i.e., all users are randomly distributed and experiment different received average SNR). For both channel profiles, the maximum value of JFI is always reached by RR-MC-TDMA-FLA regardless of the number of users in the cell and thus, results in an ideally fair distribution of common resources. Moreover, it is shown that the fairness performance of the proposed PF­MUS-FLA clearly outperforms MUS-FLA and remains very close to the ideal case. The J F I of PF-MUS-FLA for Channel profiles B and E lie in the ranges (0.99,0.96) and (0.95,0.92), respectively, for a number of users in the cell varying from 5 to 50. In contrast, for the MUS-FLA case, as the number of users increases in the cell, the J F I decreases to values below 0.15 for both channel profiles as MUS-FLA mostly schedules those users experiencing good channel realizations.

VI. CONCLUSION

This paper has considered the use of multicarrier MU­MIMO techniques in the context of multiantenna receivers where fairness should be taken into account when maximizing the system throughput. The proposed scheme treats multiple­antenna receivers as virtual users with just one receive antenna. It works by first selecting those (virtual) users experienc­ing good channel conditions while fulfilling a prescribed subcarrier-wise spatial orthogonality criterion and taking into account a proportional fairness factor. Then, the most appropri-

,-, -, '- ,- D-. - '-0-' - , -, -, ,-, - 'D ,- ,-

0.8

o. __ MUS-FLA � PF-MUS-FLA -+- RR-MC-TDMA-FLA

°5�� 10�- 1�5-�2�0-�25��-�-�-�� 50 Users

Fig. 4. Jain's fairness index versus the number of users in the cell for different channel profiles. N R = 2.

ate MCS mode for each of the selected virtual users is chosen using FLA. Results based on IEEE 802.11ac parameters show that the proposed technique clearly outperforms opportunistic MC-TDMA-FLA in terms of throughput yet provides a high degree of fairness among users. At large SNRs, the through­put of PF-MUS-FLA outperforms that of opportunistic MC­TDMA-FLA by a factor given by the quotient of the number of transmit and receive antennas.

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