AbstractâThis paper presents a practical scheme to exploit opportunistic multiuser multiple-input multiple-output (MU-. MIMO) diversity in multicarrier systems ...
2011 8th International Symposium on Wireless Communication Systems, Aachen
Fast link adaptation for opportunistic multiuser MIMO-OFDM wireless networks ∗ Mobile
Mounir Esslaoui∗† , Felip Riera-Palou∗ and Guillem Femenias∗ Communications Group, University of the Balearic Islands - 07122 Mallorca (Illes Balears), Spain and Telecom Systems Lab, Abdelmalek Essaadi University - 93000 Tetouan, Morocco Email: {mounir.esslaoui, felip.riera, guillem.femenias}@uib.es
† Information
Abstract—This paper presents a practical scheme to exploit opportunistic multiuser multiple-input multiple-output (MUMIMO) diversity in multicarrier systems using orthogonal frequency division multiplexing. The scheme is based on a multicarrier user selection algorithm to schedule the users that should transmit simultaneously and a fast link adaptation (FLA) technique that, in light of the instantaneous channel state information (CSI), determines the most appropriate transmission parameters for each user. Numerical results based on parameters typically used in modern wireless local area networks (WLANs) show that, when compared to an opportunistic TDMA scheme, the proposed system can improve the system throughput performance by a factor proportional to the number of transmit antennas.
I. I NTRODUCTION In recent years, owing to its abilities to provide high data rates in a spectrally efficient way, multiantenna multicarrier wireless technology has become the dominant architecture for the physical layer (PHY) of state-of-the-art wireless communication systems (LTE-Advanced, WiMAX or IEEE 802.11n/ac). In particular, it has been shown that combining multiple-input multiple-output (MIMO) systems with orthogonal frequency division multiplexing (OFDM) is an effective technique that is able to exploit spatial as well as frequency diversity, thus allowing high data rates with a large degree of robustness [1]. More recently, the exploitation of channel state information (CSI) at the transmitter in the context of MIMO has attracted substantial research efforts. To this end, different precoding strategies have been designed that are able to increase system capacity and/or reduce the complexity of the receiver [2]. The use of precoding techniques has fueled the research transition from single-user MIMO (SU-MIMO) to multiuser MIMO (MU-MIMO) [3]. The rational behind MU-MIMO is to combine the high capacity achievable with MIMO processing with the benefits of space division multiple access when many spatially uncorrelated users are to be served. Focusing on the downlink scenario, different combinations of scheduling strategies and MIMO processing have been proposed in the literature (see, for instance, [3] and references therein). Nevertheless, it has been long known that, in such setups, dirty paper coding (DPC) [4] is the optimal method from a system capacity point of view. Unfortunately, deploying this technique in practice is rather difficult due to the high computational complexity it entails, especially for a large number of users. An alternative and practical scheduling strategy that achieves a sum-rate close to the optimal rate promised by DPC, but at a
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much lower computational complexity, was proposed in [5] in the context of single carrier systems. This suboptimal strategy combines the idea of opportunistic beamforming transmission [6] with the simultaneous transmision to a selected group of users by virtue of their spatial separability, i.e., those users that can be more easily orthogonalized by means of linear beamforming are selected for simultaneous transmission. Recently, there has been an extension of this work to a multicarrier architecture based on OFDM [7], where user multiplexing takes place using a combination of TDMA and SDMA. The multiple access scheme proposed in [7] is made of a user selection step that takes care of selecting those users experimenting the best channel realizations measured over all subcarriers, and a subcarrier-specific precoder designed to minimize inter-user interference. It is shown in [7] that the proposed multicarrier user selection scheme effectively translates the sum-rate capacity gain obtained in a single carrier system to the multicarrier case. Nevertheless, it remains to be seen how these capacity-based approaches can be applied in practice when using finite modulation constellations and practical coding schemes. Our objective in this paper is to introduce a scheme that, based on the MU-MIMO-OFDM user selection procedure presented in [7], is suitable for implementation in systems employing practical modulation and coding schemes such as those found in state-of-the-art WLAN systems (IEEE 802.11n, IEEE 802.11ac). To this end, the scheme in [7] is complemented with a fast link adaptation (FLA) technique that effectively implements an adaptive modulation and coding (AMC) policy [8] to determine the transmission parameters used for each of the selected users. The rest of the paper is organized as follows: Section II introduces the system model. An overview of the FLA methodology is provided in Section III. The multicarrier user selection algorithm with FLA is described in Section IV and the numerical results are shown in Section V. Finally, Section VI summarizes the main outcomes of the paper and provides hints for further work. This introduction concludes with a brief notational remark. Vectors and matrices are denoted by lower- and upper-case bold letters, respectively, while non-bold letters are used for scalars, D(X) is a (block) diagonal matrix with X at its main diagonal, |U| is the cardinality of set U , T and H serve to denote transpose and complex transpose respectively, [A]i,j is
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IFFT+GI
…
Linear precoding & Power allocation
…
Mode selection (AMC)
…
User selection (MUS)
…
User Data
the receive antenna of the uth user over the qth subcarrier, T x[q] = [x1 [q] · · · xNT [q]] is the transmitted symbol vector on subcarrier q and ηu [q] is a zero-mean white Gaussian noise sample with variance ση2 . For a particular user selection set U , let us define H U [q] as the |U| × NT matrix collecting the channel coefficients for the selected users on subcarrier q. The transmitted symbol vector x[q] is then obtained from the vector of information symbols su [q], belonging to the selected users, by means of linear precoding as
IFFT+GI
CSI Fig. 1. Block diagram of MU-MIMO-OFDM base station with NT transmit antennas and fast link adaptation.
x[q] =
|U |
Pu [q]W U [q]su [q],
(2)
u=1
the (i, j)-element of matrix A, I P is the P ×P identity matrix and a denotes the Euclidean norm of a vector a. II. S YSTEM MODEL A single cell-based MIMO-OFDM downlink system is considered operating in a total bandwidth W that is exploited by means of Nc subcarriers of which Nd are used to transmit user data while the rest correspond to pilots and guard subcarriers. The base station (BS), depicted in Fig. 1, is equipped with NT transmit antennas and, similar to the scenario used in [5], it serves Nu (≥ NT ) homogeneous users (i.e., all users experiment the same average SNR) each equipped with a single receive antenna. At a given time slot, a set U of orthogonal users is selected for simultaneous transmission from the total user pool. The information bits for every user u ∈ U are encoded using a convolutional encoder with generator polynomials [133, 171] and basic code rate Rc = 1/2. The coded bits are then punctured to one of the available code rates (1/2, 2/3, 3/4 or 5/6). The resulting bit stream is subsequently interleaved and mapped to complex symbols drawn from one of the allowed constellations (BPSK, QPSK, 16-QAM or 64-QAM). 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 be transmitted to the current channel state. Finally, the modulated symbols are processed using a conventional OFDM modulator formed by an IFFT stage and the addition of a guard interval (GI). The Nd × NT matrix H u = [hu,1 . . . hu,NT ], with u ∈ U , represents the user-specific channel matrix, where T hu,k = [hu,k [1] · · · hu,k [Nd ]] denotes the frequency response over the Nd subcarriers of the link between the kth transmit antenna and mobile station (MS) u. Assuming perfect frequency synchronization between transmitter and receiver and a cyclic prefix duration exceeding the channel delay spread, the received signal for user u on subcarrier q for an arbitrary OFDM symbol can be expressed as yu [q] = hu [q]x[q] + ηu [q]
(1)
where hu [q] = [hu,1 [q] · · · hu,NT [q]] represents the frequency response between the NT BS transmit antennas and
where Pu [q] is the power allocated to user u on subcarrier q, |U | Nd chosen so that the power constraint u=1 q=1 Pu [q] = PT is satisfied and W U [q] = [w1 [q] · · · wU [q]] is the precoding matrix, which for zero forcing beamforming (ZFBF) is given by −1 H W U [q] = H H [q] H [q]H [q] . (3) U U U Plugging (2) into the reception equation (1), it is found that the received symbol estimate for an arbitrary user u ∈ U is yu [q] =
|U | Pu [q]hu [q]wu [q]su [q] + ηu [q].
(4)
u=1
After some straightforward calculations it can be seen that the combined precoder-channel gain for user u on the qth subcarrier can be expressed as −1 −1 H γu [q] = H U [q]H U [q] . (5) u,u
This was the basic metric to be maximised in the capacitybased approach introduced in [7]. In order to obtain a scheme suitable for implementation, the use of an adaptive modulation and coding (AMC) strategy with a mode selection done on the basis of the gain in (5) is proposed in this paper. III. FAST LINK ADAPTATION (FLA) A. FLA review Adaptive techniques based on AMC have been widely used for a long time to increase throughput, reliability, and spectrum efficiency of wireless networks. AMC adapts the modulation and coding rate according to the CSI fed back from the receiver to the transmitter [9]. Link adaptation (LA) is a general term used to denote the body of algorithms and protocols governing adaptive modulation and coding schemes. Fast link adaptation (FLA), in particular, relies on instantaneous (rather than average) CSI to determine the transmission parameters. To this end, in light of the available CSI, FLA determines the MCS maximising the system throughput while satisfying a predetermined quality of service (QoS) contraint, usually in the form of an outage probability Pout of a target packet error rate (PER) P ER0 [10]. The search for the optimum MCS inevitably requires of a PER prediction methodology
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that can accurately match CSI and PER. While closed-form PER expressions for single-carrier systems are at hand, PER estimation in MIMO-OFDM systems is not straightforward due to the unequal SNR levels in the different subcarriers, as well as in the spatial streams. 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 [11], [12], [10]. In the context of MIMO-OFDM, authors in [13] focused on a particular LQM mapping, known as effective SNR, whose PER prediction methodology is briefly outlined next. B. PER estimation methodology In [13] a mapping is found between the 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 [14]. Using, for instance, the exponential effective SNR metric (EESM), it can be analytically expressed as
Nd 1 −SN Ru [q] (m) (m) SN Ref f [u] = −α1 ln , exp (m) Nd q=1 α2 (6) (m) (m) where the parameters α1 and α2 are optimized for each MCS m ∈ L and obtained following the calibration procedure detailed in [13] and SN Ru [q] is the output SNR corresponding to a transmitted symbol on subcarrier q for a given user u that can be calculated as Pu [q] SN Ru [q] = γu [q]. (7) ση2 Look-up tables are available from the calibration phase map(m) (m) ping SN Ref f [u] to the corresponding BER, namely, Pb [u]. An estimate of the operating PER can then be obtained as RL m P ERu(m) = 1 − 1 − Pe(m) [u] , (8) (m)
where Rm represents the MCS m code rate and Pe [u] is the error event probability for a convolutionally encoded packet that can be approximated by (m)
Pe(m) [u] ≈ Pb
[u]/df ,
(9)
with df representing the free distance of the convolutional (m) code. Using (1) and (9) the BER0 for each MCS m ∈ L can be expressed as a function of the established P ER0 as follows Rm (m) BER0 = 1 − (1 − P ER0 ) L df . (10)
AWGN channel is almost ideal, and then the mode decision (m) thresholds SN RT h can be approximated for each MCS m as (m)
(m)
(m)
Pr{BERAWGN (SN RT h ) > BER0 } = Pout
(11)
(m) BERAWGN
(·) represents the BER for MCS m over the where AWGN channel. C. MCS Search mechanism The search mechanism selects MCS m ∈ L that maximizies the throughput while satisfying (m)
(m)
SN Ref f [u] ≥ SN RT h .
(12)
The selection process is made by first ordering the MCSs in a decreasing order of their throughput and then evaluating its effective SNR. The first MCS m that satisfies (12) is selected for the next packet transmission. If none of the available MCSs fulfills (12), the no-transmission mode is selected and, consequently, no information is sent to that user. IV. FLA IN MULTIUSER MIMO-OFDM The main objective of FLA in MU-MIMO multicarrier networks is to exploit the varying wireless channel conditions (over time, frequency and space) by dynamically adjusting the MCS of each selected user u ∈ U to the changing environmental and interference conditions observed between the transmitter and the receivers. Algorithm 1, outlined on the next page, describes a multicarrier user selection FLA (MUS-FLA) algorithm to maximize the system throughput by transmitting simultaneously to a group of users U , selected on the base of their orthogonality over all subcarriers. The MUSFLA algorithm (Algorithm 1) combines the multicarrier user selection (MUS) algorithm introduced in [7] with the effective SNR-based FLA technique introduced in the previous section to determine the set M of most efficient MCSs for the selected user set U . A. Multicarrier user selection (MUS) The objective of the MUS step is to determine the set of users to be scheduled in the current time slot using as a selection criterion the degree of orthogonality, averaged over all subcarriers, among them. Starting from an initial user pool T1 = {1, . . . , Nu } containing all active MSs (step I.a), the selection procedure works as follows. In step (I.b), and for each successive iteration (indexed by i), the vector g u [q] is found as the component of hu [q] most orthogonal to the subspace spanned by g π(1) [q], . . . , g π(i−1) [q] where {π(1), . . . , π(i − 1)} denote the indexes of the previously selected users, that is, ⎞ ⎛ i−1 H g π(j) [q]g π(j) [q] ⎠. (13) g u [q] = hu [q] ⎝I NT − g π(j) [q]2 j=1 Step (I.c) selects the best user π(i) corresponding to the largest projected norm g u averaged across subcarriers,
It has been shown in [13] for the single stream case, that mapping the effective SNR to the corresponding BER over the
374
π(i) = argmax u∈Ti
Nd q=1
g u [q],
(14)
300
Algorithm 1 : FLA for multicarrier user selection (MUS-FLA) (I) Multicarrier user selection: (a) Initialize: i = 1, T1 = {1, . . . , Nu }, U = ∅. while (|Ti | = 0)&(U < NT ) do (b)Orthogonality measure computation: for Each user u ∈ Ti do for Each subcarrier q do gH π(j) [q]g π(j) [q] g u [q] = hu [q] I NT − i−1 j=1 g [q]2
Nu=50
Throughput (Mbps)
250
π(j)
end for end for (c)Choose most d orthogonal user: π(i) π(i) = argmax N q=1 g u [q] ; U = U
200
100
0
Fig. 2.
Opportunistic MC TDMA
0
5
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SNR (dB)
20
25
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Throughput for different number of users. Channel profile B.
π(i)
i=i+1 end while (II) MCS selection: (a)Initialize: Ω = {mmax , . . . , mmin }, M = ∅, for Each user u ∈ U do (b)Evaluate effective SNR: i=1 Nd (Ω(i)) (Ω(i)) −SN Ru [q] 1 SN Ref f [u] = −α1 ln Nd q=1 exp (Ω(i)) (Ω(i))
u
50
(d)Discard poorly orthogonal users: d |hu [q]gH π(i) [q]| < θ Ti+1 = u ∈ Ti , u = π(i) : N1d N H q=1 h [q]g [q]
(Ω(i))
u
N =5
150
u∈Ti
u
MUS FLA
N =10
index of the first MCS that satisfies (12). Finally, in step (II.c) the index of each selected MCS is included in the list M of used MCSs for the selected users in U . The algorithm stops when an MCS has been selected for each user u ∈ U. V. N UMERICAL RESULTS
α2
The simulations consider the use of parameters currently
while (SN Ref f [u] < SN RT h )&(Ω(i) > mmin ) do found in the latest WLAN standard IEEE 802.11n. The system i=i+1 has been configured to operate at 5.25 GHz carrier frequency (Ω(i)) (Ω(i)) −SN Ru [q] d ln N1d N SN Ref f [u] = −α1 (Ω(i)) q=1 exp on a bandwidth of W = 20 MHz with Nc = 64 subcarriers end while (c)Select MCS: M = M Ω(i) end for
α2
and includes this user in the selected user set U . Finally, in step (I.d), poorly orthogonal users are discarded from the user pool in order to simplify the computational requirements of the MUS algorithm. To this end only those users in Ti whose orthogonality coefficient θu =
Nd |hu [q]g H 1 π(i) [q]| Nd q=1 hu [q]g H π(i) [q]
(15)
is below a certain threshold θ (0 ≤ θ ≤ 1) are kept. Note that, effectively, θ controls the minimum degree of orthogonality between the already selected user(s) {π(1), . . . , π(i)} and those users that still remain in the pool of potentially selectable users. The process stops when the number of users in the active subset equals the number of transmit antennas NT or the list of remaining users is empty. B. MCS selection In this part, the most efficient MCS is selected for each user u ∈ U based on their corresponding precoding-channel gain γu [q]. The MCS selection works as follows. In step (II.a), a list Ω is initialized by ordering the MCSs in a decreasing order of throughput. In step (II.b) and depending on the pre(m) calculated switching thresholds SN RT h , the effective SNR corresponding to each selected user u ∈ U is evaluated for each MCS m ∈ Ω in decreasing throughput order to find the
out of which Nd = 52 are used to carry data. The base station is equipped with NT = 4 transmit antennas and the different MSs have all a single antenna architectures. The channel profiles used to generate the frequency-selective channel responses correspond to profiles B (residential, rather flat frequency response) and E (large office, very frequency selective) from channel models developed within the IEEE (m) (m) 802.11n standard [15]. The value of parameters α1 and α2 have been obtained from [13]. The target PER value has been fixed to P ER0 = 0.1 with an outage probability Pout = 0.05. For each SNR level, 10000 packets of length L = 1664 bits are transmitted. Eight different MCSs are available for transmission yielding bit rates between 6.5 Mbps (BPSK, 1/2) and 65 Mbps (64-QAM, 5/6). For all the results shown next, uniform power allocation among the selected users is assumed. Figure 2 compares the system throughput of the proposed MUS-FLA algorithm with that achieved with opportunistic multicarrier TDMA (MC-TDMA) scheme for different number of users over channel profile B. In opportunistic MCTDMA systems, the BS schedules the user experimenting the best channel realization who will be allocated all the spectrum and power resources. In this case, the multiple antennas at transmission are used to implement maximal ratio transmission. It can be observed that MC-TDMA’s throughput saturates to the rate provided by the highest MCS at an SNR around 10 dB. In contrast, the throughput for MUS-FLA does not reach a saturation point until an SNR=25 dB and it grows proportionally to NT , eventually reaching a throughput exceeding 250 Mbps. For both schemes, and thanks to the multiuser diversity, the more users in the pool the lower is the SNR required to achieve a given throughput. In Fig. 3 the
375
300 Channel profile E Channel profile B
Throughput (Mbps)
250
MUS FLA
200 150 100 50
Opportunistic MC TDMA
0 5
0
Fig. 3.
10
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SNR (dB)
20
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Throughput for different channel profiles. Nu = 10.
Throughput/Capacity
400
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Optimum MC MU MIMO FLA MUS FLA Opportunistic MC TDMA
scheme consists of two steps: on one hand, the MUS algorithm selects those users experimenting good channel realizations while satisfying orthogonality conditions that guarantee their spatial separability. On the other hand, a FLA strategy based on PER prediction is used to select the highest throughput transmission mode for each selected user that fulfills prescribed QoS guarantees in the form of an outage probability on the target PER. Results obtained for a modern WLAN setup have shown that the proposed method, in comparison to opportunistic MC-TDMA, leads to significantly higher throughputs. Remarkably, at high SNRs, the throughput increase reaches a factor given by the number of transmit antennas. Further work seeks to incorporate user fairness in the user selection while also explores the use of multiple antennas at the receivers as well as the application of more powerful coding schemes such as turbo codes or low-density parity check (LDPC) codes. ACKNOWLEDGEMENTS This work is supported in part by MEC and FEDER under project COSMOS (TEC2008-02422), Spain.
200
R EFERENCES
Capacity
100
0 5
Fig. 4.
Throughput
0
5
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15
SNR (dB)
20
25
30
Throughput/Capacity comparison. Channel profile B. Nu = 10.
system throughput achieved for MUS-FLA and opportunistic MC-TDMA is shown for different channel profiles when the number of users has been fixed to Nu = 10. Again, it can be appreciated that MUS-FLA outperforms the opportunistic MC-TDMA by a factor NT at large SNRs under different propagation environments. Noticeably, channel profile E leads to lower throughputs than profile B. This is due to its large frequency selectivity that complicates the task of finding NT near-orthogonal users. Finally, results in Fig. 4 measure how far MUS-FLA and opportunistic MC-TDMA are from capacity bounds. In this graph the theoretical capacity for each scheme is depicted in dashed lines. For completeness the capacity and throughput of MU-MIMO with optimum user selection (MC-MU-MIMO-FLA) is shown. Optimum user selection is implemented by exhaustively evaluating each possible user grouping and selecting the one leading to the highest capacity/throughput [7]. Given its large computational complexity it is only feasible for small user pools. Results show that there is still a gap between any of the practical schemes and the corresponding theoretical capacity. It is to be expected that use of more powerful coding/modulation schemes would result in a significant shrinkage of this gap. VI. C ONCLUSION This work has introduced a methodology to implement opportunistic multiuser MIMO-OFDM systems. The proposed
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