Dynamic Rate-Adaptive MIMO Mode Switching Between Spatial Multiplexing and Diversity

In this article, we propose a dynamic multiple-input multiple-output (MIMO) mode switching scheme between spatial multiplexing and diversity modes, which also includes adaptive modulation. At each transmission, we select the modulation level and the MIMO mode that maximize the spectral efficiency while satisfying a given target bit error rate. The dynamic MIMO mode scheme considers instantaneous spectral efficiency whereas the conventional static scheme considers only the average SNR. As for adaptive modulation, a new method is proposed to compute the SNR thresholds for adaptive modulation in each MIMO mode, and it can avoid the computational difficulty of the conventional Lagrangian (optimal) method at high average SNR. To deal with the case where the rates of the two MIMO modes are the same, we also propose a new measure based on the BER exponent, which has lower computational complexity than a conventional measure. Numerical results show that the proposed dynamic mode switching improves over the conventional static mode switching in terms of average spectral efficiency. Introduction Today’s wireless communication systems demand high data rate and spectral efficiency with increased reliability. Multiple-input multiple-output (MIMO) systems have been popular techniques to achieve these goals because increased data rate is possible through spatial multiplexing scheme [1] or improved diversity order is possible through transmit diversity scheme (e.g., space-time block code, STBC) [2]. Other ways are link adaptation techniques, where transmission parameters such as modulation and coding are dynamically adapted to the varying channel condition [3]. A typical link adaptation technique is adaptive modulation in which an adequate modulation level is selected by means of the current signal-to-noise ratio (SNR). Recently, adaptive modulation schemes in conjunction with MIMO techniques have been investigated [4-11]. The prior study in the literature mainly tried to maximize the average spectral efficiency (ASE) for only one MIMO mode, either spatial multiplexing [8] or transmit diversity [5-7,11]. In [12], the mode switching between diversity and multiplexing was first proposed. But the authors focused on the situation where both MIMO *Correspondence: [email protected] School of Electrical Engineering and Computer Science, Seoul National University, Seoul, Korea modes have equal spectral efficiency without considering adaptive modulation, so that they showed the result that spatial multiplexing is preferred in low SNR region. The mode switching scheme combined with adaptive modulation was proposed in [9,10], but the analysis was focused on the static mode switching which depends only on the average SNR. In this article, we propose a dynamic MIMO mode switching scheme which considers instantaneous channel condition in conjunction with rate adaptation. Although the adaptive modulation part is based on the existing methods [5,7-9,11], we compare the performance of the existing techniques, and also propose a sub-optimal method to obtain the SNR thresholds for the average BER constraint. Its complexity is lower than that of the optimal method using a Lagrange multiplier, but the performance degradation is negligible. The proposed mode switching scheme is based on the instantaneous spectral efficiency (ISE). In case the ISE’s of the two modes are equal, an additional rule is necessary for mode selection. Although the Demmel condition number proposed in [12] can be a choice, we propose a new method which has lower complexity than the Demmel condition number without performance loss. This article is organized as follows. In the section of System overview, we outline the system and the channel model as well as the structure of the considered © 2012 Kim and Lee; licensee Springer. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Kim and Lee EURASIP Journal onWireless Communications and Networking 2012, 2012:238 Page 2 of 12 http://jwcn.eurasipjournals.com/content/2012/1/238 MIMO mode switching system. The dynamic MIMO mode switching scheme combined with adaptive modulation is then proposed in the section of rate-adaptive MIMO mode switching. In the section of Simulation results, we compare the performance of the proposed algorithm with that of the existing methods. Since numerical methods are necessary in order to get the SNR thresholds for the average BER constraint, we shows detailed results in this section. Finally, conclusions are drawn in the last section. System overview We consider a MIMO system with M transmit antennas and N receive antennas. The block diagram of the proposed system is shown in Figure 1. The system consists of a transmitter with a switch between a multiplexing and a diversity modulator, a receiver unit with the corresponding pair of receivers, a modulation level and mode selector, and a low rate feedback path. At the receiver side, the modulation level and the MIMO mode are selected according to the current channel condition. The information about the selected modulation level and the MIMO mode is sent to the transmitter through the feedback path. The transmitter then switches the MIMO mode with the modulation level based on the feedback information. Suppose that the N × M flat fading channel matrix H has i.i.d. complex Gaussian random entries. The (i, j)th entry [H]i,j = hij is distributed as CN (0, 1)a. The channel is assumed to be quasi-static (channel coefficients do not change during one time interval, and change independently in the next interval). The input-output relation for the MIMO channel is given by y = √ Es M Hs+ n, (1) where y is theN×1 received signal vector, Es is the average energy per symbol, s is the transmitted signal vector with energyM, i.e., E[ sHs]= Mb, and n is an N × 1 i.i.d. complex additive white Gaussian noise (AWGN) vector with the distribution CN (0,N0IN ). Let ρ be the average SNR at the receiver, which is given by ρ = Es N0 . We have omitted the time index in (1) for convenience.We also assume perfect channel knowledge at the receiver and zero feedback delay. Rate-adaptive MIMOmode switching In this article, we propose a new rate-adaptive MIMO mode switching algorithm. The goal is to maximize the ASE while satisfying a given bit error ratio constraint. The proposed algorithm can be summarized by the following three steps. 1. Calculate the post-processing SNR in each MIMO mode. 2. Decide the modulation order in each MIMOmode. 3. Decide one MIMO mode based on a given selection rule. For analysis, we consider a linear receiver for the spatial multiplexing mode, and orthogonal space-time block codes (OSTBC) for the diversity mode. In Step 2, we analyze several adaptive modulation techniques subject to an instantaneous BER constraint as well as an average one. In Step 3, we propose the mode selection rule based on the ISE as well as the rule which can be applied to the case when both of the two MIMO modes have the same data rate. Post-processing SNR calculation (Step 1) The post-processing SNR at the receiver is calculated separately in each MIMO mode with a given detection algorithm. At first, in the spatial multiplexing mode, the post-processing SNR of the mth (m = 1, 2, . . . , M) output data stream of the zero forcing (ZF) receiver, denoted as γm,ZF, is given by ([13], Eq. (7.43)) γm,ZF = ρ M 1 [( HHH )−1] m,m , (2) and the SNR of the minimummean-square error (MMSE) receiver, denoted as γm,MMSE, is given by ([13], Eq. (7.49)) Figure 1 Block diagram of MIMOmode switching scheme combined with adaptive modulation. Kim and Lee EURASIP Journal onWireless Communications and Networking 2012, 2012:238 Page 3 of 12 http://jwcn.eurasipjournals.com/content/2012/1/238 γm,MMSE = 1 [( ρ MHH+ IM )−1] m,m − 1. (3) The post-processing SNR of the OSTBC system, denoted as γOSTBC, is given by γOSTBC = ρ ζM ∥∥H∥∥2F = ρ ζM N ∑ i=1 M ∑ j=1 ∣∣hi,j∣∣2, (4) where ζ is the code rate of the OSTBC. Decision of the modulation order (Step 2) Using the post-processing SNR obtained in Step 1, we can choose an appropriate modulation order for each MIMO mode which enhances spectral efficiency without exceeding a given target BER at the receiver. Since adaptive modulation for one MIMO mode with a given BER constraint has been studied in [4-8,11], we take a similar approach of the literature. For analysis, we consider a discrete rate adaptive system for which the constellations are restricted to a finite setM = {M0, M1, . . . , ML} with Gray coded quadrature amplitude modulation (QAM), where Ml denotes the constellation size and Ml−1 < Ml, ∀l. The SNR range is subdivided into L + 1 bins bounded by the switching threshold θl (l = 0, 1, . . . , L+ 1) where θ0 = 0. Let γ be the post-processing SNR. The receiver chooses the constellation Ml whenever θl ≤ γ < θl+1. If γ < θ1, data transmission is suspended for the corresponding channel since the respective BER constraint cannot be satisfied. Moreover, the maximum SNR threshold is set to infinity, i.e., θL+1 = ∞. SNR thresholds for instantaneous BER constraint An easy way to set the switching thresholds θl ’s is to use the instantaneous BER (I-BER). In this approach, the BER of every reception has to be less than or equal to the target BER δ0. In order to meet the constraint, the BER for a QAM in AWGN channels can be used. Although the exact BER expressions forM-QAMare shown in [14], they are not easily inverted with respect to the SNR, so that a numerical method is necessary. Instead, in the adaptive modulation literature [5-8], an exponential function form is used, which is given by Pe(γ ,Ml) ≈ al exp(−clγ ), (5) where al = 0.2 and cl is a constellation specific constant defined as [4] cl = { 6 5·2l−4 for rectangular QAM (odd l) 3 2(2l−1) for square QAM (even l) . (6) If we want a more accurate form than the above approximation, we can find the modulation specific constants al and cl numerically using curve-fitting methods [11]. Table 1 shows those values of M-QAM’s which are used Table 1 Constellation specific constants for BER approximation in AWGN channels [11] Modulation BPSK QPSK 16-QAM 64-QAM al 0.1978 0.1853 0.1613 0.1351 cl 1.0923 0.5397 0.1110 0.0270 in [11]. Inverting (5) with respect to γ , the switching threshold is determined as θl = 1 cl ln ( al δ0 ) . (7) Although it is simple, I-BER approach keeps the instantaneous BER at all time instants below the target BER δ0. This is so conservative that the average BER (A-BER) is lower than δ0. In order to make the A-BER be equal to δ0, SNR thresholds should be lowered. Therefore, there is potential for improving the ASE by adjusting the switching threshold of each modulation. SNR thresholds for average BER constraint Generally, the ASE η for one channel use is given by