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Combined MMSE-SIC Multiuser Detection for STBC-OFDM Systems Xuan Nam TRAN†a) , Member, Anh Tuan LE† , Nonmember, and Tadashi FUJINO† , Member
SUMMARY In this letter, we propose a combined scheme of minimum mean square error (MMSE) detection and successive interference cancellation (SIC) for multiuser space-time block coded orthogonal frequency division multiplexing (STBC-OFDM) systems. With the same complexity order, the proposed scheme provides significant bit error rate (BER) performance improvement over the linear MMSE multiuser detector. key words: STBC, OFDM, multiuser detector, MMSE, SIC
1.
Introduction
Multiuser detection is a key technique to support broadband wireless multiuser communications. Among multiuser detection (MUD) techniques, the linear minimum mean square error (MMSE) is popular as it can provide relatively good performance at low cost of complexity. Recently, an MMSE multiuser detector for space-time block coded (STBC) orthogonal frequency division multiplexing (OFDM) has been proposed in [1]. However, as the MMSE detector is suboptimal in terms of minimizing bit error rate (BER), its BER performance deteriorates significantly as the number of users increases [1]. The non-linear maximum likelihood (ML) MUD outperforms MMSE-MUD in this case but requires excessive complexity, thus its implementation is limited. Recently, a combined scheme of MMSE-MUD and successive interference cancelation (SIC) was proposed as a compromise between the BER performance and computational complexity [2]. This combined MMSE-SIC technique was originated from multiuser detection in the code division multiple access (CDMA) systems, and recently developed in the vertical Bell-Labs layered space-time (VBLAST) system [2] for detecting signals from different transmit antennas in the context of spatial multiplexing. The main idea of the MMSE-SIC technique is to provide a feedback from the demodulation to the linear combining process as in a decision feedback equalizer and use iterative processing to reduce residual co-channel interference (CCI) at the outputs of the MMSE detector at each detection iteration. BER performance of the combined MMSE-SIC detector was reported to be significantly improved over the conventional MMSE detector at the same complexity order [2]. Manuscript received March 18, 2005. Manuscript revised October 10, 2005. † The authors are with Department of Information and Communication Engineering, The University of Electro-Communications, Chofu-shi, 182-8585 Japan. a) E-mail:
[email protected] DOI: 10.1093/ietcom/e89–b.5.1696
In this letter, aiming at improving the BER performance for the MMSE-MUD proposed in [1], we propose a combined MMSE-SIC multiuser detector for STBC-OFDM systems. Different from the previous MMSE-SIC detectors for spatial division multiplexing (SDM) systems [2], [3], where each user has only one transmit antenna, our proposed MMSE-SIC algorithm is applied for a multiuser STBC system in which two transmit antennas are equipped for each user. To solve this difference we propose detecting transmitted symbols from two transmit antennas of each user in one detection iteration. This means that the ordering and cancellation process are associated with two MMSE outputs and two channel vectors corresponding to each user. Simulation results show significantly improved BER performance over the linear MMSE detector in [1]. In the next part of the letter, we review the signal model and MMSE-MUD for STBC-OFDM in Sect. 2. The proposed combined MMSE-SIC detector is presented in Sect. 3. Simulation results are shown in Sect. 4, followed by the conclusion in Sect. 5 2.
MMSE-MUD for STBC-OFDM
2.1 Signal Model Consider an up-link STBC-OFDM system with Q users using Alamouti’s STBC-OFDM to transmit binary phase shift keying (BPSK) symbols X1(q) [k] and X2(q) [k] to the base station (BS) over their two antennas [1]. At BS, after discarding the cyclic prefix (CP) (assumed larger than the maximum channel delay spread) and performing FFT the demodulated signal in the frequency domain is given by [1] Ym,t [k] =
Q 2
(q) (q) S n,t [k]Hm,n [k] + Zm,t [k],
(1)
q=1 n=1 (q) where S n,t [k] represents the n-th output of the Alamouti’s space-time encoder [4] at time slot t; Zm,t [l] are the frequency-domain independent noise samples at antenna m and time slot t, modeled by complex Gaussian random variables with mean 0 and variance N0 per complex dimension. (q) (q) − j 2πkp K [k] = P−1 is the channel frequency reHm,n p=0 αm,n,p e sponse between the m-th receive antenna and the n-transmit (q) antenna of user q, where αm,n,p is the complex path gain assumed quasi-static and modeled using the Jakes’s fading model [5]; P is the maximum channel delay spread. We
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now apply the method presented in [1] to express the system equation (1) in vector form. We first define the following vectors T x(q) [k] X1(q) [k], X2(q) [k] , (2) T (q) (q) (q) hn(q) [k] H1,n [k], H2,n [k], . . . , H M,n [k] , (3) T yt [k] Y1,t [k], Y2,t [k], . . . , Y M,t [k] , (4) T zt [k] Z1,t [k], Z2,t [k], . . . , Z M,t [k] , (5) where (•)T denotes the transpose operator. Then by defining T y[k] yT1 [k], yH (6) 2 [k] , T z[k] zT1 [k], zH (7) 2 [k] , ⎤ ⎡ (q) ⎢⎢ h [k] h2(q) [k] ⎥⎥⎥⎥ 1 H(q) [k] ⎢⎢⎢⎣ (q)∗ (8) ⎥⎦ , h2 [k] −h1(q)∗ [k] T (9) x[k] x(1)T [k], x(2)T [k], . . . , x(Q)T [k] , (10) H[k] H(1) [k], H(2) [k], . . . , H(Q) [k] , we can express (1) in the vector format as [1] y = Hx + z.
(11)
Note that for simplicity we have ignored the common subcarrier index k and here (•)H denotes the Hermitian transpose operator. 2.2 MMSE-MUD Define the linear combining weight matrix used to decouple user’s transmitted signals x(q) as W W (1) , W (2) , . . . , W (Q) , (12) where W (q) w1(q) , w2(q) ∈ C2M×2 . Using the MMSE method, W is given by [1]
−1 W = HΛH H + N0 I2M HΛ, (13) where Λ = diag{Λ1 , Λ1 , . . . , ΛQ , } is the diagonal power matrix with Λq = ζq2 I2 ; Iκ is a κ-by-κ identity matrix; and ζq2 = E |X (q) [k]|2 is the transmit signal power of user q. Assume that the channel matrix H is known then upon obtaining W from (13), the decision statistics for each user are given via the linear combining (14) x˜ (q) = W (q)H y, (q) (q) T where x˜ (q) = X˜ 1 , X˜ 2 . These decision statistics are then sent to a decision device (demodulator) to make final decision as (15) xˆ (q) = sgn x˜ (q) = sgn W (q)H y , (q) (q) T where xˆ (q) Xˆ 1 , Xˆ 2 , sgn{•} denotes the signum function, and {•} represents the real-part operator. It is noted that the complexity order of the MMSE MUD is O(M 3 ).
3.
Proposed Combined MMSE-SIC MUD
In this section, we develop a combined MMSE-SIC multiuser detector for the Alamouti’s STBC-OFDM system based on the MMSE detector presented in the previous section and the V-BLAST algorithm proposed in [2]. The principle of the MMSE-SIC multiuser detector is to detect signal from each user in one iteration by nulling out CCI from other users using the combining weight matrix obtained from the MMSE detector. The detection order is decided based on the signal to noise ratio (SNR) or mean square error (MSE) computed for each user. Only user with the highest SNR or the minimum MSE is detected in each detection iteration. The detected signal is then fed back to the linear combining process and its contribution is canceled from the received signal in the next detection iteration. This combined MMSE-SIC detection algorithm is also referred to as nulling and cancellation with ordering in the V-BLAST system [2]. Using the MMSE-SIC algorithm, the signal to be detected in the next iteration is provided with larger diversity gain due to increased degree of freedom in the receive array. As a result, BER performance of the detector is significantly improved over the linear MMSE multiuser detector [2]. For STBC systems using the Alamouti’ STBC, as each user is equipped with two transmit antennas transmitting orthogonal signals, we propose detecting transmitted symbols from the two transmit antennas in one detection iteration. As a result, the cancellation process is associated with two outputs of the MMSE multiuser detector and two columns of the channel matrix H. The detection order in each iteration is decided by finding the minimum MSE given in [1] as
(q) (q)H (q) (16) MSE(q) ≈ MSE1 = ζq2 1 − H1 w1 , where MSE1(q) represents the MSE resulted from detecting the symbol X1(q) [k], and H1(q) denotes the first column of the channel matrix H(q) , i.e., the (2q − 1)-th column of H. The combined MMSE-SIC algorithm for the STBCOFDM system is given below with denoting the iteration index. Combined MMSE-SIC Algorithm 1) Initialization: set = Q 2) For = 1 to Q[] : • Calculate the combining weight matrix using (13):
−1 W [] = H[] Λ[] H[]H + N0 I2M H[] Λ[] • Upon obtaining W [] , compute the MSE for each user q ∈ Q[] using
(16) as: w1(q)[] MSE(q)[] = ζq2 1 − H(q)[]H 1 • Find the dominant user q[] with minimum MSE, i.e. q[] = arg min MSE(q)[] q[] ∈Q[]
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• Detect and demodulate the estimates of q[] using (15): xˆ (q)[] = sgn W (q)[]H y[] • Update the detector by removing the contribution of user q[] signal from the received signal y[] , i.e. y[+1] = y[] − H(q)[] xˆ (q)[] • Update the channel matrix H[] by removing the (2q[] − 1)-th and 2q[] -th columns. • Update the number of effective users for next iteration: Q[+1] = Q[] − 1.
noted before, the complexity order of the combined MMSESIC detector is the same as that of the MMSE detector, and is much smaller than O(22Q ) of the ML detector. Therefore, the combined MMSE-SIC detector can be regarded as a suitable multiuser detector for STBC-OFDM systems. Performance improvement of the combined MMSE-
3) End. Note that most complexity associated with the MMSESIC detector is that for computing the weigh matrix W. Thus the complexity order of the MMSE-SIC detector is also the same as that the MMSE detector, i.e., O(M 3 ). 4.
Simulation Results
We setup a simulation model similar to that in [1] with important parameters listed in Table 1. BER performance of the combined MMSE-SIC detector under the 2-path equipower channel with 2 receive antennas and 4 receive antennas are illustrated in Figs. 1(a) and (b), respectively. Two users are assumed for Fig. 1(a), and four for Fig. 1. All users are assumed to have the same transmit power normalized to one. For comparison BER performance of the MMSE and ML detection are also shown in the figures. As clearly shown in the two figures, the combined MMSE-SIC detector provides significantly improved BER over the linear MMSE detector, but still less than the ML detector. However, as Table 1
(a) The typical urban (TU) channel Fig. 2
(b) The hilly terrain (HT) channel
Channel impulse responses used for simulation [6].
Simulation parameters.
Parameter Channel bandwidth Number of sub-carriers Cyclic prefix length Doppler frequency Delay channel model Number of receive antennas
Value 1 MHz K = 256 C = 40 µs fD = 25 Hz 2-path equi-power channel TU and HT channel 2 and 4
Fig. 3 BER Performance of combined MMSE-SIC multiuser detectors using 3-path indoor channel models in Fig. 2, user 1 with the TU channel, user 2 with the HT channel, fD = 25 Hz.
(a) 2 users, 2 receive antennas. (b) 4 users, 4 receive antennas. Fig. 1 BER performance of combined MMSE-SIC: 2-path channel model, SIR=0 dB, fD = 25 Hz. Performance is shown for one user.
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SIC in a more practical multipath channel is shown in Fig. 3. The typical urban (TU) and hilly terrain (HT) channel [6] were used for simulation (see Fig. 2). User one is assigned with the TU channel impulse response, while user two with the HT channel. Large BER improvement is realized for both the users. User 2 exhibits a slightly better improved BER due to large energy obtained from multipaths in its CIR. 5.
Conclusion
In this letter, we have proposed a combined MMSE-SIC multiuser detector for STBC-OFDM systems. The proposed detector has the same complexity order while providing significant BER improvement over the linear MMSE multiuser detector in [1]. It is thus regarded as a suitable multiuser detector for STBC-OFDM systems.
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