Heterogenous Information Aided Semiblind Group MUD ... - IEEE Xplore

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Abstract—This paper presents an effective semiblind group multiuser detector (MUD) for uplink multiple-input multiple- output (MIMO) multi-carrier code division ...
Heterogenous Information Aided Semiblind Group MUD for MIMO MC-CDMA Systems Hoang-Yang Lu

Wen-Hsien Fang, Yie-Tarng Chen and Kuo-Liang Yeh

Dept. of Computer Science and Information Engineering Lee-Ming Institute of Technology Taipei, Taiwan, R.O.C. Email: [email protected]

Department of Electronic Engineering National Taiwan University of Science and Technology Taipei, Taiwan, R.O.C. Email: whf, [email protected]

Abstract— This paper presents an effective semiblind group multiuser detector (MUD) for uplink multiple-input multipleoutput (MIMO) multi-carrier code division multiple access (MCCDMA) systems. The MUD considered is a two-stage linear constrained minimum variance (LCMV) detector which uses heterogenous information (both hard and soft) to enhance the interference cancellation capability. The first stage LCMV detector produces a tentative detection output, while at the second stage a bank of soft LCMV detectors successively refine the estimated interference group by group with the assistance of the heterogenous information in the symbol detection process. In addition, to avoid the annoying ordering mechanism, a channelstrength criterion is employed to order the groups at the second stage. Conducted simulations show that the proposed MUD can drastically enhance the performance compared with previous works, especially when the hardware cost is at a premium.

I. INTRODUCTION With high spectral efficiency and data rate, MIMO CDMA systems have been a great promise for the next generation wireless communication systems [1]-[4]. However, it is wellknow that the performance of CDMA systems degrade substantially in interference-rich scenarios. To mitigate this setback, various MUDs, which make use of the channel structure to alleviate the interferences, have been addressed. For example, [5] proposed the V-BLAST (vertical Bell Laboratories layered space-time) [5]. Despite its effectiveness, it, however, suffers the long latency and error flooring effect [6]. Also, a semiblind group MUD was considered in [7], which used the subspace method to effectively combat both the multiple access interference (MAI) and co-channel interference (CCI). Several two-stage MUDs were also suggested to attain better QoS. For example, a hybrid minimum mean squared error (MMSE) decision feedback interference cancellation was considered in [8], and [9] proposed a successive cancellation scheme with antenna diversity to maximize the signal-to-noise-plus interference ratio (SINR). All of them, however, are designed for some special disturbances such as the MAI. Recently, [3] proposed an effective group-based MIMO CDMA system, which assign a unique spreading sequence to all users in the same group. The system considered in [3] possesses several attractive features such as the reduction

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of the resource management overhead and of the demand for feedback channel bandwidth. Unfortunately, in addition to MAI [10], the system encounters multiple stream interference (MSI) [4], invoked by the transmitted signals in the same group. To alleviate the interference, a V-BLAST based MUD, referred to as the LAST (layered space-time), has been proposed in [3]. Such a V-BLAST approach, however, suffered the same setbacks addressed above. Other aforementioned MUDs are also not applicable due to the presence of the MSI. To resolve the dilemma, this paper proposes a heterogenous information aided semiblind group MUD for the MIMO MCCDMA in [3]. The new MUD is a two-stage LCMV detector [11], where the LCMV rather than the MMSE criterion is adopted as the information of some users may be unknown. The proposed MUD proceeds as follows. First, a tentative estimation of the transmitted symbols is conducted in parallel at the first-stage LCMV detector. At the second stage, the simple channel-strength criterion in [12] is first utilized to order the groups and followed by a bank of soft LCMV detectors. These soft LCMV detectors proceed the symbol detection group by group in a power descending order, in which every LCMV detector removes the estimated interferences and then detects the symbols in the same group in parallel. It is noteworthy that the interferences removed in the detection process include both the estimated soft interferences in the previous groups and the estimated hard interferences in the succeeding groups. Note that it has been observed in [13], [14] that the soft-information approach can generally result in more precise estimation of the interferences. Consequently, as the detection proceeds progressively, more faithful interferences can be reproduced to render more thorough interference cancellation. In addition, since the detection proceeds group-by-group instead of layer-by-layer, the latency is substantially reduced. Conducted simulation results show that the proposed detector can drastically enhance performance compared with previous works, especially when the hardware cost is at a premium. II. DATA MODEL Consider a quasi-synchronous uplink MIMO MC-CDMA system, where there are K transmit antennas at the transmitter, which are divided into G groups so that each group has Mt

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transmit antennas, i.e. K = G × Mt . Each group can be regarded as a user with Mt transmit antennas. Also, assume that each group is assigned a unique, length-N PN signature (g) (g) (g) sequence, s(g) = [s1 , s2 , · · · , sN ]T , 1 ≤ g ≤ G, where T (·) denotes matrix transposition. For simplicity, assume that the number of subcarriers employed is also N . Denote G = ˜ G, ˘ where G ˜ and G ˘ are the numbers of groups in the intraG+ cell and inter-cell, respectively. Suppose that the receiver has only the knowledge of the signature sequences in the intra-cell. After removing the cyclic prefix and performing the N -point DFT, the received discrete signal in a symbol duration at the jth receive antenna can be described as [3], [15] rj =

Mt G   g=1 i=1

(g)

(g) (g)

Hji s(g) ai bi

+ nj =

G 

(g)

Qj A(g) b(g) + nj

g=1

(1) where the transmitted symbols are assumed to be i.i.d. and (g) (g) BPSK modulated, Hji = diag(FL hji ), 1 ≤ i ≤ Mt , 1 ≤ g ≤ G, is the frequency response of the channel corresponding to the ith transmitted beam of the gth group at the jth receive antenna, in which FL is constituted by the first L columns (g) of the N × N DFT kernel matrix, and the channel hji = (g) (g) (g) [hji,1 , hji,2 , · · · , hji,L ]T , corresponding to the ith transmitted beam of the gth group at the jth receive antenna, is assumed to (g) (g) (g) be known or perfectly estimated. b(g) = [b1 , b2 , · · · , bMt ]T (g) (g) (g) and A(g) = diag{a1 , a2 , · · · , aMt } are the transmitted symbol vector and the received amplitude of the gth group, rescpetively. nj is the additive white Gaussian noise with zero mean and covariance matrix σ 2 IN , where IN is the N × N (g) (g) (g) (g) · · · qjMt ], where identity matrix. Qj = [qj1 qj2 (g) (g) qji = Hji s(g) , 1 ≤ i ≤ Mt , is referred to as the effective signature vector corresponding to the ith transmitted beam of the gth group at the jth receive antenna. By staking the received signals of the Mr receive antennas, the total received signal can be expressed as ˜+Q ˘+n ˜A ˜b ˘A ˘b r=Q

(2)

˜ ˜ = [Q(1) · · · Q(G) ˜ = ], A where r = [rT1 · · · rTMr ]T . Q T T ˜ ˜ (1) (1) T (G) (G) ˜ = [b ···b ] are the diag{A · · · A }, and b effective signature matrix, received amplitude matrix, and transmitted symbol vector for the groups in the intra-cell, (g)T (g)T ˘ = respectively, in which Q(g) = [Q1 · · · QMr ]T . Q ˜ ˜ (G+1) (G) (G+1) (G) ˘ = ˘ · · · Q ], A = diag{A · · · A }, and b [Q ˜ (G+1) (G)T T [b ···b ] are the corresponding matrices in the inter-cell, respectively.

III. PROPOSED SOFT INFORMATION ASSISTED SCHEME To simultaneously combat the MAI, MSI, and CCI in MIMO MC-CDMA systems, in this section we consider a new semiblind group MUD, as depicted in Fig. 1, which refines the estimated interferences group by group and then remove them from the received signal to mitigate the interference disturbance. The proposed MUD is a two-stage LCMV

Fig. 1.

Block diagram of the proposed MUD

detector [11], in which the first stage is a preprocessing which provides a tentative (hard) decision of the transmitted symbols in parallel. To achieve this, the detector for the ith transmitted (g) symbol of the gth group, wi , is determined by (g)H

min wi (g) wi

(g)

Rwi

subject to

˜ H w(g) = e(g) Q i i

(3)

˜ where R = E{rrH } is the for 1 ≤ i ≤ Mt , 1 ≤ g ≤ G, covariance matrix of the received signal, in which E{·} is an ˜ expectation operator, (·)H denotes the Hermitian operation, Q (g) ˜ denotes the constraint matrix, and ei is a GMt × 1 vector with 1 on the ((g − 1) × Mt + i)th entry and zeros elsewhere. To solve (3), we employ the Lagrange multiplier and minimize the Lagrangian (g)

(g)H

J(wi ) = (wi

˜ Hw Rwi ) + λH (Q i (g)

(g)

(g)

(g)

− ei )

(4)

(g)

Setting the gradient of J(wi ) with respect to wi equal to zero and after some manipulations, the optimum solution of (g) wi can be readily shown to be (g)

wi

˜ (5) ˜ Q ˜ H R−1 Q) ˜ −1 e(g) , 1 ≤ i ≤ Mt , 1 ≤ g ≤ G = R−1 Q( i

The tentative (hard) detected ith symbol of the gth group is H

¯b(g) = sgn{Re{(w(g) r)}, 1 ≤ i ≤ Mt , 1 ≤ g ≤ G ˜ i i

(6)

where sgn(·) is the sigmoid function and Re{α} denotes the real part of α. Note that by using the hard detection addressed above and the corresponding effective signature vectors, the transmitted signals of the intra-cell can be reconstructed, with which, the transmitted signals in each group can be determined by removing those induced by other groups of signals. However, the symbols estimated above are rather rough, which inevitably result in imperfect interference cancellation and thus degrade the system performance. To alleviate this setback, we conside to use a set of soft LCMV detectors, which are with the assistance of heterogenous information, successively refine the estimation of the

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interference group by group in the second stage. First, to avoid the annoying ordering problem, we employ the simple channel-strength criterion [12] to order the groups, which is given by   ˜ (7) arg max E ||Q(g) A(g) ||2F , 1 ≤ g ≤ G ˜ g∈{1···G}

where Q(g) is the N Mr ×Mt effective signature matrix of the gth group in the intra-cell and ||·||F is the Frobenius norm [16]. Without loss of generality, assume that the detection order of the groups in the intra-cell, based on the channel-strength, is ˜ 1, 2, · · · , G. Next, assume that the signal from the 1st to the (g − 1)th group of the intra-cell have been estimated, then to estimate the transmitted signals of the gth group of the intra-cell, we estimate the interferences by using the soft-detection of the signal from the 1st to the (g − 1)th group and the ˜ hard- detection of these from the (g + 1)th group to the G group, where the hard- and the soft-detection outputs have been determined in the first-stage LCMV detector and the second-stage soft LCMV detectors, respectively. As such, the estimated signal of the gth group in the intra-cell can be expressed as g−1 

r(g) = r −

˜ (m) − Q(m) A(m) b

m=1

G 

¯ (l) Q(l) A(l) b

(8)

l=g+1

where r(g) is the estimate of the transmitted signal for the gth ˜ (m) = [˜b(m) · · · ˜b(m) ]T and b ¯ (l) = group of the intra-cell, and b 1 Mt (l) (l) T [¯b1 · · · ¯bMt ] are the soft-detection outputs of the mth group and the hard-detection outputs of the lth group, respectively. Therefore, the soft LCMV detector for the ith symbol of the (g) ˜ i , can be determined by gth group, w (g)H

˜i min w (g)

˜i w

(g)

˜i R(g) w

subject to

H

(g)

˜i Q(g) w

˜i =e

(9)

˜ where R(g) = E{r(g) r(g) H } for 1 ≤ i ≤ Mt , 1 ≤ g ≤ G, denotes the covariance matrix of r(g) , the N Mr × Mt constraint matrix Q(g) is the effective signature matrix of the gth ˜i is Mt × 1 vector with 1 on the ith entry and group, and e zeros elsewhere. Similar as (4) and (5), setting the gradients (g) ˜ i equal to zero yields of (9) with respect to w (g)

˜i w

−1

H

−1

˜i = R(g) Q(g) (Q(g) R(g) Q(g) )−1 e

(10)

Thereafter, the output of the detector for the ith symbol of the gth group is given by (g)

z˜i

(g)H (g)

˜i =w

r

˜ , 1 ≤ i ≤ Mt , 1 ≤ g ≤ G

(11)

If we assume that the output signal is approximately Gaussian (g) (g)2 [13], the equivalent strength m ˜ i and the variance σ ˜i of the noise, after some manipulations, can be expressed, respectively, as (g)

m ˜i and

2

(g) σ ˜i

= =

(g) (g)

(g)H

˜i E{˜ z i bi } = w H

(g) ˜i var{w

n} = σ

2

(g)

qi

(g) ˜ i ||2 ||w

(12) (13)

(g)

where qi , the ith column of Q(g) , is the effective signature vector of the ith symbol of the gth group. Then, the corresponding soft detection output can be expressed as (g)

(g)

(g)

2˜ z m zi |bi = +1) ˜ ˜ (g) ) = log p(˜ = i (g)2i λ(b i (g) p(˜ zi |bi = −1) σ ˜i

(14)

˜ Then, the soft estimated symbol for i = 1 · · · Mt , g = 1 · · · G. ˜b(g) = E{b(g) } = tanh( 1 λ(b ˜ (g) )), i = 1 · · · Mt , g = 1 · · · G ˜ i i i 2 [13] and can be used to construct the new soft estimation of the transmitted signal for the ith transmitted symbol of the gth (g) group. Finally, taking the soft estimated symbol ˜bi into the sigmoid function attains the estimate of the ith transmitted symbol of the gth group. It is noteworthy that as detection (g) proceeds, the number of soft estimated symbols, ˜bi , i = 1 · · · Mt , grow, while those of the hard estimated symbols, ¯b(g) , i = 1 · · · Mt , diminish, as shown in (8). The latter i are obtained by the LCMV in the first-stage and is thus less accurate, while the former are determined by the soft LCMV detectors in the second stage and is more accurate. As such, the estimated interferences are refined group by group so that they can be more thoroughly removed. As a whole, the proposed MUD consists of the following two stages: (g) Stage 1 (Preprocessing): Compute the LCMV detecor wi by (5) and (6), and determine the tentative (hard) detection ¯b(g) , i = 1 · · · Mt , g = 1 · · · G, ˜ in parallel, respectively. i Stage 2: Order the detection groups by (7). Next, repeat (8) and (10)-(14) to conduct the soft LCMV detectors to estimate (g) ˜ the soft symbols ˜bi , i = 1 · · · Mt from g = 1 to g = G. IV. EXPERIMENTAL RESULTS AND DISCUSSIONS Some simulations are conducted in this section to assess the proposed MUD. Assume that each transmit antenna simultaneously sends i.i.d. BPSK modulated symbols in frequency selective channels and the number of resolvable paths of the channel for each user, L, is 3. The power profiles for the group in the intra-cell and inter-cell are 1 and 0.2, respectively. i.e. 2 Mt (g)2 ˜ and Mt a(g) = 0.2, 1 ≤ = 1, 1 ≤ g ≤ G i=1 ai i=1 i ˘ Also, assume that the received amplitudes for the g ≤ G. transmitted signals in the same group are all equal, which can be achieved by the power control schemes. Three MUDs: the LAST [3], the group blind MUD [7], and the proposed one , are carried out for comparisons in terms of the average bit error rate (BER) performance. Example 1 First, we investigate two different scenarios. The first one is with 5 groups in the intra-cell and 1 group in the inter-cell, and the other is with 3 groups in both of the intra-cell and intercell. The number of antenna elements deployed at the receiver of the base station, Mr , is 6, the length of the PN signature sequence, N, is 12, and the number of the transmitted symbols, Mt , for each group is 2. The BER performance versus SNR based on the aforementioned three detectors are as shown in

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Example 2 This example intends to illustrate the effect of the receive antenna gain. Consider the same scenario as above i.e. 5 groups in the intr-cell and 1 group in the inter-cell, but Mr =5 and 7. The BER performance is as shown in Fig. 6. From Fig. 6, we can note that increasing the number of the receive antennas can enhance the performance owing to the antenna gain. As Example 1, the proposed MUD still outperforms the other two. V. CONCLUSIONS In this paper, a new heterogenous information aided semiblind group MUD is addressed for the MIMO CDMA systems in [3]. The MUD considered consists of two stages of LCMV detectors. At the first stage, based on the LCMV metric, a tentative (hard) estimation of the transmitted symbols are conducted in parallel and then forwarded to the next stage to refine

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Fig. 2. We can observe from Fig. 2 that the proposed MUD outperforms the other two detectors. This is due to the fact that the LAST in [3] is a V-BLAST based MUD and thus is sensitive to the channel estimation errors. Therefore, with the disturbance of the unknown MAI, MSI, and CCI, the LAST inevitably degrades significantly in both scenarios and exhibits the error flooring effect. The group blind MUD in [7] is also inferior, especially in the second scenario when there are more unknown interferences, which include the MSI of the intracell and the inter-cell. In contrast, with the assistance of the heterogenous information, the proposed MUD can effectively combat all of the MAI, MSI, and CCI to attain significant performance gain, even when half of the signature of the transmitted signals are unknown. Next, to assess the MAI effect, we consider the same scenarios as the above except that the number of groups in the intra-cell is increased by one, as shown in Fig. 3. We can observe from Fig. 3 that the performance of the proposed MUD is almost the same as those in Fig. 2, whereas the other two detectors degrade substantially. This implies that the proposed scheme is more effective in the alleviation of the MAI than the other two detectors. Furthermore, to investigate the CCI effect, we consider the same scenarios except that the number of groups in the inter-cell is increased by one, as shown in Fig. 4. We can observe from Fig. 4 that the perform of all these three detectors degrade compared to that in Fig. 2, but the proposed MUD still outperforms the other two, which implies that the proposed MUD can substantially suppress the disturbance of the CCI. Finally, to assess the MSI effect, we again consider the same scenario as above, except that the number of transmitted symbols of each group, is increased by one, as shown in Fig. 5. We can see from Fig. 5 that the proposed MUD outperforms the other two when SNR ≥ 2 d.B., which implies that it can mitigate the MSI more effectively than the other two. Also, it is interesting to note from Fig.5 that in high-SNR scenarios such as 8. d.B., the proposed MUDs with smaller numbers of groups in the intra-cell can attain better performance.

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the estimation of interference. A heterogenous information approach is then adopted at the second stage to refine the estimation of interferences group by group. The symbols are then detected based on a set of soft LCMV detectors. Furnished simulations show that the proposed MUD outperforms previous works, especially for interference-exuberant scenarios or when the hardware cost is at a premium. Acknowledgement This work was supported by National Science Council of R.O.C. under contract NSC 95-2221-E-011-024 and NSC 952218-E-011-008. R EFERENCES [1] V. K. Garg, IS-95 and cdma 2000, Prentice Hall, Upper Saddle River, NJ, 2000. [2] P. Rao and V. K. Prabhu, “A successive interference cancellation multiuser detector for MIMO CDMA systems,” in Proc. IEEE VTC, pp.1075-1079, 2003.

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