Adaptive Grouping-Modulation Aided Transceiver Design for High-Order MIMO Systems

Transcription

1 013 8th International Conference on Communications and Networking in China (CHINACOM) Adaptive Grouping-ulation Aided Transceiver Design for High-Order MIMO Systems Jie Xiao, Pinyi Ren, Qinghe Du, and Li Sun Department of Information and Communications Engineering Xi an Jiaotong University, Xi an, Shaanxi , China {pyren, duqinghe, Abstract Recently, high-order Multi-Input Multi-Output (MI- MO) systems with tens of antennas and large constellation have attracted a great deal of research attention as the data rate and required spectral efficiency drastically increase. One of the major challenges for such systems is the design of low-complexity detector. In this paper, we propose an adaptive groupingmodulation aided transceiver design (AGM-TD) for high-order MIMO systems. By adopting adaptive grouping-modulation at the transmitter, AGM-TD algorithm divides the transmit antennas with different SNR level into two groups employing different modulation order. At the receiver end, two sub-mimo systems associated with the two groups perform independent detection by applying orthogonal grouping. Moreover, in order to gain better bit error rate () performance with an affordable complexity, an adaptive detector selection scheme for each sub-mimo system is applied. Simulation evaluations demonstrate that the proposed algorithm can obtain 3dB performance gain when targeting at as compared to the existing orthogonal grouping based detection algorithm (OGNO). Index Terms high order MIMO, adaptive groupingmodulation, orthogonal grouping, adaptive detector selection I. INTRODUCTION The equipment of multi-antennas at both the transmitter and receiver is a critical technology in modern wireless communication systems and is termed as multi-input multi-output (MIMO) systems. The great potential of MIMO systems lies in the parallel transmission of data streams without cost of extra spectrum resource [1] []. Recently, as the urgent requirement on the increasing of data rate and spectral efficiency, high order MIMO systems which are equipped with tens of antennas have been researched [3]. For example, evolution of next generation IEEE 80.11ac, which aims to realize multi-gigabit transmission rate and very high throughput, now takes antenna equipment into consideration [4]. Such high order MIMO systems can be applied on the large/medium mobile devices. Moreover, the devices such as top box and laptop at the indoor environment can be also e- quipped with such systems to fulfill some special applications, e.g. HDTV [5]. However, the main bottleneck of high order MIMO systems is the high complexity consumption. The detectors for high order MIMO systems are gradually developed, which can approach a good tradeoff between The research work reported in this paper is supported by the National Natural Science Foundation of China under Grant No , the National Science and Technology Major Project under Grant No. 01ZX , the Specialized Research Fund for the Doctoral Program of Higher Education under Grant No and the Project on the Integration of Production, Education and Research, Guangdong Province and Ministry of Education of China under Grant No. 011B complexity and bit error rate () [6] [7] [8]. The likelihood ascent search (LAS) algorithm which is inspired from the Hopfield neural network (HNN) searches a better signal vector within the neighborhood vectors collection of the current solution and is superior in the low complexity [9] [10]. However, the near optimal performance of LAS algorithm can be achieved only when equipped with a lot of antennas. Several grouping detection algorithms for high order MIMO systems have also been proposed to reduce the complexity. The orthogonal grouping based detection algorithm (OGNO) proposed in [11] divides the original MIMO system into certain number of low-dimension sub-systems which execute independent QR decomposition based M-algorithm (QRD-M) detection. However, the streams belonging to one group which is generated in [11] have no common character, e.g. the SNR level which can be exploited to achieve further performance improvement. Motivated by the potential of OGNO algorithm, an adaptive grouping-modulation aided transceiver design (AGM-TD) is proposed in our paper to improve the system performance at an affordable complexity. First, the transmitted streams are divided into two groups with different modulation order according to their post-detection signal-to-noise ratio (SNR). Second, the original MIMO system is separated into two sub- MIMO systems which are associated to different stream groups by exploiting orthogonal grouping. Third, perform adaptive detector selection scheme to flexibly adjust the detector for each sub-system according to the modulation order and the number of antennas. Specially, QRD-M is employed to both sub-systems when the the antenna number is less than a threshold N. With more antennas, in order to avoid the further increasing of complexity, a hybrid detection scheme is employed. That is, QRD-M detector is still applied in the sub-system with high order modulation, but the detector for the sub-system with low order modulation is changed as LAS. Finally, merge the detection vectors of different groups into the final solution. The rest of this paper is organized as follows: the system model is introduced in Section II. The proposed AGM-TD scheme is present in Section III. In Section IV, the performance analysis is given. The simulation results are described in Section V. Finally, the concluding remarks are present in Section VI. II. SYSTEM MODEL Consider a spatial multiplexing MIMO system with N t transmit antennas and N r receive antennas in Fig. 1. Specifically, we assume that N r = N t = N. At the transmitter, IEEE

2 S/P ulation ulation ulation ulation s 1 s s 3 s N H y 1 y y 3 y N Orthogonal grouping Detector I Detector II Smallest SNR value of each antenna Largest Orthogonal Grouping QRD-M LAS QRD-M LAS Calculation of SNR value for each stream Perfect channel estimation Fig.. Structure of the proposed AGM-TD scheme Fig. 1. System model the data bits are first divided into N parallel streams by de-multiplexing. Before signal modulation, the selection of modulation order for each stream is carried out by calculating its post-detection SNR, which results in two groups of streams with different modulation. Specifically, the stream whose SNR value is relatively small adopts low modulation order Q 1 and the stream whose SNR value is large adopts high modulation order Q. It is also worth noting that the perfect channel estimation is assumed and feedback to the transmitter. Then N 1 symbol vector s which is generated by signal modulation is transmitted through the Rayleigh channel H at a time period. Mixing with the Gaussian white noise, the received vector y can be expressed by y = Hs + n, (1) where s is the signal vector in which the entries are modulated from two different constellation sets, N 1 vector n denotes complex Gaussian noise with E [ nn H] = σni, H denotes N N channel matrix in which the elements are independent and identically distributed. It is worth noting that the set of M-QAM constellation is denoted as Ω = { ± 1 a ± j 1 a, ± 3 a ± j 3 a,, ± M 1 a ± j M 1 a to ensure unit transmitted power at each antenna, where a = 6/ (M 1). At the receiver, in order to execute independent detection for two groups of streams, orthogonal grouping is adopted to generate two sub-mimo systems. And a suitable detector can be selected adaptively to improve the performance according to the characteristic of each sub-system. III. ADAPTIVE GROUPING-MODULATION AIDED TRANSCEIVER DESIGN FOR HIGH-ORDER MIMO SYSTEMS As mentioned in Section I, the potential of high order MIMO systems is the drastically increasing of data rate and spectral efficiency, which will bring a great challenge on the design of low-complexity detector. To deal with this problem, OGNO algorithm is proposed in [11] to divide original MIMO system into certain number of low-dimension sub-systems which execute independent QRD-M detection by adopting orthogonal grouping. However, the streams belonging to one sub-system have no common character, e.g. the SNR level which can be exploited to achieve further performance improvement. Motivated by the potential of OGNO algorithm, an adaptive grouping-modulation aided transceiver design (AGM- TD) is proposed in our paper. At the transmitter, considering } the difference of SNR level, the adaptive grouping-modulation is adopted to realize the regulation of the modulation order for each stream. At the receiver end, two sub-mimo systems associated with the two groups perform independent detection by applying orthogonal grouping. Moreover, in order to gain better bit error rate () performance with an affordable complexity, an adaptive detector selection scheme for each sub-mimo system is applied. The structure of the proposed AGM-TD scheme is illustrated in Fig., which involves the design both at the transmitter and the receiver end. Therefore, the algorithm description naturally consists of two parts. A. Adaptive Grouping-ulation at the Transmitter With equal power assigned to each transmit antenna, the aim of adaptive grouping-modulation at the transmitter is to regulate the modulation order for each data stream according to its SNR, which is shown as the left part of Fig.. First, SNR value of each stream is calculated using the perfect channel estimation which is feedback to the transmitter. According to [1], the calculation of SNR for the ith stream can be written as SNR i = E s σ n w i i =1,,, N, () where E s represents the signal energy and W i stands for the ith row of the ZF weight matrix in W = ( H H H ) 1 H H. (3) Then sort the SNR value from the smallest to the largest with their antenna indexes. Set the SNR value which is located at the (N/)th of the sorting result to be the threshold for deciding the modulation order. Then the stream whose SNR is smaller than the threshold or equal to will adopt Q 1 modulation order and the stream whose SNR is larger than the threshold will employ Q modulation order. So the modulation order for the ith stream can be written as { Q1, SNR i = i SNR N/. (4) Q, SNR i >SNR N/ Then the adaptive grouping-modulation process is accomplished, which results in half of the streams with higher interference degree adopt low order modulation and the remaining streams with lower interference degree adopt high order modulation, as the orange part and the blue part shown in Fig. respectively. B. Adaptive Grouping based Detection at the Receiver The detection scheme of the proposed AGM-TD algorithm is composed by the orthogonal grouping process and the 659

3 adaptive detector selection, which is shown as the right part of Fig.. First, for independent detection, the original MIMO system is separated into two sub-mimo systems which are associated to the two groups of streams at the transmitter by adopting orthogonal grouping [11]. Let the matrix H represent the channel matrix by column replacement to ensure the corresponding streams s are arranged from the one with lowest SNR level to the one with highest SNR level, which leads to the streams with low modulation order arrange from 1 to N/ and the streams with high modulation order arrange from N/+1 to N. Especially, H i indicates the ith group set, which is given as H =[h 1 h h N/ h N/+1 h N 1 h N ]. (5) }{{}}{{} H 1 H The orthogonal matrix V j for the ith group which meets the requirement V j H i = 0, i = j can be deduced by QR decomposition of channel matrix. Define H j = H i j = i. By performing QR decomposition, H j can be expressed as H j = Q H j R j. (6) Take the row N/ +1 to N of the matrix Q H j to be V j. Multiplying by the orthogonal matrix of each group, the receive vector for each sub-mimo systems can written as ỹ i = H i s i +ñ i i =1,, (7) where H i = V i H i is the equivalent channel matrix with the dimension of N/ N/. Until now, two sub-mimo systems with different modulation order are obtained. In order to achieve better performance at an affordable complexity, an adaptive detector selection is applied for each sub-system. As mentioned in Section I, QRD-M detector proposed in [13] is a breadth-first tree search algorithm in which the problem of searching the ML solution is converted into finding the shortest path in the tree structure, and the solution is searched layer by layer. The method of QRD-M algorithm is to obtain a fixed number of surviving nodes at each layer as the parent nodes for the expansion to the next layer. As a result, the constant throughput and near optimal performance make QRD-M algorithm outstanding in the detectors. Nevertheless, with the drastic increasing of the antenna number, it suffers from the error propagation and relatively high complexity. Therefore, QRD-M algorithm is suitable for the situation when the channel condition is well and the interference level of streams is small. On the other hand, LAS algorithm proposed in [9] is a local search algorithm, which searches a better signal vector within the neighborhood vectors collection of the current solution. The superiority of LAS detector lies in its low linear complexity per iteration and the insensitivity to error propagation. However, it needs relatively major number of antennas to approach near optimal performance. Therefore, when the channel conditional is not very well and the antenna number is large, LAS algorithm is prefer. For the sake of catering the advantages of different algorithms, an adaptive detection scheme is proposed. Specifically, when the number of antennas is less than a threshold N, QRD-M detector is employed to both sub-systems to achieve the better performance under an acceptable complexity. However, with more antennas, which is larger than the threshold, in order to avoid the further increasing of complexity, a hybrid detection scheme is employed. That is, QRD-M detector is still applied in the sub-system with high order modulation in which low degree of error propagation will be produced, but the detector for the sub-system with low order modulation is changed as LAS algorithm, which can reduce the complexity at a large extent. After the adaptive detection process, the optimal sequence of each sub-mimo systems can be obtained. Then merge the sequences into the final detection result. IV. COMPLEXITY ANALYSIS In this Section, the complexity of several existing algorithms and the proposed algorithm is analyzed, which is measured by the number of floating point arithmetic (flops). Specially, the number of real addition and real multiplication are involved and summed as the total flops. We also assume that a complex multiplication/division is equal to 4 real flops and a complex addition/subtraction is equal to real flops [11]. From the description of QRD-M algorithm in Section III, we notice that the complexity is mainly consumed on the calculation of node metric. Assuming M surviving nodes are obtained at the ith layer, the metric calculation of all the child nodes at the (i + 1)th layer needs (M + 1)Q + Mi complex multiplications and MQ + Mi complex additions. Thus, when searching to the last layer, the total number of complex multiplications is N M/ +NMQ and the total number of complex additions is N M/ +NMQ, where Q denotes the constellation order. Converted to real flops, the complexity of QRD-M detector is 3N M +8NMQ. (8) For OGNO algorithm, QRD-M detector is adopted for each sub-system. Therefore, as the method of orthogonal grouping is introduced to convert a high order MIMO system into two independent sub-systems, the complexity of OGNO algorithm is can be expressed as 3N M/+8NMQ. (9) Similar to OGNO algorithm, orthogonal grouping is also introduced in AGM-TD scheme to reduce complexity. What s more, in order to further obtain performance improvement, an adaptive detector selection scheme is employed according to the relationship between the antenna number N and the threshold N. As a result, except the analysis of QRD-M algorithm, it is also necessary to analyze the complexity of LAS algorithm. The total complexity of LAS detector is related to the number of iterations I and the complexity per iteration. As applying real model, the original system with (N/)th antennas is converted into a N N system. At each iteration, the update process needs N multiplication operations and N addition operations. Consequently, the entire flops of LAS algorithm is 4N I. As a result, for the proposed AGM-TD algorithm, the complexity can be written as { 3N C = M/+4NM (Q 1 + Q ) N N 3N M/4+4NMQ +4N I N > N, (10) 660

4 TABLE I THE COMPUTATIONAL COMPLEXITY OF DIFFERENT ALGORITHMS Detection The number of antennas algorithm N N N>N QRD-M 3N M +8NMQ 3N M +8NMQ OGNO 3N M/+8NMQ 3N M/+8NMQ AGM-TD 3N M/+4NMQ 1 3N M/4+4NMQ +4NMQ +4N I SNR=6dB The threshold where Q 1 and Q denote the modulation order for different sub-systems in AGM-TD algorithm. The complexity of different algorithms corresponding to the antenna number is summarized in Table I. V. SIMULATION EVALUATION In this Section, we first give the simulation result for determining the appropriate value of N. Then the performance and the complexity of the proposed AGM-TD algorithm are evaluated on the condition of uncoded system with Rayleigh fading channel which is constant during a signal period. We use the following statement: 1) AGM-TD(Q 1, Q ) denotes the proposed algorithm with different modulation orders Q 1 and Q. ) QRD-M(Q) denotes the QRD-M algorithm with modulation order Q. 3) SQRD-M(Q) denotes SNR sorting based QRD-M algorithm with modulation order Q. 4) OGNO(Q) denotes the OGNO algorithm with modulation order Q. 5) SQRD-OGNO(Q) denotes SNR sorting based OGNO algorithm with modulation order Q. And the number of the surviving nodes at each layer is fixed as M =16in all the algorithms. A. Selection of Parameter N In order to determine an appropriate parameter N as the threshold to realize the adaptive transition of detection scheme, we give the average performance of the proposed algorithm with different detection schemes at 6dB as the increasing of antenna number in Fig. 3. Specially, scheme 1 and scheme denote adopting QRD-M detector to both subsystems and adopting a hybrid detection involving QRD-M and LAS to different sub-systems respectively. We can observe from Fig. that the reasonable value of N is equal to 40. Thus, when the number of antennas is less than 40, 0QRD- M detector is applied to both sub-systems to approach the performance gain while consuming an affordable complexity. When the number of antennas is more than 40, a hybrid detection is employed to obtain the complexity reduction and better performance. B. Evaluation Fig. 4 and Fig. 5 indicate the average performance of different algorithms in the MIMO systems with different antenna equipment. As the SNR sorting of the streams is used to separate the streams with different modulation orders, we also give the evaluation of SQRD-M and SQRD-OGNO scheme 1 scheme number of antennas, N =N r t Fig. 3. performance of different detection schemes in AGM-TD(4,16) at 6dB N t =N r =16 S SQRD Fig. 4. performance of different algorithms when N t = N r =16 algorithms which also employ the SNR sorting of the streams for fair comparison. Moreover, it is worth noting that 8QAM is selected as the modulation mode for QRD-M and OGNO algorithms which are free of grouping modulation to guarantee the same data rate. It can be observed in Fig. 4 and Fig. 5 that compared to QRD-M algorithm, the orthogonal grouping introduced in OGNO algorithm has some bad influence on the performance. However, when adopting the SNR sorting, the performance improvement of SQRD-M algorithm is much more obvious than SQRD-OGNO algorithm as it is more sensitive to the detection order. It can be also observed that the proposed AGM- TD detection scheme can obtain 3dB performance gain when targeting at as compared to SQRD-OGNO algorithm. That is to say, the performance gain is obtained as we dynamically regulate the assignment of modulation order for data streams according to their received interference level. C. Complexity Comparison As mentioned in Section IV, when the antenna number is less than N, the complexity of the proposed AGM-TD algorithm is half of the QRD-M detector, which is almost the 661

5 N t =N r = x S SQRD Complexity Fig. 5. performance of different algorithms when N t = N r =48 Fig. 7. The complexity of different algorithms when N t = N r =48 Average iteration number Fig. 6. The average iteration number decreases with the increasing of N t Nt=Nr=48 Nt=Nr= The average iteration number in AGM-TD(4,16) same as the QRD-OGNO algorithm. However, as the hybrid detection scheme is employed when equipping with more antennas, the complexity of the AGM-TD algorithm is changed in which the only variable is the iteration number I. Fig.6 gives the average iteration number curves in MIMO system with N r = N t = 48 and N r = N t = 64 when adopting AGM-TD detection scheme. The simulation result shows that the iteration number is fluctuant with SNR and the antenna number. Moreover, it is a small number at low SNR and reduces sharply with the increasing of SNR, which leads to the drastic reduction of the detection complexity of the proposed algorithm. In order to reveal the degree of complexity reduction, the total flops of different algorithms when N r = N t = 48 is illustrated in Fig. 7, from which we can observe that with the hybrid detection, the complexity of AGM-TD algorithm can be further reduced while maintaining the performance gain. VI. CONCLUSIONS In this paper, an adaptive grouping-modulation aided transceiver design (AGM-TD) was investigated for highorder MIMO systems. At the transmitter, adaptive groupingmodulation was adopted to regulate the modulation order for each stream according to its post-detection SNR. At the receiver, in order to achieve better performance with an affordable complexity, the adaptive detector selection scheme was applied. Simulation results demonstrated that the proposed AGM-TD algorithm can obtain 3dB performance gain when reaching the target at than OGNO algorithm. REFERENCES [1] G. J. Foschini, and M. J. Gans, On limits of wireless communications in a fading environment when using multiple antennas, Wireless Personal Commun.,vol. 6, pp , March [] G.J. Foschini, Layered space-time architecture for wireless communication in a fading environment when using multiple antennas, Bell Lab. Tech. J., 1996, 1(), pp [3] K. Vishnu Vardhan, S. K. Mohammed, A. Chockalingam, and B. Sundar Rajan, A low-complexity detector for large MIMO systems and multicarrier CDMA systems, IEEE JSAC Spl. Iss. on Multiuser Detection for Adv. Commun. Systems and Networks, vol. 6, no.3, pp , April 008. [4] G. Breit et al., 80.11ac Channel eling, doc. IEEE /0088r0, submission to Task Group TGac, 19 Jan [5] N. Srinidhi, Tanumay Datta, A. Chockalingam, and B. Sundar Rajan, Layered tabu search algorithm for large-mimo detection and a lower bound on ML performance, in Proc. of IEEE GLOBECOM010. [6] M. Hansen, B. Hassibi, A. G. Dimakis, and W. Xu, Near-optimal detection in MIMO systems using Gibbs sampling, in Proc. IEEE ICC, Dec [7] P. Som, T. Datta, A. Chockalingam, and S. Sundar Rajan, Improved large-mimo detection based on damped belief propagation, in Proc. IEEE ITW, Jan [8] N. Srinidhi, S. K. Mohammed, A. Chockalingam, and B. Sundar Rajan, Low-complexity near-ml decoding of large non-orthogonal STBCs using reactive tabu search, in Proc. IEEE ISIT, July 009. [9] Saif K. Mohammed, A. Chockalingam, and B. Sundar Rajan, A lowcomplexity near-ml performance achieving algorithm for large MIMO detection, in Proc. IEEE ISIT008, July 008. [10] K. Vishnu Vardhan, S. K. Mohammed, A. Chockalingam, and B. Sundar Rajan, A low-complexity detector for large MIMO systems and multicarrier CDMA systems, IEEE JSAC, vol. 6, pp , April 008. [11] Y.Lan, Z.Zhang, and H. Kayama, Orthogonal Grouping-based Near Optimal Detection Algorithm for High Order MIMO Systems, in Proc. IEEE PIMRC, pp , Sept.009. [1] Cho, Y., Kim, J., Yang, W., and Kang, C., MIMO-OFDM Wireless Communications with MATLAB, Wiley-IEEE Press, 1st Edition, 010. [13] W. H. Chin, QRD based tree search data detection for MIMO communication systems, in Proc. IEEE VTC 005-Spring, Stockholm, Sweden, pp ,