AEU - International Journal of Electronics and Communications
Performance of variable-power adaptive MQAM with transmit antenna selection and delayed feedback in Nakagami Fading channel
Introduction
The increasing demand of high data rate services always looks for spectrally efficient communication systems under limited radio spectrum. Adaptive modulation (AM), as a powerful technique for improving spectrum efficiency (SE), has received much attention recently. It can take advantages of the time-varying nature of wireless channels to transmit data at higher rates under favorable channel conditions and to maintain reliability by varying transmit power, symbol rate, and/or code rate under poor channel condition. Thus it can provide good SE without sacrificing bit error rate (BER) [1], [2], [3], [4], [5], [6]. Antenna selection (AS), is a promising approach to achieve the goal of providing performance benefits while significantly decreasing the hardware complexity and cost, has received considerable studies [7], [8], [9], [10]. It can provide a good tradeoff between the performance, cost, and complexity, and be realized at both ends. Therefore, effective combination of adaptive modulation and antenna selection techniques will receive much attention for practical purpose.
The transmit antenna selection (TAS) scheme with maximal-ratio combining (MRC) is an effective diversity scheme [8], [9], its basic idea is that a single (group of) transmit antenna(s), has the maximum total received signal power at the receiver, is selected for data transmission based on channel state information (CSI) feedback [8], [9]. Using this antenna selection scheme and adaptive modulation, [11] gives the performance analysis of discrete-rate adaptive M-ary quadrature amplitude modulation (MQAM) with TAS in MIMO systems, where average frame error rate and constant transmitter power are considered. The performance of adaptive MQAM with TAS and constant-power (CP) is studied in [12], where the average BER and spectrum efficiency is analyzed. An adaptive MQAM scheme with space-time block code (STBC) [13] and CP is investigated in [14]. Based on the constant transmitter power, the impact of feedback delay on adaptive modulation with single antenna and STBC can be found in [15] and [16], respectively. The above systems, however, basically employ CP-AM scheme. This CP approach restricts the systems to perform because the freedom of VP has been ignored.
Variable-power (VP) in AM has been considered in [3], [4], [5], [6]. The VP schemes in [3] and [5] are both designed for single antenna systems with AM. Moreover, closed-form optimal power partition for maximizing average SE is not yet developed in their work. The power control scheme for AM-MIMO systems over Rayleigh fading in [6] is basically a single-input single-output (SISO) VP scheme under the unitary transformation of singular value decomposition. For the optimization of SE of most of the above-mentioned schemes, Lagrange multiplier technique is used to integrate constraints to the optimization problem. However, the existence and uniqueness of Lagrange multiplier have not yet been studied in the literatures. Furthermore, no practical algorithm for computing the Lagrange multiplier has been developed.
In this paper, the performance of a MIMO system with VP AM and transmit antenna selection over Nakagami-m fading channels for perfect CSI or delayed feedback will be analyzed. With the exact BER expression of BPSK and a tight BER bound for modulation size ≥ 4, the switching thresholds for attaining maximum SE under a target BER and an average power constraint are derived. Unlike the VP schemes in [3] and [4] that fail to meet the target BER at low SNR, the derived VP control scheme is shown to fulfill the target BER for different SNRs. The existence and uniqueness of the Lagrange multiplier for the constrained optimization are investigated for the VP-AM scheme with TAS in Nakagami fading channel. It is found that the conditions of Nakagami channel are quite different from those of Rayleigh channel in [4] (which is only suitable for VP-AM with STBC). Moreover, [4] does not consider feedback delay, and the SE in [4] will be reduced for more than two transmit antennas since the rate of STBC with more than two transmit antennas is lower than 1. When the existence condition is satisfied, the Lagrange multiplier is unique, and a Newton's method for finding this Lagrange multiplier is proposed. For performance evaluation, the theoretical BERs of VP and CP systems are derived, which are shown to provide better agreement with simulation. Besides, the impact of delayed feedback on the BER performance of the VP-AM and CP-AM scheme with TAS is analyzed, and corresponding BER expressions are derived.
The notations we use throughout this paper are as follows. Bold upper case and lower case letters denote matrices and column vectors, respectively. The superscripts (·)H, (·)T and (·)* denote the Hermitian transposition, transposition, and complex conjugation, respectively.
Section snippets
System model
In this section, we consider a wireless multi-antenna communication system with N transmit antennas and K receive antennas operating over a flat and quasi-static Nakagami fading channel represented by a K × N fading channel matrix H = {hkn}. The complex element hkn = αkn exp (jθkn) denotes the channel gain from the nth transmit antenna to the kth receive antenna, which is assumed to be constant over a frame and varied from one frame to another. For Nakagami-m fading channel with integer m, the
Variable-power adaptive MQAM for MIMO with antenna selection
A MIMO system with VP adaptive modulation and TAS is referred to a VP-AM-TAS system. The adaptive modulator in the system employs square MQAM due to its inherent SE and ease of implementation. For discrete-rate MQAM, the constellation size Ml is defined as {M0 = 0, M1 = 2, and Ml = 22l − 2, l = 2, …, q − 1}, where M0 means no data transmission. The instantaneous SNR range is divided into q fading regions with switching thresholds {γ0, γ1, …, γq − 1, γq; γ0 = 0, γq = +∞}. The MQAM of constellation size Ml is used
Effect of delayed feedback
In this section, we will investigate the effect of delayed feedback on the performance of VP-AM systems. The channel is assumed to be perfectly known at the receiver, and be fed back to the transmitter with time delay τ. is the τ time-delayed version of H, and it is drawn from the same Gaussian process as H. The entries of , {} are correlated with {hk,n} with correlation coefficient c = J0(2πfdτ) [15], where J0(·) is the zero-order Bessel function of the first kind [19], and fd is the
Simulation results and numerical analysis
In this section, we use the derived theoretical performance formulae and computer simulation to evaluate the SE and average BER of the VP-AM-TAS. In the simulation, we consider wireless MIMO communication system with VP adaptive modulation and transmit antennas selection, and the system employs N transmit antennas and K receive antennas. For comparison, the MIMO system with VP adaptive modulation and STBC (referred as VP-AM-STBC) is also considered. The simulation is performed over Nakagami
Conclusions
The control strategy of a MIMO system with VP-AM and transmit antenna selection over Nakagami fading channels is presented. The optimal switching thresholds for the control strategy are derived. The existence and uniqueness of the Lagrange multiplier for the constrained optimization of SE are presented. It is shown that the Lagrange multiplier will exist and be unique when the condition of existence for Lagrange multiplier is satisfied. In the derivation, the exact BER expression of BPSK and a
Acknowledgement
The authors would like to thank the anonymous reviewers for their valuable comments. The work described in this paper is supported by National Natural Science Foundation of China (61172077), Doctoral Fund of Ministry of Education of China (20093218120021), Open Research Fund of National Mobile Communications Research Laboratory of SEU (N200904), and NUAA Research Funding (NS2010113).
Xiang-bin Yu received his Ph.D. in Communication and Information Systems in 2004 from National Mobile Communications Research Laboratory at Southeast University, China. From 2004 to 2006, he worked as a Postdoctoral Researcher in the Information and Communication Engineering Postdoctoral Research Station at Nanjing University of Aeronautics and Astronautics, Nanjing, China. He has been an Associate Professor with the Nanjing University of Aeronautics and Astronautics since May 2006. Currently,
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Xiang-bin Yu received his Ph.D. in Communication and Information Systems in 2004 from National Mobile Communications Research Laboratory at Southeast University, China. From 2004 to 2006, he worked as a Postdoctoral Researcher in the Information and Communication Engineering Postdoctoral Research Station at Nanjing University of Aeronautics and Astronautics, Nanjing, China. He has been an Associate Professor with the Nanjing University of Aeronautics and Astronautics since May 2006. Currently, he works as a Research Fellow in the Department of Electronic Engineering, City University of Hong Kong, Hong Kong. Dr. Yu has served as a technical program committee of Globecom 2006, International conference on communications systems 2008 (ICCS’08), ICCS’10, and reviewer of some conferences and journals. He has been a member of IEEE ComSoc Radio Communications Committee (RCC) since May 2007. His research interests include Multi-carrier CDMA, space-time coding, adaptive modulation and space-time signal processing.
Xin Yin is currently working towards the M.Sc. degree at Nanjing University of Aeronautics and Astronautics, Nanjing, China.
Xiao-shuai Liu is currently working towards the M.Sc. degree at Nanjing University of Aeronautics and Astronautics, Nanjing, China.
Da-zhuan Xu was graduated from Nanjing Institute of Technology, Nanjing, China, in 1983. He received the M.S. degrees and Ph.D. in Communication and Information Systems from Nanjing University of Aeronautics and Astronautics in 1986 and 2001, respectively. He is now a full professor in College of Information Science and Technology, Nanjing University of Aeronautics and Astronautics, Nanjing, China. Prof. Xu is a Senior Member of China Institute of Electronics (CIE). His research interests include digital communications, software radio, coding theory, medical signal processing.