协作分集的NAF波束成形

Abstract—In this paper, we present three new detection schemes for the nonorthogonal amplify and forward (NAF) protocol in a cooperative diversity system based on a multiuser detection approach, namely, a channel inversion type detector, a maximal-ratio combining (MRC) type detector, and a biased maximum likelihood (ML) detector. The decision variables in these schemes are linear functionals of the transmitted symbol vector and therefore they are termed as “linear” detectors. A cooperative relay network using the NAF protocol with N − 1 ree the source transmits symbols in N − 1 blocks of two time slots in a Rayleigh fading environment. For the case of a general linear space-time block coding scheme using K symbols, we present the performance of this protocol in terms of the code symbol error probability when the symbols come from an M -ary phase-shift keying constellation. The approach is further extended to the transmission in N − 1 blocks of L time slots. Numerical results show that the performance of the MRC type detector is superior to that of the channel inversion type detector, while the biased ML detector has the best performance. However, the MRC type detector has the lowest complexity while the biased ML detector the highest. Index Terms—Code symbol error probability, cooperative diversity, nonorthogonal amplify and forward (NAF) protocol, Rayleigh fading.
ULTIPLE-INPUT multiple-output systems offer significant advantages for data transmission in wireless networks. Data transmission from source to destination via multiple relay nodes cooperating among themselves offers similar advantages. This idea is used in cooperative diversity, where single antenna mobile units share their antennas for transmission from source user to destination [1]. The cooperative relaying schemes are classified in mainly two categories: amplify and forward (AF) relaying and decode and forward relaying [2]. In the AF relaying scheme, the relay retransmits the noisy signal received from the sender to the destination after amplification. This scheme is advantageous because of its simplicity of implementation. AF relaying schemes have been analyzed for their error performance and closed form approximations or bounds for their symbol error probability have been obtained [3]. A variant of AF relaying is the nonorthogonal amplify and forward (NAF) relaying protocol. In this protocol, the
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IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 8, NO. 2, FEBRUARY 2009
Linear Detection for the Nonorthogonal Amplify and Forward Protocol
Aakanksha Chowdhery, Student Member, IEEE, and Ranjan K. Mallik, Senior Member, IEEE
signal is transmitted to the destination using a different relay for each frame out of a set of N − 1 relays in a round robin manner. The setup becomes similar to multiuser detection. The nonorthogonal transmission from relay nodes leads to higher spectral efficiency. It has been shown in the literature that this protocol performs better than AF relaying at sufficiently high signal-to-noise ratios (SNRs) because it achieves the optimal Zheng-Tse [4] diversity-multiplexing tradeoff (DMT) [5] under certain conditions. Works have also constructed optimal space-time block codes (STBCs) for this protocol to achieve the optimal DMT [6], [7], [8]. However, the parameters used for comparing the NAF protocol to other AF relaying schemes have been outage probability [5] and upper bounds on pairwise error probability [9]. This paper focuses on analyzing the code symbol error probability for the NAF protocol for a general linear STBC scheme using K symbols with three new linear detectors. The use of code symbol error probability as a performance benchmark gives a simple way to quantify the reliability of data at the receiver in practical systems. The three new detection schemes for the NAF protocol are based on a multiuser detection approach. In these schemes, the decision variables are linear functionals of the transmitted symbol vector. Hence these schemes are simpler than the optimal maximum likelihood (ML) detector in terms of computational complexity. The detection schemes are referred to as a channel inversion type detector, a maximal-ratio combining (MRC) type detector, and a biased ML detector. The NAF protocol uses N − 1 relays where the source transmits symbols in N − 1 blocks of two time slots each in a Rayleigh fading environment [5]. The odd time slots employ direct transmission from source node to destination and the even time slots achieve the same through a certain relay. Since general linear STBCs are used for analysis, the results obtained also apply to DMT optimal codes. The code symbol error probability is analyzed for the case when the symbols come from an M -ary phaseshift keying (PSK) constellation. For binary PSK (BPSK) constellation, the block error probability is also analyzed. In addition, we extend this approach to the transmission in N − 1 blocks of L time slots. Numerical results comparing the three detectors consider examples of STBCs like the Alamouti code [10] and the golden code [11] (which achieves optimal DMT). The paper is organized as follows. The system model for the two-time-slots case is given in Section II. Three linear detectors, based on a multiuser detection approach, are presented in Section III. In Section IV, the error performance for the three detectors in case of a linear STBC scheme with M -ary PSK (MPSK) symbols is analyzed. Section V extends