On the user performance of orthogonal projection signal alignment scheme in MIMO relay systems

In this article, an orthogonal projection signal alignment (OP-SI) scheme is proposed for multiple-input and multiple-output (MIMO) relay systems, and the user performance is studied with and without perfect channel state information (CSI). Particularly we focus on an important scenario in cellular systems, where the base station exchanges messages with multiple users via a relay. By jointly designing the precoding matrices at the base station and the relay, information exchanging can be accomplished within two time slots. When the perfect CSI is available, closed form expressions of ergodic sum rate are developed for the proposed scheme, where we can demonstrate that the proposed scheme yields a better performance than the existing zero-forcing signal alignment scheme. When the channel estimation is not perfect, both the intra-stream and inter-stream interference cannot be completely removed. To evaluate the impact of channel estimation error, an approximation of ergodic sum rate for the OP-SI scheme is developed to show that the system performance could significantly decrease as the covariance of channel estimation error increases. Moreover, the outage capacity is also analyzed. Furthermore, an enhanced relay precoding scheme is also introduced to improve the transmission performance. Numerical results are provided to show the accuracy of the developed analytical results. Introduction To increase the system throughput and enlarge the coverage for cellular systems, relaying is introduced as a key technology for the next generation mobile telecommunication systems [1]. However, the extra radio resource consumed by relay transmissions could lead to a loss of the spectrum efficiency and system throughput as well. As a promising method to overcome such shortcomings of relaying, the application of network coding in wireless communications has been studied recently, specifically in cellular communication scenarios [2-5]. Network coding was first introduced to two-way relaying systems, where two source nodes exchange messages via a relay. By asking the relay to broadcast the mixture of the source messages, the communication between two source nodes can be accomplished within two time slots, where each *Correspondence: [email protected] 1Wireless Signal and Network Lab, Key Laboratory of Universal Wireless Communications, Ministry of Education, Beijing University of Posts and Telecommunications, Beijing, China Full list of author information is available at the end of the article source recovers its desired message by first subtracting self-interference. Compared to the traditional four timeslot schemes, network coding can double the spectrum efficiency, and increase the throughput dramatically. Recently the combination of network coding with multiple-input and multiple-output (MIMO) technique has attracted a lot of attention [6-10], where MIMO provides another reliable approach to improve the performance of relay transmissions [11]. Particularly the signal alignment schemes have been proposed in MIMO relaying channels. By properly designing precoding, the desired messages can be aligned together and therefore interstream interference can be canceled when the perfect channel state information (CSI) is available. The idea of signal alignment was first introduced for MIMO Y channels [9]. In the context of bi-directional communications, [6,10] design the signal alignment protocols in amplifyand-forward (AF) MIMO relay systems, where the interstream interference is eliminated by applying precoding, and the intra-stream interference is coped with by using network coding. The performance of network coding in © 2012 Zhao et al.; licensee Springer. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Zhao et al. EURASIP Journal onWireless Communications and Networking 2012, 2012:308 Page 2 of 17 http://jwcn.eurasipjournals.com/content/2012/1/308 decode-and-forward (DF)MIMO relay systems was investigated in [7]. The application of analog network coding toMIMO two-way relaying channel was researched in [8], where the optimal design of beamforming was provided. Most of these existing works assume the perfect CSI either at the transmitters or the receivers. In this article, we proposed an orthogonal projection signal alignment (OP-SI) scheme in MIMO relaying channels. The main contribution of this article are as follows: first, we propose a new signal alignment scheme for a classical cellular communication scenario, where a base station exchanges messages with multiple users with the help of one relay. By jointly designing the precoding at the base station and the relay, the messages from and to the same user can be aligned together. Different to [10], the precoding matrix at the relay is constructed by projecting each aligned message on a single carefully chosen direction of the null space, respectively, where the inverse of large size matrices can be avoided. Since the co-channel interference can be eliminated, the multiple uplink and downlink transmissions can be accomplished within two time slots. Second, the analytic results, such as the user ergodic sum rate and the outage capacity with and without channel estimation error, are derived to evaluate the performance of proposed OP-SI scheme. When the channel estimation is free of error, our developed analytic results clearly show that theOP-SI scheme achieves higher ergodic sum rate at the user nodes than the zero-forcing signal alignment (ZF-SI) scheme proposed by [10]. Furthermore, the impact of channel estimation error on the OP-SI scheme is also evaluated. Such analysis is rarely introduced in the existed works: Different to the work in [12-14], we focus on the MIMO relaying channels in this article, which is a more challenging scenario compared to the one-hop MIMO system studied in previous works. Moreover, many existing analysis of signal alignment transmissions is based on the assumption that the perfect global CSI is available, such as in [6,7,10]. However, the channel estimation error cannot be avoided completely in practical wireless systems. And such error causes severe interference, especially in the context of signal alignment transmissions, where the incompletely removed selfinterference, an unique phenomenon for signal alignment, will severely degrade the transmission reliability. Based on practical channel estimation error models, we are able to fully characterize the impact of channel estimation error in this article. Finally, an improved OP-SI scheme with optimal relay precoding selection is introduced, which can furthermore provide significant performance gains in the presence of channel estimation error. The rest of this article is organized as follows. Section ‘System model and protocol description’ describes the system model, and introduces the proposed OP-SI transmission scheme. In Section ‘Performance analysis for the proposed OP-SI scheme’, the performance analysis with and without channel estimation error is derived, and the comparison with the ZF-SI scheme is also presented. Then in Section ‘The enhanced precoding design for the OP-SI scheme at the relay’ the enhanced relay precoding design for OP-SI is provided, which can improve the transmission performance. Then the numerical results are shown in Section ‘Numerical results’, and followed by the conclusions in Section ‘Conclusion’. Notation: Vectors and matrices are denoted as boldface small and capital letters, respectively, e.g., A and b. The trace for A is denoted as tr(A), and DA is the determinant for A. (A)i,j represents the element located at the ith row and the jth column ofA. E{x} is the expectation of various x. |x| denotes the norm for x, and x can be a number, a vector or a matrix. a is denoted as the floor function for a. (·) is Gamma function. ci(·) and si(·) are the cosine integral and the sine integral, respectively.ψ(·) is the Euler psi function, and Ei(·) is the exponential integral function. Systemmodel and protocol description Consider a communication scenario including M users, one base station and one relay. As shown in Figure 1, the base station and the relay are both equipped with multiple antennas, whose antenna numbers are M and N, respectively, and each user is equipped with a single antenna. It is assumed that the number of relay antennas satisfies N > M in order to meet the power constraint, as well as ensures that enough degrees of freedom can be provided. The half-duplexing constraint is applied to all nodes. All the channels are assumed to be quasi-statically independent and identically Rayleigh fading, and there is no direct link between the base station and the users. Both the base station and the relay have the access to the global CSI. For such a scenario, the base station is required to transmit M messages to the M users individually, while each user wants to send its own information to the base station Figure 1 System diagram for the addressed bidirectional communication scenario. This figure is provided as an illustration for the system model, which helps the readers better understand the transmission procedure. Zhao et al. EURASIP Journal onWireless Communications and Networking 2012, 2012:308 Page 3 of 17 http://jwcn.eurasipjournals.com/content/2012/1/308 simultaneously. By jointly designing the precoding matrices at the base station and the relay, the messages from and to the same user can be aligned together, and transmitted to the users without co-channel interference, if the perfect CSI can be obtained. In the following part, we will introduce such a signal alignment scheme, which can accomplish the transmission between the base station and theM users in two time slots.Unlike the ZF-SI scheme proposed by [10], the orthogonal projection is applied for relay precoding design in the proposed OP-SI scheme, which avoids severe relay noise amplification caused by the ZF-SI scheme and achieves significant performance gains. During the first time slot, the base station and all the users transmit their messages to the relay simultaneously. To ensure that the matched messages from the base station and the users can be grouped together at the relay, the precoded messages are transmitted from the base station. Then the relay receives