Mehdi Maleki

Space Modulation With CSI: Constellation Design and Performance Evaluation

In this paper, we investigate the effect of channel state information at the transmitter (CSIT) on the performance of a class of transmission schemes for multi-input–multi-output (MIMO) systems that can be collectively called space modulation (SMod) schemes. Space shift keying (SSK) is a simple example of SMod. In SMod, multiple antennas at the transmitter are employed to spatially modulate the information. The constellation vectors at the receiver are linear combinations of columns of the channel matrix, and therefore, the symbol error rate (SER) performance of the system highly depends on the Euclidean distance between each pair of these vectors. In this paper, we propose two novel methods to design the transmit vectors using CSIT such that the distance between each pair of constellation vectors at the receiver becomes larger, which, in turn, reduces the SER. Whereas in the first method we do not impose any constraint on the structure of the transmit vectors, in the second method, we confine the transmit vectors to have only one nonzero entry, and as such, it can be looked at as a modified SSK (MSSK) transmission scheme. This is to avoid interantenna synchronization (IAS) as only one transmit antenna is active at a time. Compared to SSK, the first method provides a significant performance improvement at the expense of increased complexity at the transmitter due to IAS. The second method provides an appealing SER improvement while keeping the complexity the same as that of SSK. Therefore, one can look at the second method as a modified version of SSK in which instead of transmitting a fixed symbol from one of the transmit antennas, in our proposed method, different transmit powers and phases are assigned to different transmit antennas. As acquiring full CSIT is difficult in some cases, we also consider the case of imperfect CSIT and derive alternative SMod transmission schemes in this case. By simulation, we show that the proposed SMod transmission schemes provide a significant performance improvement in terms of the SER in the presence of full or imperfect CSIT.

On the Performance of Spatial Modulation: Optimal Constellation Breakdown

Spatial modulation (SM) is a new transmission technique for multi-antenna systems in which the transmit antennas are used to modulate the signal. In this paper, the symbol error rate (SER) performance of SM is investigated. In SM, a signal domain modulation (i.e. amplitude-phase modulation) and an antenna domain modulation (i.e. space shift keying) are combined together to achieve a certain transmission rate while exploiting the properties of two independent modulation domains. A key question is the fine balance between the constellation sizes in the two domains when a constant rate is targeted. For a fixed rate, there are many ways to assign constellation vectors to the spatial and signal domains. In this paper, we investigate optimal constellation breakdown between space and signal domains. The analysis is based on the union bound of the error probability of SM with two typical APM schemes, i.e. phase-shift keying (PSK) and square quadrature amplitude modulation (S-QAM). It is shown that, at any transmission rate, there exists an optimal APM dimension in which the SER is minimized. Furthermore, a trade-off between the number of transmit antennas and the transmit power is introduced.

Performance Analysis of Spatial Modulation in Overlay Cognitive Radio Communications

We study the application of spatial modulation (SM) in overlay cognitive radio (CR) networks, in which the primary and secondary networks work concurrently over the same spectrum band. We assume that the direct link between the primary transmitter and receiver is not available, i.e. broken, and that the CR transmitter assists the primary network as a relay to amplify-and-forward the transmitted symbols of the primary. SM is used in the secondary to split the transmission space into two amplitude-phase modulation (APM) and spatial domains. In the proposed scheme, the secondary transmitter retransmits the primary symbols in APM domain, while its own information is transmitted by the index of transmitting antenna, similar to space shift keying, without causing any interference to the primary receiver. We analyze the performance of the optimal detectors at both the primary and secondary receivers for the case of phase shift keying modulation in terms of the average symbol error rate (ASER). We also study the asymptotic behavior of the ASER at both the primary and secondary at high signal-to-noise ratios. Simulation results show that the SM can be effectively used in overlay CR systems.

Spatial Sensing and Cognitive Radio Communication in the Presence of a

We study the feasibility of cognitive radio (CR) communication in the presence of a K-user multi-input multi-output (MIMO) interference channel as the primary network. Assuming that the primary interference network has unused spatial degrees of freedom (DoFs) , we first investigate the sufficient condition on the number of antennas at the secondary transmitter under which the secondary system can communicate while causing no interference to the primary receivers. We show that, to maximize the benefit, the secondary transmitter should have at least the same number of antennas as the spatial DoFs of the primary system. We then derive the secondary precoding and decoding matrices to have zero interference leakage into the primary network while the signal-to-interference plus noise ratio (SINR) at the secondary receiver is maximized. As the success of the secondary communication depends on the availability of unused DoFs, we then propose a fast sensing method based on the eigenvalue analysis of the received signal covariance matrix to determine the availability of unused DoFs or equivalently spatial holes. Since the proposed fast sensing method cannot identify the indices of inactive primary streams, we also provide a fine sensing method based on the generalized likelihood ratio test (GLRT) to decide the absence of individual primary streams. Simulation results show that the proposed CR sensing and transmission scheme can, in practice, provide a significant throughput while causing no interference to the primary receivers, and that the sensing detects the spatial holes of the primary network with high detection probability.

K

The problem of joint precoder design for the source and relay nodes of a cooperative cognitive radio (CR) system is investigated. We consider a non-regenerative relaying secondary CR system with underlay spectrum sharing methodology with the primary users. Based on an expression for the achievable throughput of secondary system, we develop an optimization problem to maximize the throughput subject to power constraints at the secondary source and relay, and an interference power constraint at the primary due to secondary source and relay transmission. First, we derive the structure of each of the relay and source precoding matrices separately assuming the other is known. Then, we propose an iterative technique to jointly design the source and relay precoding matrices. The results are also extended to the case where the direct source-destination link is available. Through simulation, we demonstrate the effectiveness of our proposed approach in improving the achievable throughput, and compare its performance with that of numerical optimization, source only precoding, relay only precoding, and a naive amplify-and-forward method.

-User Interference Primary Network

The problem of antenna subset selection (ASS) and constellation breakdown (CBD) for spatial modulation (SM) is investigated. Assuming the availability of the channel state information, an ASS scheme is introduced such that the symbol error rate of SM is minimized. A graph-based heuristic search algorithm is then proposed to significantly reduce the search complexity of ASS compared to the exhaustive search, while maintaining the performance. As it is not always optimal to use all the transmit antennas, optimal CBD in conjunction with ASS is then considered to develop an adaptive low-complexity ASS-CBD scheme.

Iterative Source and Relay Precoder Design for Non-Regenerative MIMO Cognitive Relay Systems

In this paper, the performance of suboptimal detection of spatial modulation (SM) based on the so-called maximum ratio combining (MRC) is investigated. In this detection scheme, in contrast to maximum likelihood (ML) detection, transmit antenna index and amplitude-phase modulation(APM) symbols are detected separately in two stages. Therefore, the detection complexity of SM can be significantly reduced. We analyze the instantaneous and average symbol error rate (SER) of such a detection scheme and compare it with that of the optimal ML detection. Also, we propose an adaptive space modulation scheme to minimize the SER of MRC detection by utilizing the channel state information. Finally, the problem of constellation breakdown of SM in the presence of the MRC detection for the special case of the phase-shift keying (PSK)-modulated SM is investigated. The derived analytical results are further validated using extensive simulations.

Adaptive Antenna Subset Selection and Constellation Breakdown for Spatial Modulation

A layered spatial modulation (LSM) scheme is proposed for the downlink of multiuser wireless communication systems. The proposed scheme falls in the class of the well-known point-to-point SM as it employs only one antenna in each transmission interval. However, it is designed based on assigning different sets of transmit antennas, rather than single antenna elements, to transmit different symbols of each user. We first study the error performance of the proposed LSM. In order to improve the overall error performance of the system, we employ a graphical approach to adaptively allocate antennas to different users. We also propose some techniques to increase the spectral efficiency of LSM. Extending the proposed method to the generalized LSM, we also compare the maximum transmission rate of the proposed scheme with that of the existing SM-based multiuser schemes, and show that this technique can significantly improve the spectral efficiency of the SM-based multiuser communications.

On MRC-Based Detection of Spatial Modulation

The problem of adaptive space modulation (ASM) design using partial channel state information at the transmitter (CSIT) is investigated. ASM relies on adaptive modulation of information symbols in the spatial domain using multiple antennas based on some sort of CSIT. The CSIT is exploited to adjust the transmission such that the distances between the receive constellation vectors are increased to reduce the probability of error. We assume that the spatial correlation matrices are available as the partial CSIT and introduce two different approaches to design ASM. In the first approach, we consider that all the transmit antennas are active at each transmit interval and, using an upper bound on the average probability of error, design the transmit vectors based on the spatial correlation matrices to improve the performance. In the second approach and to avoid interantenna synchronization, we assume that only one transmit antenna is active at each transmit interval, and we modify a space shift keying (SSK) transmission by transmitting different complex values from different transmit antennas. Finally, we derive a power allocation to improve further the performance in nonstationary channels. By simulation, we show the effectiveness of the proposed approaches in improving the performance in terms of the symbol error rate (SER).

Layered Spatial Modulation for Multiuser Communications

Conventional amplitude-phase modulations (APMs) are designed such that the minimum Euclidean distance between constellation points is maximized. Unlike these modulations, the error performance of spatial modulation (SM) is not only a function of the Euclidean distances but also the energy of each symbol, i.e. constellation point. Therefore, conventional APM schemes that are designed solely based on the notion of Euclidean distance are not necessarily suitable for SM transmission. In this paper, the constellation design for SM is investigated and it is shown that, by a proper constellation design, a significant performance gain is obtained compared to the well-known phase shift keying (PSK) or quadrature amplitude modulation (QAM). It is shown that in many cases multi-ring star-QAM is a suitable constellation for SM. However, when the number of transmit antennas is large, the numerically derived constellation converges to the conventional phase shift keying (PSK) constellation, especially at small number of receive antennas.