Wireless Communications and Mobile Computing

Volume 2017 (2017), Article ID 4359843, 12 pages

https://doi.org/10.1155/2017/4359843

## Performance Improvement of Space Shift Keying MIMO Systems with Orthogonal Codebook-Based Phase-Rotation Precoding

^{1}School of Computer and Communication Engineering, Universiti Malaysia Perlis (UniMAP), Perlis, Malaysia^{2}Department of Electrical Engineering, College of Engineering at Wadi Aldawaser, Prince Sattam Bin Abdulaziz University, Wadi Aldawaser 11991, Saudi Arabia

Correspondence should be addressed to Essam Sourour

Received 27 May 2017; Revised 27 September 2017; Accepted 2 October 2017; Published 9 November 2017

Academic Editor: Xianfu Lei

Copyright © 2017 Mohammed Al-Ansi et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

This paper considers codebook-based precoding for Space Shift Keying (SSK) modulation MIMO system. Codebook-based precoding avoids the necessity for full knowledge of Channel State Information (CSI) at the transmitter and alleviates the complexity of generating a CSI-optimized precoder. The receiver selects the codeword that maximizes the Minimum Euclidean Distance (MED) of the received constellation and feeds back its index to the transmitter. In this paper, we first develop a new accurate closed-form Bit Error Rate (BER) for SSK without precoding. Then, we investigate several phase-rotation codebooks with quantized set of phases and systematic structure. Namely, we investigate the Full-Combination, Walsh-Hadamard, Quasi-Orthogonal Sequences, and Orthogonal Array Testing codebooks. In addition, since the size of the Full-Combination codebook may be large, we develop an iterative search method for fast selection of its best codeword. The proposed codebooks significantly improve the BER performance in Rayleigh and Nakagami fading channels, even at high spatial correlation among transmit antennas and CSI estimation error. Moreover, we show that only four phases are sufficient and further phase granularity does yield significant gain. This avoids hardware multiplication during searching the codebook and applying the codeword.

#### 1. Introduction

Spatial Modulation (SM) is a novel technique to achieve low complexity and energy efficient Multiple Input Multiple Output (MIMO) systems [1]. In SM, part of the user data bits is conveyed through the index of a single transmit antenna (TA), while the second part is conveyed through classic selection of an Amplitude and Phase Modulation symbol [1, 2]. One special form of SM-MIMO is the Space Shift Keying (SSK) proposed in [3] to tradeoff receiver complexity for data rate. In SSK, the data bits are encoded only in the index of TA, which transmits an unmodulated data such as +1 symbol. When the number of TAs is not sufficient, Generalized SSK and Generalized SM are introduced, respectively, in [4] and [5] to increase the spectral efficiency by activating multiple TAs and availing larger TA combinations and indexes.

In comparison to the conventional MIMO schemes, SM has potential advantages. Notably among them are the avoidance of interchannel interference and relaxation of the need for interantenna synchronization, due to the transmission from a single antenna at each time instant. The complexity of the transceiver is also reduced and the energy efficiency is enhanced since only one Radio Frequency (RF) chain is required. Furthermore, the configurations related to the number of transmit and receive antennas are flexible in contrast to the restrictions applied in MIMO spatial multiplexing [1–3, 6]. Initial research was dedicated to improve the SM and SSK systems performance through designing low complexity receiver algorithms that minimize the Bit Error Rate (BER) [7–9]. However, Transmit Precoding (TPC) as a preprocessing technique on the transmitter side, with possible feedback from the receiver side, has lately shown remarkable performance gains [10, 11].

TPC assumes downlink Channel State Information (CSI) is known at least at the receiver, and a common precoding codeword is employed by the transmitter and the receiver. In the transmitter side, the codeword is used to scale the TAs. In the receiver side, it is used in Maximum Likelihood (ML) detection of the TA index and the transmitted symbol [8]. In most research, the design objective of TPC codeword is maximizing the Minimum Euclidean Distance (MED) between pairs of received symbols, which is the dominant factor affecting the BER performance [3]. Finding the codeword that fulfills MED maximization has been the subject of considerable research, which can be categorized into three main approaches as described below.

*The first approach*, which is a noncodebook approach, captured the most attention in the TPC research. This approach develops algorithms to find the TPC codeword that realizes a design objective for the given CSI [12–20]. This algorithm should be used in the transmitter and receiver to yield the same codeword, and it requires full knowledge of the CSI at both sides. The most widely used design objective is the maximization of the MED subject to fixed transmit power. This is sometimes termed as the Maximum Minimum Distance (MMD), and it is used as the first method in [12, 13]. Another utilized design objective is the transmit power minimization subject to Guaranteed Euclidean distance (GED), which is utilized as the second method in [12, 13]. Other design objectives include Signal-to-Noise Ratio (SNR) maximization [14], direct BER minimization [15], and phase alignment [16]. In [12–14, 17, 18], the designed codeword involves amplitude scaling, while, in [15, 16], it is based on phase rotation only. Therefore, this approach yields a codeword matching the instantaneous channel, leading to a significant reduction in BER. It is more practical in Time Division Duplex (TDD) systems where the uplink and downlink channels are the same. However, there are some limitations to this approach. The solution for the codeword is typically iterative. Depending on the number of transmit and receive antennas the complexity of the algorithm may be an issue. Also, the required number of iterations is variable and depends on the instantaneous CSI and SNR, leading to a nonfixed processing time. Moreover, when the RF chain specifications and processing power of the receiver and transmitter are different, the reciprocity may be an issue. Besides, huge overhead is required to obtain full CSI through feedback with infinite rate, particularly in the Frequency Division Duplex (FDD) systems [21]. To solve this latter problem, the research in [19] suggests quantizing the channel phase angles at the receiver, and feeding them back to the transmitter with limited number of bits, to be used for phase compensation at the transmitter. Also, [20] proposes a simplified power allocation method. The receiver uses the CSI to update the power allocation for only two antennas that are associated with MED and feeds back only their indices and updated power allocation using a limited number of bits.

*The second approach* is the CSI-independent codebook-based approach [22, 23]. This approach is proposed to overcome the aforementioned limitations of the first approach through utilizing a codebook with a limited predefined number of codewords known by the transmitter and receiver. Given the CSI, the receiver selects the codeword that maximizes the MED and feeds back the index of the selected codeword to the transmitter. This feedback can be considered as a limited knowledge of CSI at the transmitter. The second method of codebook construction proposed in [22] follows this approach. The codebook is the DFT matrix, where the codebook size should be less than or equal to the number of TAs. Interestingly, a modified DFT matrix is also utilized in [24] as a precoding matrix for a special form of Generalized SSK system, under spatially correlated channels. The precoding matrix is constructed by multiplying a complex random unitary matrix by the DFT matrix. It is worthwhile to mention that [24] does not assume any feedback from the receiver to the transmitter. The precoding codeword is selected by the bit sequence to be transmitted, rather than the instantaneous CSI. However, the utilization of the CSI-independent precoder falls into the second approach. In [23], a codebook was constructed of randomly generated matrix of complex Gaussian random variables with zero mean and unit variance. Significant performance gain has been shown in [22–24] with CSI-independent codebooks. In [25], the authors of this paper presented two small-size codebooks that are subsets of all possible combinations of codewords (denoted as Full-Combination codebook). The first codebook is the Factorized Full-Combinations codebook, which is based on restructuring the Full-Combination codebook for faster codeword search. The second codebook is the Statistically Filtered Full-Combinations codebook, which is based on selecting the codewords which are most frequently used. While these two codebooks provide good performance, they do not have a predefined structure. The CSI-independent codebook-based approach is suitable for FDD systems that are widely used in 3G and 4G systems, where the uplink and downlink channels are not reciprocal. Also, these codebooks require only a limited knowledge of CSI at the transmitter. However, the drawback of this approach is that the selected codeword does not match the channel exactly. Hence, the MED is not globally maximized, which may lead to performance loss compared to the first approach.

*The third approach* is a hybrid approach [26], where a codebook is designed to match the channel* on the average*. The first method of codebook construction proposed in [22], as well as the method in [27] by the same authors, follows this approach. In [22], the codebook is constructed by generating a large set of random codewords. Then, this set is filtered to select the best codebook with the desired number of codewords. The selection criterion is the maximization of the statistical expectation of the MED. In [27], the codebook is generated iteratively using the concept of the Lloyd algorithm [28] and the nearest neighborhood and centroid criteria. A training set of 6000 random channel realizations are used as the training set for codebook construction. In [22, 27], once the codebook is constructed, codeword is selected based on maximizing the MED and the index is fed back from the receiver to the transmitter. In [24], in addition to the DFT-based precoder mentioned in the second approach, the authors also propose two codebook construction methods based on zero-forcing and matched filter of the transmit correlation matrix. Hence, these codebooks fall in the third approach. While this approach achieves the advantages of the codebook-based approach, it suffers from two shortcomings. The codebook may need to be updated if the channel long-term characteristics change and the update must be reciprocal in the transmitter and receiver. The second is the lack of a systematic algebraic structure of the codebook. The codeword elements are random-like, which may be an issue when they are quantized for practical implementation and fed back from the receiver to the transmitter, although at a low rate.

In consideration of the foregoing, this research focuses mainly on the second approach (i.e., channel-independent and codebook-based), primarily motivated by its advantages. This approach is extensively utilized in MIMO spatial multiplexing [26] and it is also employed in LTE-A system [29]. Nevertheless, this approach did not get enough attention in the SM and SSK literature. Thus, this work introduces several codebook-based precoding methods for SSK assuming phase-only precoding. There are several reasons to prefer the phase-only precoding, in contrast to the joint amplitude and phase precoding. First, it is shown in [16] that amplitude precoding may require a large dynamic range in the precoding gain, which requires high cost linear power amplifier at the transmitter. This was also noted as the reason for phase-only precoding in [15]. Second, we find in the numerical results that four phases are sufficient for performance improvement. Increasing number of phases does not provide worthwhile gain. This considerably reduces the complexity of codebook search in the receiver and codeword scaling in the transmitter.

The contribution of this paper is dedicated for SSK-MIMO system, and it can be summarized as follows:(1)New and more accurate closed-form BER formula is derived for SSK without precoding and compared to the existing formulas in the literature.(2)New codebooks for SSK are introduced and their performance is investigated, including the Full-Combination (FC), Walsh-Hadamard (WH), Quasi-Orthogonal Sequences (QOS), and Orthogonal Array Testing (OAT) codebooks. They are based on phase rotation only and require limited feedback.(3)Iterative Search (IS) method is developed in order to solve the challenging task of selecting the best codeword iteratively from the FC codebook when its size is large.(4)It is shown that codebooks with elements are sufficient to achieve all the performance gain from this type of codebooks. This greatly simplifies the practical implementation since channel scaling becomes a sign inversion and/or swapping real and imaginary parts.(5)The performance of the proposed codebooks is investigated under imperfect CSI estimation and correlated channel for both Rayleigh and Nakagami fading channels.(6)The performance of the proposed codebooks is compared to selected published performance in the literature.

The remainder of this paper is organized as follows: in Section 2, the system model of SSK-MIMO is introduced. Development of the new closed-form BER for conventional SSK-MIMO system is presented in Section 3. Section 4 explains the codebook-based TPC and investigates the FC, WH, QOS, and OAT codebooks. Also, this section presents the IS method to select the codeword from the FC codebook. Simulation results and performance comparisons are presented in Section 5. Finally, Section 6 concludes the paper.

*Notation*. , and indicate conjugate, transpose, and Hermitian transpose, respectively. Boldface uppercase and lowercase letters denote matrices and vectors, respectively. Italic upper or lower case letters represent the scalar variables. The notation denotes a diagonal matrix with vector in its diagonal elements. The notation refers to the Euclidean norm. The gamma function of an integer is defined as , where is the factorial of the integer .

#### 2. SSK-MIMO System Model

Consider SSK-MIMO system with transmit antennas and receive antennas. Information bits are divided into sections of length bits, where we assume that is a power of 2. Each section is converted from binary to decimal to yield the index of the antenna to be activated, . The signal of SSK-MIMO systems can be expressed as follows:where is the complex received signal vector and is the () complex channel matrix, which is known to the receiver only.** H** consists of * channel vectors *. The elements of are denoted as which indicate the channel path gain between the th transmit antenna and the th receive antenna. The elements are assumed to be identical and independently distributed (i.i.d.) complex Gaussian random variables with zero mean and unit variance. The () Phase-Rotation Precoding (PRP) matrix has a diagonal structure to satisfy the SSK requirements of a single active antenna at a transmission time. The () transmission vector is given bywhich indicates that only the th antenna is activated. The () noise vector is the white noise whose elements are i.i.d. complex Gaussian random variables with zero mean and variance , where is the SNR per receive antenna.

Let us define the codebook matrix that includes codewords as follows:Each row in represents a codeword of length that is used to scale the TAs. If the selected codeword is , then the precoding matrix . Without precoding all elements in are ones. Figure 1 shows the SSK system with codebook-based TPC.