This dissertation does not contain the writings of other persons, unless specifically acknowledged as a source by other researchers. Thus, the second contribution of this dissertation is the application of circular constellations, in particular amplitude phase shift keying (APSK) modulation to existing SM, GSM and GSM-CR systems.

## Introduction

### Motivation and Context

In these conventional MIMO systems, diversity techniques are used to improve the overall link reliability of a wireless communication system. In this scheme, the Alamouti structure was incorporated to improve the error performance over traditional GSM systems.

### Research Aim and Objectives

As hypothesized, the M-APSK GSM-CR system outperforms the corresponding M-APSK GSM and M-APSK SM systems. Derive a closed form expression for the average BER for the M-APSK SM, M-APSK GSM and M-APSK GSM-CR systems.

## Contributions

### Organization of Dissertation

Zhang, “Dual learning-based channel and signal estimation in massive MIMO with generalized spatial modulation,” IEEE Transactions on Communications, vol. Cheng, “Low-complexity ML detection for MIMO spatial modulation with APSK constellation,” IEEE Transactions on Vehicle Technology, vol.

## Introduction

Previous bit error rate (BER) performance studies of M-APSK SM systems have only been presented using simulation results and have not been verified by an analytical framework. The theoretical average BER expressions are shown to have a tight bound in the high signal-to-noise ratio (SNR) region compared to Monte Carlo simulation results. The theory expression verified the simulation results of a 6 bit/s/Hz system configuration presented in a previous study.

The performance study in this paper is then extended by presenting theory and simulation results for 7 bit/s/Hz and 8 bit/s/Hz system configurations. Performance analysis of APSK in Spatial Modulation 12 M-APSK SM system and compare it with the simulation results. The theoretical BER expressions for the 16-APSK and 32-APSK constellations in SM are derived in Section IV.

## System Model

The entries of Hand are independent and identically distributed (i.i.d) according to the complex Gaussian distribution CN(0,1). The constellation diagrams and the corresponding bit allocation for the two modulation schemes are shown in Fig. In the 16-APSK constellation, the ratio of the outer and inner rays is indicated by β0 = R2/R1, while the ratios in the 32-APSK constellation are defined as β1 =R2/R1 and β2=R3/R1.

## Performance Analysis of M -APSK SM System

### Analytical BER of Symbol Estimation in AWGN (P d )

An upper bound is obtained by considering only the nearest neighbors for each PEP in (2.11). The process for deriving the 32-APSK BER is the same as in the 16-APSK case.

Analytical BER of Symbol Estimation in Rayleigh Fading (P d )

Analytical BER of Transmit Antenna Index Estimation (P a )

Results and Discussion

## Conclusion

Sinanovic, Chang Wook Ahn, and Sangboh Yun, “Spatial Modulation,” IEEE Transactions on Vehicular Technology, vol. Haas, “Energy evaluation of spatial modulation in a multi-antenna base station,” in 2013 IEEE 78th Vehicular Technology Conference (VTC Fall), 2014, p. ,” IET Communications, vol.

Hanzo, "Star-QAM Signaling Constellations for Spatial Modulation," IEEE Transactions on Vehicular Technology, vol. Al-Mumit Quazi, "Spatial modulation: Optimal Detector Asymptotic Performance and multiple-stage detection," IET Communications, vol. Generalized Spatial Modulation ( GSM) is a recently developed multiple-input multiple-output (MIMO) technique that aims to improve data rates over conventional Spatial Modulation (SM) systems.

## Introduction

### Context of Research

An analytical bound on the average BER of the proposed M-APSK GSM and M-APSK GSM-CR systems over fading channels is derived. The overall spectral efficiency in GSM is improved by the base-two logarithm of the number of transmit antennas compared to SM. Several schemes have been developed to improve the reliability of traditional GSM systems [6-11, 13].

In their paper Zhou et al designed APSK constellations based on the theoretical symbol error probability (SER) of the NCSM system. The design objective is to ensure that adjacent symbols are spaced further apart in the secondary mapper than the primary mapper. The first approach is to use geometric heuristics, but to the best of the authors' knowledge, heuristics for generalized APSK constellations have not yet been presented.

### Contributions

However, the resulting constellations in these works [19–22] have certain limitations that make them unsuitable for the M-APSK GSM and GSM-CR systems proposed in this chapter: a) they are specifically designed for coded systems b) they deviate from those recommended by the DVB-S2 standard. The challenge of developing an M-APSK GSM-CR system is the design of a secondary mapper for a given M-APSK mapper. Even after reducing the search space, Samra et al [15] report that the algorithm is still too complex for constellations where M¿16.

Recently, a new approach for mapping based on GA was proposed by Patel et al [23, 24]. This algorithm allows the design of higher modulation scheme designers, with possible computational complexity. Thus, this algorithm is applied in this chapter to design secondary mappers for the proposed M-APSK GSM-CR system.

Structure and Notation

## System Model

The signal domain in the GSM-CR system consists of two symbols mapped by bs = log2M bits, where M indicates the order of the APSK modulation scheme used. The same process was applied for the proposed M-APSK GSM and M-APSK GSM-CR. Alternatively, the received vector for the APSK GSM-CR can be represented as: . ejθk is the transmitted symbol pair and hk = h. is a Nr ×2 dimensional channel matrix corresponding to the active antenna pair index k. The receiver uses the ML detection rule for estimating the transmit antenna pair index and the transmitted symbol as shown in Eq. Performance analysis of M-APSK generalized spatial modulation with constellation.

These schemes are referred to as n1 + n2+..+nl APSK where l is the total number of rings and nl is the number of points on the 1th ring. Furthermore, it is worth noting that 4+12 APSK and 4+12+16 APSK are the chosen modulation schemes in the latest DVB-S2 standard for satellite communication over non-linear channels [18]. The constellation diagrams for 16-APSK and 32-APSK and the corresponding bit allocation for mappers ω1 and ω2 in decimal are shown in Fig.

## BER Performance Analysis

Analytical BER of Transmit Antenna Index Estimation (P a )

### Analytical BER of Symbol Pair Estimation (P d )

The average BER for the transmit antenna index is calculated assuming that the transmitted signal is correctly detected. Quazi [34] showed that choosing n greater than 6 has sufficient accuracy of numerical integration. The PEP conditioned on H defined in Eq. 3.13) is averaged by integrating the attenuation distribution.

Hence, the average BER expression of symbol estimation can be obtained by the unconditional probability expressed in Eq.

## Constellation Reassignment Mapper Design

### Description of Genetic Algorithm

The genetic algorithm described by Patel et al [23] deals with the case where ω1 is known and ω2 is desired. The block diagram in Figure 3.3 provides a high-level illustration of the genetic algorithm designed by Patel et al[23]. The set of chromosomes considered at each iteration of the algorithm is called a "population".

In the remainder of this section, the authors provide a summarized discussion of each phase of the genetic algorithm. Generating a population of chromosomes The population of chromosomes refers to the set of candidate secondary mappers evaluated by the genetic algorithm at each iteration. In the genetic algorithm for mapping design, 2× z2. chromosomes are discarded at the end of each iteration.

## Results and Discussion

The transmit antenna pairs used for M-APSK GSM and M-APSK GSM-CR were obtained from Basar et al. for a 4×Nr and 6×Nr and are shown in Table 3.2 and Table 3.3 [9], respectively. To ensure a fair comparison, identical spatial mappings were used for both GSM and GSM-CR systems. It is also clear that the GSM-CR outperforms the GSM and SM systems in all cases.

As the graphs in Fig. 3.5, the 16-APSK GSM-CR system achieves a gain of 2.5 dB over its equivalent GSM system and 1.5 dB over its equivalent SM system at BER of 10−5. It can be seen in Fig. 3.7 that the 16-APSK GSM-CR system achieves a gain of 2.5 dB over its equivalent GSM system and 1.5 dB over its equivalent SM system at BER of 10−5. 3.8, 32-APSK GSM-CR systems achieve gains of 2 dB and 1.2 dB at BER of 10−5 compared to its equivalent GSM and SM systems, respectively.

## Conclusion

-CR systems achieve gains of 2.2 dB and 2 dB at BER of 10−5 compared to its equivalent GSM and SM systems respectively. It should be noted that similar performance improvements were observed in M-QAM GSM-CR over SM and GSM in the original work done by Naidoo et al[13]. The performance benefits for the M-APSK GSM-CR system over the M-APSK GSM system at different AASCs are attributed to the improved symbol pair estimation error performance, Pd.

Since Pd was significantly improved using Eq. 3.8), we can conclude that the overall probability of the system is now bounded by Pa. Therefore, for future works, the next logical step would be to improve the average BER estimate of the pair of transmit antennas, Pa, in order to further improve the connection reliability of GSM systems.

## Future Works

Second, this chapter shows that the GSM-CR system is bound by the error probability of antenna par estimation. Future work should focus on improving Pa to further improve the link reliability of GSM and GSM-CR systems. Finally, there are more advanced SM systems that further improve performance compared to GSM-CR, such as Space-Time Quadrature Spatial Modulation (ST-QSM), Generalized QSM (GQSM), and Extended QSM (EQSM) [36–38].

## Appendix: Derivation of the Q-function Derivation

Haas, “General Spatial Modulation,” in Conference Proceedings of the 2010 Asilomar Forty-Fourth Conference on Signals, Systems, and Computers, Nov. Yuan, “Incoherent spatial modulation and optimal design of APSK multi-ring constellation,” IEEE Communications Letters, vol. . Martinez, “Performance Analysis of Turbo Coded APSK Modulations over Nonlinear Satellite Channels,” IEEE Transactions on Wireless Communications, vol.

Ba¸sar, "Space-time Quadrature Spatial Modulation," in 2017 IEEE International Black Sea Conference on Communications and Networking (BlackSeaCom), 2018, pp. Therefore, an M-APSK GSM-CR system was developed to improve the overall link reliability of the conventional GSM system. The presented results show that the M-APSK GSM-CR system outperforms its equivalent GSM and SM systems for various AASC.

Block Diagram for the Alamouti System [12]

Block Diagram for the Labelling Diversity System [15]

Block Diagram for the Proposed Systems

System Model for M -APSK SM

APSK Constellations

Average BER - 6 bits/s/Hz Configuration

Average BER - 6 bits/s/Hz and 7 bits/s/Hz Configurations

Average BER - 7 bits/s/Hz and 8 bits/s/Hz Configurations

System Model for GSM-CR

GSM-CR Constellations, Key=ω 1 /ω 2

Block Diagram of Genetic Algorithm for CR Mapper Design

Illustrating the position of Genes in M -APSK Constellations

Average BER - 6 bits/s/Hz Configuration

Average BER - 7 bits/s/Hz Configuration

Average BER - 7 bits/s/Hz Configuration

Average BER - 8 bits/s/Hz Configurations