A new multi-carrier M -ary differential chaos shift keying system with code index modulation, referred to as CIM-MC-M -DCSK, is proposed in this paper. In the proposed CIM-MC-M -DCSK system, the reference and information-bearing signals for each subcarrier can be transmitted simultaneously by using the orthogonal sinusoidal carriers, where the informationbearing signal adopts the M -DCSK modulation to further increase the data rate. With an aim to making full use of the system energy resources, the reference signals in all subcarriers are coded by a Walsh code to carry additional information bits. The analytical bit-error-rate (BER) expressions of the proposed CIM-MC-M -DCSK system are derived over additive white Gaussian noise (AWGN) as well as multipath Rayleigh fading channels. Furthermore, a noise-reduction scheme and a hierarchicalmodulation scheme are designed for the proposed system. In particular, the former scheme can significantly improve the BER performance while the latter scheme can provide different quality of service (QoS) for the transmitted bits according to their different levels of importance. Simulation results verify the accuracy of the analytical expressions and the superiority of the proposed systems.

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Low-density parity-check (LDPC) codes have attracted much attention in the past two decades since they can asymptotically approach the Shannon capacity in a variety of data transmission and storage scenarios. As a type of promising structured LDPC codes, the protograph LDPC codes not only inherit the advantage of conventional LDPC codes, i.e., excellent error performance, but also possess simple representations to realize fast encoding and efficient decoding. This paper provides a comprehensive survey on the state-of-the-art in protograph LDPC code design and analysis for different channel conditions, including the additive white Gaussian noise (AWGN) channels, fading channels, partial response (PR) channels, and Poisson pulse-position modulation (PPM) channels. Moreover, the applications of protograph LDPC codes to joint sourceand-channel coding (JSCC) and joint channel-and-physical-layernetwork coding (JCPNC) are reviewed and studied. In particular, we focus our attention on the encoding design and assume the decoder is implemented by the belief propagation (BP) algorithm. Hopefully, this survey may facilitate the research in this area.

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In wireless communications, spatial diversity techniques, such as space-time block code and single-input multipleoutput (SIMO), are employed to strengthen the robustness of the transmitted signal against channel fading. This article studies the performance of protograph-based low-density parity-check (LDPC) codes with receive antenna diversity. The authors first propose a modified version of the protograph extrinsic information transfer algorithm and use it for deriving the threshold of the protograph codes in a SIMO system. The authors then calculate the decoding threshold and simulate the biterror rate (BER) of two protograph codes (accumulate-repeat-by-3-accumulate (AR3A) code and accumulate-repeat-by-4-jagged-accumulate (AR4JA) code), a regular (3,6) LDPC code and two optimised irregular LDPC codes. The results reveal that the irregular codes achieve the best error performance in the low signal-to-noise-ratio (SNR) region and the AR3A code outperforms all other codes in the high-SNR region. Utilising the theoretical analyses and the simulated results, the authors further discuss the effect of the diversity order on the performance of the protograph codes. Accordingly, the AR3A code stands out as a good candidate for wireless communication systems with multiple receive antennas.

Hybrid beamforming (HBF) array structure has been extensively demonstrated as the practically-feasible architecture for massive MIMO. From the perspectives of spectral efficiency (SE), energy efficiency (EE), cost and hardware complexity, HBF strikes a balanced performance tradeoff when compared to the fully-analog and the fully-digital implementations. Using the HBF architecture, it is possible to realize three different subarray structures, specifically the fully-connected, the sub-connected and the overlapped subarray structures. This paper presents a novel generalized framework for the design and performance analysis of the HBF architecture. A parameter, known as the subarray spacing, is introduced such that varying its value leads to the different subarray configurations and the consequent changes in system performance. Using a realistic power consumption model, we investigate the performance of the generalized HBF array structure in a cellular infrastructure-toeverything (C-I2X) application scenario (involving pedestrian and vehicular users) using the single-path terahertz (THz) channel model. Simulation results are provided for the comparative performance analysis of the different subarray structures. The results show that the overlapped subarray implementation maintains a balanced tradeoff in terms of SE, EE and hardware cost when compared to the popular fully-connected and the sub-connected structures. The overlapped subarray structure, therefore, offers promising potentials for the beyond-5G networks employing THz massive MIMO to deliver ultra-high data rates whilst maintaining a balance in the EE of the network.

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A multi-access multiple-input multiple-output (MIMO) relay differential chaos shift keying cooperative diversity (DCSK-CD) system is proposed in this paper as a comprehensive cooperation scheme, in which the relay and destination both employ multiple antennas to strengthen the robustness against signal fading in a wireless network. It is shown that, with spatial diversity gains, the bit error rate (BER) performance of the proposed system is remarkably better than the conventional DCSK non-cooperation (DCSK-NC) and DCSK cooperative communication (DCSK-CC) systems. Moreover, the exact BER and close-form expressions of the proposed system are derived over Nakagami fading channels through the moment generating function (MGF), which is shown to be highly consistent with the simulation results. Meanwhile, this paper illustrates a trade-off between the performance and the complexity, and provides a threshold for the number of relay antennas keeping the user consumed energy constant. Due to the above-mentioned advantages, the proposed system stands out as a good candidate or alternative for energy-constrained wireless communications based on chaotic modulation, especially for low-power and low-cost wireless personal area networks (WPANs).Index Terms-multiple-input multiple-output (MIMO), relay, bit error rate (BER), differential chaos shift keying cooperative diversity (DCSK-CD), Nakagami fading channel.