The mixed analog-to-digital converters (ADC) architecture is a promising solution to the problem of high energy consumption of multiple-input multiple-output (MIMO) systems. In such a scheme, part of the received signals at the base station are quantized by high-resolution ADCs, while the others are quantized by one-bit ADCs. The signals quantized by the mixed-ADC architecture are correlated and non-identically distributed, which is different from the one-bit quantized MIMO systems. Moreover, unlike the previous works focusing on the achievable rate of mixed-ADC MIMO systems under linear detectors, we derive a closed-form expression of the ergodic mutual information between the transmit signals and the quantized outputs of the mixed-ADC architecture over Rayleigh channels, where the statistical property of the equivalent channel is characterized by random matrix theory. Then, we derive the power scaling law, which shows that reducing the transmit power will not sacrifice the transmission efficiency when the number of receive antennas increases. Furthermore, for any given number of antennas and user transmit power, the optimal number of one-bit ADCs for maximizing the energy efficiency is obtained. Moreover, constrained by a given hardware energy consumption, the theoretical mutual information shows obvious gains over the one of unquantized MIMO systems for low user transmit power.

Probabilistic shaping (PS) combined with bipolar amplitude shift keying modulation is a promising transmission scheme. However, such 1-dimensional PS scheme inevitably suffers shaping loss in Rayleigh fading channels due to the lack of signal diversity. In this paper, we design a rotated quadrature amplitude modulation based PS strategy. With the discrete inputs, the ergodic constellation constrained (CC) capacity is derived based on the mutual information conditioned on full channel state information available at the receiver, which is found to be mutually influenced by both the probability mass function (PMF) and the rotation angle (RA) of the input signals. Furthermore, the closed-form cutoff rate is also derived to simplify the analysis, which is the lower bound of the mutual information with finite decoding complexity. Correspondingly, the optimizations of RA and PMF are both considered for maximizing the ergodic CC capacity and the cutoff rate, respectively, where the single parameter RA is firstly obtained by the exhaustive search. And then, the optimal PMFs of the subproblem for the fixed RAs and the fixed constellation scaling factor are obtained. Furthermore, with this non-equiprobable transmission scheme, the closed-form pairwise error probability is derived for the first time, which also validates the superiority of the proposed PS scheme in comparison with the uniform schemes with elaborate rotations.

With the common property of the sparse structure, multi-carrier low density signature (MC-LDS) and low density parity-check (LDPC) codes can be combined into a joint sparse factor graph (JSFG) while the joint detection and decoding (JDD) algorithm could bring significant gains in terms of the bit error rate (BER). In this paper, considering the coupling character of the soft information interaction in the elaborate JSFG, we carve the distribution of the merged decoding soft information from both sides and theoretically analyze the error performance of the uplink LDPC-coded MC-LDS system. Correspondingly, not only the average BER but also the practical decoding threshold could be effectively derived for any given number of iterations. Furthermore, based on the theoretical analysis, we optimize the degree distribution of the JSFG by leveraging the differential evolution method. Finally, simulation results show that the practical threshold of the JDD receiver with the optimized code approaches the signal to noise ratio of the theoretical capacity.

Probabilistic shaping (PS) combined with amplitude shift keying modulation is a spectrally efficient transmission scheme. To exploit the shaping gain in fading channels, we design a rotated quadrature amplitude modulation (QAM) based PS strategy. With discrete inputs, we first derive the ergodic constellation constrained (CC) capacity, which is found to be mutually influenced by both the probability mass function (PMF) and the rotation angle (RA) of input signals. Correspondingly, the optimal PMF and RA for maximizing the ergodic CC capacity are attained by the alternative optimization method. Furthermore, based on this non-equiprobable transmission scheme, the closed- form pairwise error probability is obtained for the first time. Finally, compared with the uniform scheme with elaborate rotation, the proposed PS strategy shows more than 1 dB gain in terms of both the efficiency and the error performance.

Probabilistic shaping (PS) combined with bipolar amplitude shift keying modulation is a promising transmission scheme to increase spectral efficiency. Different from the existing design of the point to point communications, we propose a PS-based uplink nonorthogonal multiple access (NOMA) scheme for fading channels to support multiple connections simultaneously, where successive interference cancellation (SIC)-based maximum a posterior (MAP) detection is implemented at the receiver. To exploit the shaping gain for each user, we first theoretically analyze the ergodic channel capacity and the constellation constrained (CC) capacity with discrete-constellation inputs, respectively. And then, a multi-step optimization scheme for maximizing the ergodic CC capacity is proposed to obtain the optimal probability mass function (PMF) of these input signals. The order of optimization is inverse to the SIC decoding order so that for each specific user, the remaining multiuser interference is calculated based on the optimal PMF of the later decoded users. Furthermore, based on this non-equiprobable transmission scheme, the closed-form pairwise error probability expressions for each user are obtained for the first time. Finally, compared with the uniform scheme, the simulations show that the proposed PS NOMA strategies achieve more than 1 dB gain in terms of the error performance.

Hierarchical modulation (HM), a promising non-orthogonal multiple access scheme, is able to provide different levels of protection for data streams and achieve a rate region that cannot be realized by traditional orthogonal schemes. In this paper, we propose a novel HM system with non-uniform constellation inputs and analytically derive the bit-interleaved coded modulation (BICM)-capacity for each user by means of the mutual information. Different from the power optimization method for the superimposed uniform constellation, we directly optimize the constellation positions in conjunction with the optimal binary labels design for HM in additive white Gaussian noise channels. For maximizing the BICM-capacity, we propose a fairness balanced criterion for HM system by considering both power constraints and user QoS constraints. Multi-start interior-point algorithm is proposed to deal with the constellation optimization problems. Numerical results show that the proposed HM verify the performance gains of optimized HM compared with the optimized quadrature amplitude modulation (QAM) based HM and other orthogonal transmission methods.

Sparse code multiple access (SCMA) is a promising non-orthogonal air-interface technology for its ability to support massive connections. In this paper, we design the multiuser codebook and the advanced decoding from the perspective of the theoretical capacity and the system feasibility. First, different from the lattice-based constellation in point-to-point channels, we propose a novel codebook for maximizing the constellation constrained capacity. We optimize a series of 1-D superimposed constellations to construct multi-dimensional codewords. An effective dimensional permutation switching algorithm is proposed to further obtain the capacity gain. Consequently, it shows that the performance of the proposed codebook approaches the Shannon limit and achieves significant gains over the other existing ones. Furthermore, we provide a symbol-based extrinsic information transfer tool to analyze the convergence of SCMA iterative detection, where the complex codewords are considered in modeling the a priori probabilities instead of assuming the binary inputs in previous literature. Finally, to approach the capacity, we develop a low-density parity-check code-based SCMA receiver. Most importantly, by utilizing the EXIT charts, we propose an iterative joint detection and decoding scheme with only partial inner iterations, which exhibits significant performance gain over the traditional one with separate detection and decoding.