Abstract
Improved low-density spreading (LDS) code designs based on the Gaussian separability criterion are conceived. We show that the bit error rate (BER) hinges not only on the minimum distance criterion, but also on the average Gaussian separability margin. If two code sets have the same minimum distance, the code set having the highest Gaussian separability margin will lead to a lower BER. Based on the latter criterion, we develop an iterative algorithm that converges to the best known solution having the lowest BER. Our improved LDS code set outperforms the existing LDS designs in terms of its BER performance both for binary phase-shift keying (BPSK) and for quadrature amplitude modulation (QAM) transmissions. Furthermore, we use an appallingly low-complexity minimum mean-square estimation (MMSE) and parallel interference cancellation (PIC) (MMSE-PIC) technique, which is shown to have comparable BER performance to the potentially excessive-complexity maximum-likelihood (ML) detector. This MMSE-PIC algorithm has a much lower computational complexity than the message passing algorithm (MPA).Code sets for MPA are designed similar to low-density parity-check (LDPC) codes to avoid cycles and to increase girth of the Tanner graph, code sets that are “optimal” for MMSE-PIC might not be optimal for MPA.
Highlights
H Igh spectral- and power-efficiency, massive connectivity and low latency are among the requirements for generation communications and these requirements are expected to increase in the future, as researchers turn their efforts towards sixth generation (6G) wireless communications
Used design criteria conceived for developing the low-density spreading (LDS) matrices have been presented
We conceived an improved LDS sequence design based on the Gaussian separability criterion
Summary
H Igh spectral- and power-efficiency, massive connectivity and low latency are among the requirements for generation communications and these requirements are expected to increase in the future, as researchers turn their efforts towards sixth generation (6G) wireless communications. Xiao et al [52] proposed a codebook design for multicarrier-lowdensity spreading aided multiple access (MC-LDSCMA) based on the maximization of the minimal user rate for practical finite alphabet signalling Another LDS signature spreading vector extension (LDSSVE) method is introduced by Zhang et al [38] for uplink OFDM systems. A joint sparse graph (JSG) based FBMC transceiver termed as JSG-FBMC was proposed for combining the single graphs of LDS, a low-density weight matrix, and LDPC codes, which represent popular NOMA, multicarrier modulation and channel coding techniques, respectively. All boldface lower case letters indicate column vectors and upper case letters indicate matrices, ()T denotes transpose operation, sgn denotes the sign function, |.| is the scalar magnitude, || · ||p denotes p norm, || · || || · ||2 is vector norm and E{·} denotes expected value
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