Wireless Communications and Mobile Computing

Volume 2018 (2018), Article ID 7603797, 11 pages

https://doi.org/10.1155/2018/7603797

## Nonuniform Code Multiple Access

^{1}Key Laboratory of Universal Wireless Communications, Ministry of Education, Beijing University of Posts and Telecommunications, No. 10 Xitucheng Road, Beijing, China^{2}Wuxi BUPT Sensory Technology and Industry Institute Co., Ltd., Wuxi, China

Correspondence should be addressed to Guixia Kang; nc.ude.tpub@gnakxg

Received 21 October 2017; Accepted 13 March 2018; Published 18 April 2018

Academic Editor: Güneş K. Kurt

Copyright © 2018 Cheng Yan 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

For sparse code multiple access advanced (SCMAA), the quality of initial information on each resource node and the convergence reliability of the detected user in each decision process were unsatisfactory at the message passing algorithm (MPA) receiver. Driven by these problems, this paper proposes a nonuniform code multiple access (NCMA) scheme. In the codebook design of NCMA, different transmitted layers are generated from different complex multidimension constellations, respectively, and a novel basic complex multidimension constellation design is proposed to increase the minimum intrapartition distance. Then a novel criterion of permutation set is proposed to maximize the sum of distances between interfering dimensions of transmitted codewords multiplexed on any resource node, where the number of nonzero elements of transmitted codewords is more than 1. On the other side, an advanced MPA receiver is proposed to improve the reliability of detection on each transmitted layer of NCMA. Simulation results show that the block error rate performance of NCMA outperforms SCMAA and sparse code multiple access (SCMA) under the same spectral efficiency.

#### 1. Introduction

Higher spectral efficiency is one of main requirements in future 5G system [1]. Compared with 4G system, future 5G system improves spectral efficiency by 5~15 times [1]. Driven by this requirement, nonorthogonal multiple access, such as sparse code multiple access (SCMA), is proposed. SCMA [2–5] was a multidimension codebook-based nonorthogonal multiple access [5, 6]. In SCMA, there were transmitted layers multiplexed on resource nodes. Each layer (a transmitted layer represents a transmitted user) had its dedicated codebook. A codebook contained a plurality of -dimension codewords [3, 4]. A -dimension codeword was a sparse column vector, where there were nonzero elements, and was generated from a complex -dimension constellation point by a binary mapping matrix. In order to improve spectral efficiency, more than one layer was multiplexed on limited resource nodes. The constellation length and size were the same in all the transmitted layers of SCMA.

In the SCMA scheme, the initial information of message passing algorithm (MPA) receiver was susceptible to noise and multipath fading, and the criterion of permutation set failed to increase power differences between transmitted codewords [4, 7]. Driven by these problems, a sparse code multiple access advanced (SCMAA) scheme was proposed [7]. Under the same minimum Euclidean distance, SCMAA increased the sum of distances between interfering dimensions of transmitted codewords multiplexed on each resource node, which could improve the quality of initial information of MPA receiver on its corresponding resource node compared with SCMA [7–9]. However, in the SCMAA scheme, the increase of the sum of distances between interfering dimensions of transmitted codewords multiplexed on each resource node was limited by the suboptimal minimum intrapartition distance (the minimum intrapartition distance is the minimum Euclidean distance between basic complex multidimension constellation points in each partition). Moreover, the criterion of permutation set of SCMAA failed to maximize the sums of distances between interfering dimensions of transmitted codewords on some resource nodes (detailed explanation is offered in fifth line of Section 3.3.2). Hence the quality of initial information of MPA receiver was unsatisfactory. On the other side, the increase of differences between the reliabilities of detections on all undetected transmitted layers in each decision process was limited by the uniform characteristic of SCMAA, and the criterion of permutation set of SCMAA did not increase the variance of the set of absolute differences between the sums of distances between interfering dimensions of transmitted codewords multiplexed on all resource nodes (detailed analysis is offered in Section 3.3.2 and the sixth paragraph of Section 4.2). Hence the convergence reliability of the detected layer in each decision process was unsatisfactory at the MPA receiver of SCMAA.

Driven by these problems, this paper proposes a nonuniform code multiple access (NCMA) scheme. Compared with SCMAA, some major improvements made in the proposed NCMA scheme are as follows. (i) Different transmitted layers of NCMA are generated from different complex multidimension constellations, respectively, while all the transmitted layers of SCMAA are generated from the same complex multidimension constellation. Therefore, in NCMA, the number of nonzero elements of transmitted codewords multiplexed on each resource node is totally different or not exactly the same (detailed explanation is offered in Section 3.2), and the number of nonzero elements occupied by each transmitted layer is totally different. However, in SCMAA, the number of nonzero elements of transmitted codewords multiplexed on each resource node is the same and so is the number of nonzero elements occupied by each transmitted layer. (ii) A novel basic complex multidimension constellation design is proposed. Compared with the basic complex multidimension constellation design of SCMAA, the proposed basic complex multidimension constellation design can further increase the minimum intrapartition distance. (iii) This paper proposes a novel criterion of permutation set, which can maximize the sum of distances (detailed definition is offered in the fourth paragraph of Section 3.3) between interfering dimensions of transmitted codewords multiplexed on any resource node, where the number of nonzero elements of transmitted codewords is more than 1. (iv) This paper proposes an advanced MPA receiver. At the proposed MPA receiver, the detection order of transmitted layers is fixed, and the function of initial information is equal to the function of initial information at traditional MPA receiver (traditional MPA receiver is short for the MPA receiver of SCMAA) multiplied by an amplification factor. On the other side, the complexity of the proposed MPA receiver is less than that of traditional MPA receiver (detailed explanation is offered in the fourth paragraph of Section 4.2).

Section 2 introduces the system model of NCMA. The codebook design of NCMA is presented in Section 3. The proposed MPA receiver and the performance analysis of NCMA scheme are offered in Section 4. Finally, in Section 5, the block error rate (BLER) performance of NCMA is compared with that of SCMAA and SCMA according to simulations.

#### 2. System Model

In NCMA system, there are transmitted layers multiplexed on resource nodes. Each transmitted layer has its dedicated codebook. A codebook contains a plurality of -dimension codewords. For layer , a -dimension codeword is generated by multiplying the binary mapping matrix by a point from the complex -dimension constellation , and the size of is . includes all-zero rows, and the rest can be expressed as identity matrix after removing the all-zero rows from . Hence each codeword of layer includes nonzero elements and zero elements. In NCMA system, different transmitted layers are generated from different complex multidimension constellations, respectively; that is, , . If , , , , and , the codebooks of transmitted layers of NCMA are shown in Figure 1.