The Design of Receiver with Low Complexity for PDMA System

As one of promising non-orthogonal multiple access scheme, pattern division multiple access (PDMA) scheme is considered to be one competitive multiple access technology for the fifth generation (5G) communications. The detection algorithm is the key technology to improve the system performance. Due to the PDMA patterns sparse nature, belief propagation (BP) become one effective receiver algorithm to achieve close to maximum likelihood (ML) detection performance with lower complexity. However, the complexity order is still exponential with the row weight of the PDMA pattern and the modulation index. A novel receiver based on expectation propagation (EP) algorithm is proposed in this paper to reduce the complexity order from exponential to linear. This paper makes a comparison on the two algorithms above in terms of system performance and complexity. Link-level simulation results show that the proposed EP receiver achieves nearly the same performance as the BP receiver with orders less complexity.


Introduction
The fifth generation (5G) wireless networks have higher performance indicators such as supporting massive connectivity, low latency and better coverage [1]. As one kind of non-orthogonal multiple access (NOMA) technique, pattern division multiple access (PDMA) [2,3] has excellent performance and is considered as a promising candidate for 5G multiple access technology. Based on former research about successive interference cancellation amenable multiple access (SAMA) [4,5], PDMA was proposed to face the higher performance index of 5G. The performance analysis on PDMA is performed in [6], where the analysis and simulation results show that PDMA outperforms the conventional OMA in terms of outage probability performance and sum data rate. In [7], the relevant researches on PDMA pattern design are carried out, where the authors proposed the pattern design methods and rules for 5G for application scenarios such as the massive Machine Type Communication (mMTC) and enhanced Mobile Broad Band (eMBB). Cooperative PDMA (Co-PDMA) proposed in [8] also showed the superiority of PDMA over OMA in the system throughput when considering cooperative networks..

Figure 1.
Block diagram of uplink PDMA system transceiver At the transmitter side, the users input bits set k b are encoded by channel encoder, then the PDMA encoding modulation modulates the channel encoding bits k c into the modulation symbols k x and map them onto the PDMA resource element (RE). At the receiver side, PDMA multi-user detector is used to detect multiplexing users on the same PDMA resource. The PDMA encoding process can be simply stated as follows. K users data are mapped onto N REs in the domain of time, frequency, or space. Each user has a distinguished PDMA pattern, k g is an 1 N  binary vector with binary elements "0" or "1", where the element "1" means that the user's data are mapped onto the corresponding RE, otherwise not. A PDMA pattern matrix [  , , , The received signal where k h is the uplink channel response vector of the k th user; where " e " indicates element-wise dot product of two matrices. Define , where x denotes the estimated value of the transmission symbol x , , , denote extrinsic information and priori information, respectively. Define   It should be noted that in equation (8), we used the max-log algorithm ( log exp(a) exp(b)) max(a, b)   ( ) and we define the posterior LLR of k x as follows: where 0 s denotes specific constellation point with all-zero bit sequence.

BP Algorithm
the joint optimum solution in (10) for x can be get by the approximation of partial solution. By using Bayesian theory to further deduce equation (10), we can get where, k  is the set consisted by all the constellations of user k ; is the time & frequency resource index set corresponding to the PDMA mapping pattern of user k . The problem in (11) can be resolved by BP detection algorithm. A multiple-user detection receiver based on the BP algorithm can be represented by a factor graph in Fig.  2. Where, VN, UN and CN denote the variable node, user node and channel node, respectively. In Fig. 2, there four types of information propagation, i.e., from the VN to UN, UN to VN, UN to CN and from CN to UN, which are denoted by 2 @ (12) where, , , is the information from channel decoder to user node. When log function and iteration are considered, (7) can further impressed by where,   Although using the sparsity of PDMA codewords can reduce the complexity , BP algorithm still has exponential complexity which is too high to accept in practice, especially for the scenarios wtih large codebook size and high overload.

EP Algorithm
The essential difference between EP and BP is that EP imposes an exponential family constraint on the messages. The main core idea of EP is to approximate a complex distribution p with another simple distribution q [9], which is constrained to lie in a family of "simple" distribution set  . Mathematically, the projection is expressed as is the Kullback-Leibler (KL) deivergence. If p   , the projection is simplified to identity mapping. However, in general, p   and hence the operation is a nonlinear projection. We make and   , , 1 , Let  be the set of complex Gaussian distribution, which is given by   Secondly, the convergence of the EP algorithm is investigated. Fig. 5 shows the convergence performance of EP algorithm when inner iteration is 2, 3, 4 and 5 times without outer iteration, where the BLER curves with 4 iterations nearly superpose with that with 5 iterations. So we can get the conclusion under the conditions given in Table I, EP algorithm converges when the outer iteration is up to 4.

Figure 5.
Convergence performance of EP algorithm without outer iteration Keeping the number of inner iterations to be 4 and increasing the number of outer iterations, we get the corresponding convergence performance as Fig. 6 shown. It is revealed that when the times of outer iteration is 3, the performance of EP algorithm tends to convergence.

Performance Comparison among Two Algorithms
In this subsection, we make a comparison among two algorithms with the number of inner and outer iterations to be 4 and 3. We evaluate the BLER performance between EP algorithm and BP algorithm with different spectrum efficiencies (SEs). Fig. 7 shows the BLER versus SNR under different SEs with parameter value set of 6 active users and 4 receive antennas. It is can be seen from Fig. 7 11 proposed EP receiver has a similar performance with BP receiver for SE=0.0625~0.375, while there is a slight performance loss for SE=0.4 (about 0.3 dB loss at BLER= 0.01).

Figure 7.
Performance comparison between BP algorithm and EP algorithm with different SE

Conclusion
In this paper, two detection algorithms for PDMA are introduced. From the analysis and simulation results, we can see that BP receiver is an effective style to make multiple user's data detection, however, it has higher complexity, while EP receiver has a good performance with acceptable complexity. Uplink link-level simulation results in this paper demonstrate that the proposed EP receiver with computation complexity significant reduction has nearly the same performance as the BP receiver, which implies its potential use in future 5G practical system implementations.