Shugong Xu

Efficient architecture for soft-output massive MIMO detection with Gauss-Seidel method

In massive multiple-input multiple-output (MIMO) uplink, the minimum mean square error (MMSE) algorithm is near-optimal and linear, but still suffers from high-complexity of matrix inversion. Based on Gauss-Seidel (GS) method, an efficient architecture for massive MIMO soft-output detection is proposed in this paper. To further accelerate the convergence rate of the conventional GS method with acceptable overhead complexity, a truncated Neumann series of the first 2 terms, is employed for initialization. The architecture can meet various application requirements by flexibly adjusting the number of iterations. FPGA implementation for a 128 × 8 MIMO demonstrates its advantages in both hardware efficiency and flexibility.

Efficient matrix inversion architecture for linear detection in massive MIMO systems

Resulted by the hundreds of antennas at the base-station (BS) side, the dimension of matrices involved in linear detection for massive multiple-input multiple-output (MIMO) uplink systems increases drastically. Being an indispensable part of linear detection, the matrix inversion suffers a lot from the huge matrix size of massive MIMO, and therefore becomes inefficient for realization. By achieving good tradeoff between complexity and performance, approximate matrix inversion via Neumann series now boosts one promising solution for linear detection of massive MIMO systems. In this paper, an efficient hardware architecture for approximate matrix inversion is proposed. This architecture is hardware efficient and suitable for various applications with different approximation precisions. FPGA implementation results of matrix inversion for 4 × 32 massive MIMO system have shown that the proposed architecture can achieve 56.7% higher frequency with only 58.9% hardware resources of its existing counterparts. Look-ahead transformations which can make the proposed architecture more suitable for high speed applications are also mentioned.

Coefficient adjustment matrix inversion approach and architecture for massive MIMO systems

Thanks to hundreds of antennas, spectral efficiency of massive multiple-input multiple-output (MIMO) systems has drastically increased. However, the resulting huge dimension of matrices involved in massive MIMO MMSE detection causes prohibitive complexity. Although large scale matrix inversion with Neumann approximation achieves good tradeoff between complexity and accuracy for i.i.d. massive MIMO channel, its convergency speed degrades seriously for correlated massive MIMO channel. To this end, in this paper the matrix inversion approach based on coefficient adjustment (CA), which is more adaptable to correlated channel with higher throughput, is proposed. The corresponding hardware architecture is also given. FPGA results have shown that for 4 × 32 MIMO system, the proposed architecture can achieve 69.4% higher frequency with only 49.1% hardware cost compared to Cholesky decomposition method. CA approach can also achieve 37.9% higher throughput than Neumann scheme for correlated channel on average.

Improved symbol-based belief propagation detection for large-scale MIMO

In this paper, BP detection based on belief propagation in real domain for large-scale MIMO systems is proposed. Numerical results have shown that, with quadrature phase shift keying (QPSK) modulation, this approach can show 1 dB performance improvement at the BER of 10-2, compared to conventional single-edge based BP (SE-BP) in complex domain. Based on the proposed BP detection, its symbol-based variation is also investigated for applications in large-scale MIMO systems with a high-order modulation. This symbol-based method successfully reduces computational complexity by avoiding large dimensional matrix inversion and decomposition. Since the proposed method can also shrink the constellation size, its complexity can be further reduced. Numerical simulation results and complexity comparison have demonstrated that the proposed symbol-based BP detection can show advantages in both performance and complexity compared to existing ones. Therefore, it is suitable for large-scale MIMO system applications, especially for those with high-order modulations.

Pipelined implementations of polar encoder and feed-back part for SC polar decoder

In this paper, we first reveal the similarity of polar encoder and fast Fourier transform (FFT) processor. Based on this, both feed-forward and feed-back pipelined implementations of polar encoder are proposed. It is pointed out that the feedback part of SC polar decoder is nothing but a simplified version of polar encoder and therefore can be pipelined implemented also. Moreover, a general approach which uniformly constructs most pipelined polar encoders via folding transformation is proposed. Implementation results have shown that both proposed pipelined polar encoder architectures achieve more than 98.3% complexity reduction and more than 9.86% speed-up compared to the conventional implementation.

Efficient iterative soft detection based on polynomial approximation for massive MIMO

In massive multiple-input multiple-output (MIMO) systems, linear minimum mean square error (MMSE) detection is near-optimal but involves large dimensional matrix inversion, which results in high complexity. To this end, Neumann series expansion (NSE) approximation, which avoids the direct computation of the matrix inversion, is recently investigated due to its low implementation complexity. Unfortunately, the complexity reduction can only be achieved well when the required number of the NSE terms L is small. To solve this problem, we proposed an iterative NSE (INSE) algorithm for MMSE detection at a manageable complexity even for large L. An approximation method based on NSE is proposed to compute the log-likelihood ratios (LLRs) for channel decoders. Both analytical and numerical results have demonstrated that, the overall complexity of the proposed soft-output MMSE-INSE algorithm is significantly reduced compared with the conventional NSE method and the Cholesky decomposition method, while keeping similar detection performance.

Segmented CRC-Aided SC List Polar Decoding

Because of the existence of channel noise, channel coding serves as an indispensable part of mobile communication system and the essential guarantee for the reliable, accurate, and effective transmission of information. As one of the most competitive channel code candidates for the 5th generation (5G) mobile communication, polar codes are the first codes which can provably achieve the symmetric capacity of binary-input discrete memoryless channels (B-DMCs). In this paper, the segmented CRC- aided successive cancellation list (SCA-SCL) polar decoding scheme is proposed for better tradeoff of performance and complexity. Numerical results on binary-input additive white Gaussian noise channel (BI-AWGNC) have shown that, at SNR of 0.5 dB, this approach successfully provides as high as 41.65% complexity reduction and similar decoding performance compared to state-of-the-art ones.

Efficient stochastic detector for large-scale MIMO

In this paper, a low-complexity stochastic belief propagation (BP) detector for large-scale MIMO is first proposed. Its efficient hardware architecture, with parallel pipeline, is presented in detail. Thanks to the stochastic approach, all arithmetic operations of the detector are implemented with simple logic structures. Several approaches which can potentially improve the detection performance are exploited. Simulation results have demonstrated that the stochastic BP detector can achieve similar detection performance compared with deterministic one for 32 × 32 MIMO system with 4-quadrature amplitude modulation (4-QAM). With the increase of antenna number, the detection performance improves at the linear expense of complexity and latency. Therefore, the proposed stochastic BP detector is suitable for large-scale MIMO system applications with good balance of detection performance and implementation complexity.

Low-complexity adaptive successive cancellation list polar decoder based on relaxed sorting

Due to its advantage of performance over other algorithms, successive cancellation list (SCL) decoding has become one of the most favorable algorithms for polar codes. However, it still suffers a lot from the linear increasing complexity with list size l. In this paper, an adaptive SCL polar decoder based relaxed sorting (RS) approach is proposed, which successfully reduces the sorting complexity by simplifying the list size with proposed metrics. First, we partition the candidate list simply by the mean of metrics, which certainly results in performance degradation compared to the conventional SCL decoder. Then a scaling factor is introduced to narrow the performance gap. The scaling factor is determined on the proposed Trade-off Metric between Performance and Complexity (TMPC) via numerical simulations. Comparison results have shown that the proposed adaptive SCL decoder can achieve similar decoding performance as the conventional SCL decoder with at least 10% reduction on the average list size and overall computational complexity.

Joint detection and decoding for MIMO systems with polar codes

As well known, the near-optimal K-best detection is popular in multiple-input and multiple-output (MIMO) systems. In this paper, we first propose the joint approaches of K-best detection and polar decoding. For joint detection and decoding (JDD) approach, both hard and soft decisions are considered. The simplified successive cancellation (SSC) decoding is exploited for hard decision, and the successive cancellation list (SCL) decoding is used as soft decision. The system setup for JDD is als o introduced, in which the modulation points across several channels are considered together. Simulation results have demonstrated the performance advantage of the JDD algorithms over the separated ones. For 1/2-rate polar codes, JDD schemes show 50% complexity reduction compared to the separated ones. Furthermore, by employing SSC hard decoding, the JDD algorithm is promising for high-throughput and low-complexity application s.