MIMO Decoder Research Articles

Low-Complexity Sphere Decoding for Polar-Coded MIMO Systems

For polar-coded MIMO systems, separate detection and decoding (SDD) is the traditional scheme. In SDD systems, sphere decoding (SD) is one of the competitive MIMO detection schemes. However, SD may not utilize the coding information sufficiently in SDD systems, causing an error-correction performance loss. The existed joint detection and decoding using breadth-first SD (BSD) improves the performance than SDD, whereas the limited search space still causes a performance loss. In this paper, we propose joint detection and decoding based on SD (SD JDD) for polar-coded MIMO systems to reach maximum likelihood (ML) bound. Subsequently, two approaches are further proposed to reduce the computational complexity. The first approach reduces the layers of the SD search tree by exploiting symbol synchro sets, which could accelerate the convergence of SD JDD. The second efficient approach performs multiple tree searches. A small initial radius of the sphere for the first search is assigned to reduce the search space. The ML optimality could be preserved by the following multiple tree searches with increasing radius. It is shown from the numerical results that the proposed JDD outperforms SDD by 3.1 dB at FER <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$=10^{-3}$</tex-math></inline-formula> for <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {P}(64, 32)$</tex-math></inline-formula> polar-coded <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$4\times {4}$</tex-math></inline-formula> MIMO system with 16-QAM modulation. Furthermore, compared with BSD JDD, the proposed JDD has an average computational complexity reduction of up to an order of magnitude at high signal-to-noise ratios while achieving even better performance for short code lengths.

Decoder Design for Massive-MIMO Systems Using Deep Learning

Designing a massive multiple-input multiple-output (M-MIMO) system is complex, time-consuming, and challenging. Conventional MIMO decoders are either inefficient or complex to implement for M-MIMO scenarios. Deep learning (DL) has recently emerged to perform many complex operations more efficiently within a shorter time. In this article, a DL-based iterative network (DLNet) has been proposed for signal decoding in M-MIMO systems. The proposed DLNet decoder is a 40 layer deep neural network (DNN) that can decode M-MIMO signals for uplink Rayleigh and correlated MIMO channels. With the knowledge of the received signals and the M-MIMO channels, the proposed DLNet decoder decodes the messages of all the users. The DLNet considers complex-valued Rayleigh and correlated MIMO channels while decoding. Its training converges faster than other available deep learning (DL) based MIMO decoders. During simulations, the required number of DNN layers, training iterations, and other network parameters are estimated to improve the proposed decoder's performance. In the M-MIMO perspective, the proposed DLNet has been evaluated for symbol-error-rate (SER) performance, algorithm complexity, and runtime requirement. Simulation results show that the SER of the proposed DLNet decoder performs better by at least 2 dB than other M-MIMO decoding techniques. The DLNet consumes 800 times less time during decoding than other MIMO decoders for equal transmitting and receiving antenna configurations. At the same time, it has 13 times fewer trainable parameters than the available detection-network algorithm.

Complex artificial neural network with applications to wireless communications

We have developed a complex artificial neural network based radio receiver technology. This is based on novel complex neurons and deep networks of them. This type of radio does not have MIMO decoder or demodulator in a classical sense but instead the radio learns to demodulate through training - and can potentially adapt to jamming through a learning process. This type of radio can continuously adapt to changing environment and can potentially increase interference resistance spectral efficiency of modern radio networks.Complex neurons can natively operate on complex numbers, including multiplying (scale, rotation) of the input data. These networks, however, have proven chaotic and the convergence has proven to be highly problematic. The difficulty of determining complex coefficients, i.e. training, has made the practical use of these networks difficult or impossible.In this research, a new type of neuron is used with a network architecture that avoids most of the issues plaguing the convergence and training of the network. Combination of a new neuron weight update algorithm and the use of layers with nonlinear selection functions and methods to avoid large single error values in backpropagation allow complex neural network to be trained with fast convergence.

Short Message Noisy Network Coding With Sliding-Window Decoding for Half-Duplex Multihop Relay Networks

In this paper, we present a cooperative relaying strategy for half-duplex multihop relay networks. This scheme consists of three parts: 1) relay selection to yield a layered relay network; 2) group successive relaying that establishes a relay schedule to efficiently exploit half-duplex relays; and 3) a cooperative relaying scheme named short message noisy network coding with sliding-window decoding (SNNC-SW) that outperforms other state-of-the-art information theoretical schemes with lower decoding complexity and delay. We derive an achievable rate region of the proposed SNNC-SW scheme and attain a closed-form rate expression in the asymptotic case for several network models of interests. We then focus on the first part of our relaying strategy regarding efficient relay selection. We develop interference-harnessing routing that exploits the fact that in SNNC-SW, interference is treated as a useful signal. We show that, due to the efficient treatment of interference, this scheme can outperform routing schemes that deploy store-and-forward, a solution previously proposed for practical wireless multihop networks. Finally, we develop a low-complexity successive decoder of our scheme (implemented by a conventional MIMO decoder), which is a solution that can readily be implemented in practice. It is shown that also this practical scheme provides a significant gain over routing (based on store-and-forward) and the performance gap increases as the network becomes denser.

グループ判定高次MIMOデコーダの演算量削減手法の提案

グループ判定高次MIMOデコーダの演算量削減手法の提案

A Modified Euclidean Norm Computation for Complexity Reduction in MIMO Decoder

In this paper, we propose a modified Euclidean norm computation for breadth-first signal decoder (BSIDE) that reduces the computational complexity without sacrificing the performance. We exploit the reordered channel representation and rewrite the Euclidean norm computation in a simpler form, which results at significant reduction in number of operations required to decode the transmitted symbols. Also from the simulation results, it is observed that the reduction in complexity is 59 % for 2 × 2 and 75 % for the 4 × 4 multiple-input multiple output systems when compared to BSIDE.

A 2-D Interpolation-Based QRD Processor With Partial Layer Mapping for MIMO-OFDM Systems

The rapid growth of wideband communication devices, such as smart phones and tablets, has dramatically increased the throughput requirements of communication systems. Multiple-input multiple-output orthogonal frequency division multiplexing (MIMO-OFDM) has been widely recognized as the potential technology to achieve this requirement. The main implementation bottleneck lies in the high-complexity MIMO detections for thousands of subcarrier symbols in the MIMO-OFDM receiver. The QR decomposition processor is an essential preprocessing module for many MIMO decoders because the QR decomposition helps improve the decoding efficiency significantly by providing the tree-search structure for the MIMO detection algorithms. This paper presents a low-complexity 2-D interpolation-based QR decomposition (2-D-IQRD) with a partial layer mapping scheme to reduce computational complexity. The proposed 2-D-IQRD processor also adopts a scaling technique to reduce the signal dynamic-range problem in the traditional IQRD algorithm. These proposed methods successfully address the limitation of the interpolation-based QRD processor caused by successive multiplications in layer mapping and inverse layer mapping. Therefore, the 2-D interpolation can greatly reduce complexity and improve the BER performance of fast-fading MIMO-OFDM systems. This paper designs and implements the proposed architecture using a 90-nm CMOS technology. The implementation results show that the proposed architecture achieves 45.6 MQRD/s.

Compressive image broadcasting in MIMO systems with receiver antenna heterogeneity

In this work we consider image delivery in MIMO broadcast networks with diverse channel quality and varying numbers of antennas across receivers. In such systems, performance is normally constrained by the weakest users with either a low channel SNR or only a single receive antenna. To address both dimensions of heterogeneity, we propose a new analog image delivery system that adapts seamlessly along both dimensions simultaneously. Our sender scales the DWT coefficients according to a power allocation strategy, and generates linear combinations of the coefficients using compressive sensing (CS), before transmitting them with amplitude modulation. On the receiving side, the received physical layer symbols are passed directly to the source decoder without conventional MIMO decoding, and the DWT coefficients are recovered using a CS decoder.There are two main contributions of our system. First, integrating CS into MIMO transmission ensures that the reconstructed image quality at the receivers is commensurate with both the channel SNR and the MIMO channel dimension. Second, we introduce a power allocation strategy to achieve a performance tradeoff between receivers with different antenna numbers. Experimental results show that the proposed system outperforms both the analog reference SoftCast and the conventional digital system known as HM-STBC. The average gain is 2.92dB over SoftCast for single-antenna users and 1.53dB over HM-STBC for two-antenna users.

Complexity reduction by sign prediction in tree traversal of MIMO decoder

Complexity reduction by sign prediction in tree traversal of MIMO decoder

Reduced-Complexity Robust MIMO Decoders

We propose a robust near maximum-likelihood (ML) decoding metric that is robust to channel estimation errors and is near optimal with respect to symbol error rate (SER). The solution involves an exhaustive search through all possible transmitted signal vectors; this search has exponential complexity, which is undesirable in practical systems. Hence, we also propose a robust sphere decoder to implement the decoding with substantially lower computational complexity. For a real 4 x 4 MIMO system with 256-QAM modulation and at SER of 10^{-3}, our proposed robust sphere decoder has a coding loss of only 0.5 dB while searching through 2360 nodes (or less) compared to a 65536 node search using the exact ML metric. This translates to up to 228 times fewer real multiplications and additions in the implementation. We derive analytical upper bounds on the pairwise codeword error rate and symbol error rate of our robust sphere decoder and validate these bounds via simulation.

From Nominal to True A Posteriori Probabilities: An Exact Bayesian Theorem Based Probabilistic Data Association Approach for Iterative MIMO Detection and Decoding

It was conventionally regarded that the approximate Bayesian theorem based existing probabilistic data association (PDA) algorithms output the estimated symbol-wise a posteriori probabilities (APPs) as soft information. In our recent work, however, we demonstrated that these probabilities are not the true APPs in the rigorous mathematical sense, but a type of nominal APPs, which are unsuitable for the classic architecture of iterative detection and decoding (IDD) aided receivers. To circumvent this predicament, in this paper we propose an exact Bayesian theorem based logarithmic domain PDA (EB-Log-PDA) method, whose output has similar characteristics to the true APPs, and hence it is readily applicable to the classic IDD architecture of multiple-input-multiple-output (MIMO) systems using the general M-ary modulation. Furthermore, we investigate the impact of the EB-Log-PDA algorithm's inner iteration on the design of EB-Log-PDA aided IDD receiver. We demonstrate that introducing inner iterations into EB-Log-PDA, which is common practice in conventional-PDA aided uncoded MIMO systems, would actually degrade the IDD receiver's performance, despite significantly increasing the overall computational complexity of the IDD receiver. Finally, we investigate the relationship between the extrinsic log-likelihood ratios (LLRs) of the proposed EB-Log-PDA and of the approximate Bayesian theorem based logarithmic domain PDA (AB-Log-PDA) reported in our previous work. Despite their difference in extrinsic LLRs, we also show that the IDD schemes employing the EB-Log-PDA and the AB-Log-PDA without incorporating any inner PDA iterations have a similar achievable performance close to that of the optimal maximum a posteriori (MAP) detector based IDD receiver, while imposing a significantly lower computational complexity in the scenarios considered.

RTL Design of High-Speed Sorted QR Decomposition for MIMO Decoder

RTL Design of High-Speed Sorted QR Decomposition for MIMO Decoder

Simplified Quantisation in a Reduced-Lattice MIMO Decoder

Symbol detection in a lattice-reduction aided MIMO receiver depends upon appropriate quantisation in the reduced lattice and this has previously been achieved using a shift-and-scale method. This paper describes a novel parity-based method that avoids the need to perform inversion of the reduction matrix and simplifies the computation involved in symbol estimation in MIMO receivers using QAM and PAM modulation schemes. The new algorithm is shown to be functionally identical to the shift-and-scale method.

Soft decision decoding of the orthogonal complex MIMO codes for three and four transmit antennas

Orthogonality is a much desired property for MIMO coding. It enables symbol-wise decoding, where the errors in other symbol estimates do not affect the result, thus providing an optimality that is worth pursuing. It also paves the way for low complexity soft decision decoding, which for orthogonal complex MIMO codes is known for two transmit (Tx) antennas, i.e. for the Alamouti code. We propose novel soft decision decoders for the orthogonal complex MIMO codes on three and four Tx antennas and extend the old result of maximal ratio combining (MRC) to cover all orthogonal codes up to four Tx antennas.As a rule, a sophisticated transmission scheme encompasses forward error correction (FEC) coding, and its performance is measured at the FEC decoder instead of at the MIMO decoder. We introduce the receiver structure that delivers the MIMO decoder’s soft decisions to the demodulator, which in turn cranks out the logarithm of likelihood ratio (LLR) of each bit and delivers them to the FEC decoder. This significantly improves the receiver, where a maximum likelihood (ML) MIMO decoder makes hard decisions at a too early stage. Further, the additional gain is achieved with stunningly low complexity.

A Proposition of 600 Mbps WLAN-Like System with Low-Complexity MIMO Decoder for FPGA Implementation

This paper deals with our works on developing a high-throughput wireless LAN using a group layered space-time (GLST) system with low-complexity MIMO decoder. It achieves the throughput of 600 Mbps for 30 meter propagation distance by utilizing 80 MHz bandwidth in the 5 GHz frequency band. Run test under channel model B of IEEE802.11TGn demonstrates its excellent performance. The register transfer level results show that the developed system is synthesized successfully and the prototyping in the target FPGA chips of Stratix II EP2S180F1508C4 gives the expected results.

A MIMO Decoder Accelerator for Next Generation Wireless Communications

In this paper, we present a multi-input-multi-output (MIMO) decoder accelerator architecture that offers versatility and reprogrammability while maintaining a very high performance-cost metric. The accelerator is meant to address the MIMO decoding bottlenecks associated with the convergence of multiple high-speed wireless standards onto a single device. It is scalable in the number of antennas, bandwidth, modulation format, and most importantly, present and emerging decoder algorithms. It features a Harvard-like architecture with complex vector operands and a deeply pipelined fixed-point complex arithmetic processing unit. When implemented on a Xilinx Virtex-4 LX200FF1513 field-programmable gate array (FPGA), the design occupied 43% of overall FPGA resources. The accelerator shows an advantage of up to three orders of magnitude (1000 times) in power-delay product for typical MIMO decoding operations relative to a general purpose DSP. When compared to dedicated application-specific IC (ASIC) implementations of mmse MIMO decoders, the accelerator showed a degradation of 340%-17%, depending on the actual ASIC being considered. In order to optimize the design for both speed and area, specific challenges had to be overcome. These include: definition of the processing units and their interconnection; proper dynamic scaling of the signal; and memory partitioning and parallelism.

Coding-Assisted Blind MIMO Separation and Decoding

Despite the widespread use of forward-error correcting (FEC) coding, most multiple-input-multiple-output (MIMO) blind channel-estimation techniques ignore its presence and instead make the simplifying assumption that the transmitted symbols are uncoded. However, FEC induces code structure in the transmitted sequence that can be exploited to improve blind MIMO channel estimates. In this paper, we exploit the iterative channel estimation based on a posteriori information for blind MIMO separation and decoding. Experiments show improvements that are achievable by exploiting the existence of coding structures and that our technique can approach the performance of a Bahl-Cocke-Jelinek-Raviv (BCJR) equalizer with perfect channel-state information in a reasonable signal-to-noise ratio (SNR) range. In addition, by splitting the FEC codeword over multiple blocks, the impact in performance of a bad-conditioned channel matrix can be kept at a reasonable level.

ML-based Tracking Algorithms for MIMO-OFDM

This article addresses the problem of tracking the carrier frequency offset (CFO) and sampling frequency offset (SFO) in burst MIMO-OFDM systems. The goal is to accomplish those tasks with the smallest possible piloting overhead (highest spectral efficiency). For that, we derive a precise mathematical model that describes the joint effect of a CFO and SFO on the received MIMO-OFDM subcarriers. The model unifies simpler, well-known results found in the literature. We use it for deriving maximum likelihood (ML) estimators for both impairments based on observations of received pilot subcarriers at the output of the FFTs of the receiver branches. This approach yields estimators that are independent of the type of MIMO decoder, located further downstreams. At the same time, the estimators are the ML-optimal processors of pilot information at the MIMO channel's output. A pair of corresponding tracking algorithms based on the estimators is proposed and evaluated by simulation. The results show that the variance of our estimators decreases with larger MIMO configurations, allowing for increased synchronization accuracy at low SNR, or for reducing the number of pilot subcarriers to maintain equal estimator variance. We also show that the proposed tracking algorithms operate robustly under imperfect channel state information and with modulation sizes ranging from 4-QAM to 64-QAM. The SNR loss of the proposed algorithms is below 0.1 dB in all the cases, while a conventional tracking approach is shown to have an SNR loss between 0.8 dB and 1.2 dB.

LLL Reduction Achieves the Receive Diversity in MIMO Decoding

Diversity order is an important measure for the performance of communication systems over multiple-input-multiple-output (MIMO) fading channels. In this correspondence, we prove that in MIMO multiple- access systems (or MIMO point-to-point systems with V-BLAST transmission), lattice-reduction-aided decoding achieves the maximum receive diversity (which is equal to the number of receive antennas). Also, we prove that the naive lattice decoding (which discards the out-of-region decoded points) achieves the maximum diversity.

An approximate MAP-based iterative receiver for MIMO channels using modified sphere detection

For coded multiple-input multiple-output spatial multiplexing (MIMO-SM) systems, the iterative receiver consisting of the MIMO detector and decoding can provide near optimal performance. While the sphere detection (SD) technique can be employed to implement the MIMO maximum likelihood (ML) detection with a lower complexity, some modifications of the SD have been proposed to provide a soft-decision for iterative receivers. In the paper, we propose an alternative approach that is based on a quadratic cost function to find the maximum a-posteriori (MAP) solution for the MIMO detection. Using the proposed approach, the MAP detection with the soft-decision can be straightforwardly implemented by the SD technique. Compared to the existing approach, in the new scheme, the soft-decision is well defined and it avoids a numerical instability in computing a soft-decision (which is an approximation of the log likelihood ratio (LLR)). Through simulation results, it is shown that the performance of the proposed scheme is comparable to that of the existing approach