Soft-input Soft-output Detection Research Articles

Fast Two-Stage Max-Log MAP Detection Schemes for the Soft-Input Soft-Output Detection of Coded Generalized Spatial Modulation Signals

Fast Two-Stage Max-Log MAP Detection Schemes for the Soft-Input Soft-Output Detection of Coded Generalized Spatial Modulation Signals

A Maximum Logarithmic Maximum a Posteriori Probability Based Soft-Input Soft-Output Detector for the Coded Spatial Modulation Systems

Soft-input soft-output (SISO) detector for the iterative detection and decoding of coded spatial modulation (SM) signals needs to compute the extrinsic bit log-likelihood ratio (LLR) associated with each detected bit. The maximum logarithmic maximum a posteriori (max-log-MAP) detector is known to perform closely to the optimal logarithmic maximum a posteriori (log-MAP) detector with much lower computational complexity. In this paper, we first apply several mathematical tricks to derive a new and low-complexity algorithm for the max-log-MAP detector. The proposed algorithm features a new tree pruning technique to visit few lattice points and a smart list administration technique to retain a max-log-MAP detector. By following the proposed algorithm, we then design a hardware architecture for SISO detection of coded SM signals over the scenario of 64-QAM symbols, 8 transmit antennas, and 4 receive antennas. Under the TSMC 40 nm CMOS technology, the VLSI implementation results reveal that our architecture requires 46.4K gates and leads to detection throughput 450 Mbps, while operating at clock frequency 400 MHz and consuming power 46 mW. Being the first hardware architecture for SISO detection of coded SM signals, our proposed low-cost max-log-MAP detector is very attractive.

Rate-Splitting for Multicarrier Multigroup Multicast: Precoder Design and Error Performance

Employing multi-antenna rate-splitting (RS) at the transmitter and successive interference cancellation (SIC) at the receivers, has emerged as a powerful transceiver strategy for multi-antenna networks. In this paper, we design RS precoders for an overloaded multicarrier multigroup multicast downlink system, and analyse the error performance. RS splits each group message into degraded and designated parts. The degraded parts are combined and encoded into a degraded stream, while the designated parts are encoded in designated streams. All streams are precoded and superimposed in a non-orthogonal fashion before being transmitted over the same time-frequency resource. We first derive the optimized RS-based precoder, where the design philosophy is to achieve a fair user group rate for the considered scenario by solving a joint max-min fairness and sum subcarrier rate optimization problem. Comparing with other precoding schemes including the state-of-the-art multicast transmission scheme, we show that the RS precoder outperforms its counterparts in terms of the fairness rate, with Gaussian signalling, i.e., idealistic assumptions. Then we integrate the optimized RS precoder into a practical transceiver design for link-level simulations (LLS), with realistic assumptions such as finite alphabet inputs and finite code block length. The performance metric becomes the coded bit error rate (BER). In the system under study, low-density parity-check (LDPC) encoding is applied at the transmitter, and iterative soft-input soft-output detection and decoding are employed at the successive interference cancellation based receiver, which completes the LLS processing chain and helps to generate the coded error performance results which validate the effectiveness of the proposed RS precoding scheme compared with benchmark schemes, in terms of the error performance. More importantly, we unveil the corresponding relations between the achievable rate in the idealistic case and coded BER in the realistic case, e.g., with finite alphabet input, for the RS precoded multicarrier multigroup multicast scenario.

Model-Driven Deep Learning for MIMO Detection

In this paper, we investigate the model-driven deep learning (DL) for MIMO detection. In particular, the MIMO detector is specially designed by unfolding an iterative algorithm and adding some trainable parameters. Since the number of trainable parameters is much fewer than the data-driven DL based signal detector, the model-driven DL based MIMO detector can be rapidly trained with a much smaller data set. The proposed MIMO detector can be extended to soft-input soft-output detection easily. Furthermore, we investigate joint MIMO channel estimation and signal detection (JCESD), where the detector takes channel estimation error and channel statistics into consideration while channel estimation is refined by detected data and considers the detection error. Based on numerical results, the model-driven DL based MIMO detector significantly improves the performance of corresponding traditional iterative detector, outperforms other DL-based MIMO detectors and exhibits superior robustness to various mismatches.

Bridging the Gap Between MMSE-DFE and Optimal Detection of MIMO Systems

In this paper, we propose a novel low-complexity, near-optimal soft-input soft-output detector for $\text {N}\times \text {M}$ multiple-input multiple-output (MIMO) systems. Our algorithm is based on the combination of minimum mean square error decision feedback equalization (MMSE-DFE) and conditional optimization. In a round-robin fashion, one symbol is detected using exhaustive search in such a way that all $\text {N}\times (\text {M}-1)$ submatrices of the baseband channel matrix are considered and the one with the best metric is chosen. This search over all columns of the channel matrix, which can be performed in parallel, has the advantages of improving the performance of the hard-output version of the detector, and refining the list of candidates for efficient implementation of the soft-output detector for MIMO systems with error correcting codes. In particular, it is shown that the error performance of the soft-output system is comparable to that of the list sphere decoder (LSD) but with much smaller list size, and hence smaller complexity than the latter. We also analyze the performance and complexity of the proposed algorithm and discuss different techniques to further reduce its complexity without affecting the performance. Finally, the obtained theoretical results are validated via simulations.

Performance and Complexity Evaluation of Iterative Receiver for Coded MIMO-OFDM Systems

Multiple-input multiple-output (MIMO) technology in combination with channel coding technique is a promising solution for reliable high data rate transmission in future wireless communication systems. However, these technologies pose significant challenges for the design of an iterative receiver. In this paper, an efficient receiver combining soft-input soft-output (SISO) detection based on low-complexity K-Best (LC-K-Best) decoder with various forward error correction codes, namely, LTE turbo decoder and LDPC decoder, is investigated. We first investigate the convergence behaviors of the iterative MIMO receivers to determine the required inner and outer iterations. Consequently, the performance of LC-K-Best based receiver is evaluated in various LTE channel environments and compared with other MIMO detection schemes. Moreover, the computational complexity of the iterative receiver with different channel coding techniques is evaluated and compared with different modulation orders and coding rates. Simulation results show that LC-K-Best based receiver achieves satisfactory performance-complexity trade-offs.

Efficient Soft-Input Soft-Output MIMO Chase Detectors for Arbitrary Number of Streams

We present novel soft-input soft-output (SISO) multiple-input multiple-output (MIMO) detectors based on the Chase detection principle [1] in the context of iterative and decoding (IDD). The proposed detector complexity is linear in the signal modulation constellation size and the number of spatial streams. Two variants of the SISO detector are developed, referred to as SISO B-Chase and SISO L-Chase. An efficient method is presented that uses the decoder output to modulate the signal constellation decision boundaries inside the detector leading to the SISO detector architecture. The performance of these detectors significantly improves with just a few number of IDD iterations. The effect of transmit and receive antenna correlation is simulated. For the high-correlation case, the superiority of SISO B-Chase over the SISO L-Chase is demonstrated.

A Dominance-Based Soft-Input Soft-Output MIMO Detector With Near-Optimal Performance

Iterative detection-and-decoding for multi-input multi-output (MIMO) communication systems require a soft-input soft-output (SISO) detection algorithm, which, in the optimal formulation, is well known to be exponentially complex in the number of transmitting antennas. This paper presents a novel SISO detector for MIMO systems, named SISO king decoder. It is a tree-search branch-and-bound algorithm, which exploits the properties of the channel matrix and the a-priori information on the transmitted bits to reduce the overall computational complexity. The proposed algorithm is compared with the SISO single tree-search sphere decoder [1]. Simulation results are provided to show the complexity reduction without relevant performance loss in terms of bit-error rate.

Bit-Clusters Trellis Search Based Iterative MIMO Detection Algorithm

A bit-clusters trellis-search (BCTS) based soft-input soft-output detection algorithm is proposed for iterative Multiple-Input Multiple-Output (MIMO) receivers. Compared to the symbol nodes trellis-search (SNTS) based MIMO detection algorithm, which significantly reduces the search complexity by limiting the number of candidates in each trellis stage compared to sphere decoding algorithm, the BCTS algorithm proposed in this article further reduces the number of candidates in the trellis. In the BCTS algorithm, we replace the symbol node in SNTS algorithm with bit-cluster that represents several relative symbols whose corresponding bit is 0 or 1 while the other bits are not concerned. Because the bit-cluster number is fewer than the symbol node number, the search complexity of proposed BCTS algorithm is much less than that of the SNTS algorithm. The simulation results show, by transforming symbol nodes to bit-clusters in trellis-search detection, the performance is improved nearly 0.5 dB when the bit-error-ratio reaches $$10^{-4}$$10-4; the complexity analysis shows the number of partial-Euclidian-distance (PED) comparisons and PED computations are approximately three and one times fewer than that of the SNTS algorithm respectively when constellation size is beyond 16. And this tendency will be more obvious with the transmit antenna number and constellation size increasing.

MMSE SQRD based SISO detection for coded MIMO-OFDM systems

In this paper, we propose a minimum mean square error (MMSE) sorted QR decomposition (SQRD) based soft-input soft-output (SISO) detection algorithm for coded multiple-input multiple-output orthogonal frequency division multiplexing (MIMO-OFDM) systems. The proposed detection is derived from the SISO MMSE detection, which is a popular detection strategy for iterative receivers. For each transmitted symbol in the proposed detection, a soft successive interference cancellation (SIC) is performed based on a posteriori probabilities of past detected symbols. Simulation results show that the proposed detection, while needing less computational efforts, achieves significant performance gain compared with the SISO MMSE detection.

Factor-Graph-Based Soft-Input Soft-Output Detection for Frequency-Selective MIMO Channels

In this letter we consider a MIMO communication system with iterative detection over a frequency-selective MIMO channel. We present a soft-input soft-output MIMO detector based on a cyclic factor graph representation and the sum-product algorithm with two different message schedules (serial and parallel). Computer simulations show that both schedules provide near-optimum performance in terms of bit error rate, while achieving a remarkable reduction in complexity compared to the optimal MAP detector.

Trellis-Search Based Soft-Input Soft-Output MIMO Detector: Algorithm and VLSI Architecture

In this paper, we propose a trellis-search based soft-input soft-output detection algorithm and its very large scale integration (VLSI) architecture for iterative multiple-input multiple-output (MIMO) receivers. We construct a trellis diagram to represent the search space of a transmitted MIMO signal. With the trellis model, we evenly distribute the workload of candidates searching among multiple trellis nodes for parallel processing. The search complexity is significantly reduced because the number of candidates is greatly limited at each trellis node. By leveraging the trellis structure, we develop an approximate Log-MAP algorithm by using a small list of largest exponential terms to compute the LLR (log-likelihood ratio) values. The trellis-search based detector has a fixed-complexity and is very suitable for parallel VLSI implementation. As a case study, we have designed and synthesized a trellis-search based soft-input soft-output MIMO detector for a 4 × 4 16-QAM system using a 1.08 V TSMC 65 nm technology. The detector can achieve a maximum throughput of 1.7 Gb/s with a core area of 1.58 mm2.

Efficient Soft-Input Soft-Output Tree Detection via an Improved Path Metric

Tree detection techniques are often used to reduce the complexity of a posteriori probability (APP) detection in multiantenna wireless communication systems. In this paper, we introduce an efficient soft-input soft-output tree detection algorithm that employs a new type of look-ahead path metric in the process of branch pruning (or sorting). While conventional path metrics depend only on symbols on a visited path, the new path metric accounts for unvisited parts of the tree in advance through an unconstrained linear estimator and adds a bias term that reflects the contribution of as-yet undecided symbols. By applying the linear estimate-based look-ahead path metric to an -algorithm that selects the best paths for each level of the tree, we develop a new soft-input soft-output tree detector, called an improved soft-input soft-output -algorithm (ISS-MA). Based on an analysis of the probability of correct path loss, we show that the improved path metric offers substantial performance gain over the conventional path metric. We also demonstrate through simulations that the proposed ISS-MA can be a promising candidate for soft-input soft-output detection in high-dimensional systems.

Sparsening filter design for iterative soft-input soft-output detectors

A large body of research exists around the idea of channel shortening, where a prefilter is designed to reduce the effective channel impulse response to some smaller number of contiguous taps. This idea was originally conceived to reduce the complexity of Viterbi-based maximum-likelihood equalizers. Here, we consider a generalization of channel shortening which we term "channel sparsening". In this case, a prefilter is designed to reduce the effective channel to a small number of nonzero taps which do not need to be contiguous. When used in combination with belief-propagation-based maximum a posteriori (MAP) detectors, an analogous complexity reduction can be realized. We address the design aspects of sparsening filters, including several approaches to minimize the bit error rate of MAP detectors. We devote attention to the interaction of the sparsening filter and detector, and demonstrate the performance gains through simulation.

MIMO-Aided Near-Capacity Turbo Transceivers: Taxonomy and Performance versus Complexity

In this treatise, we firstly review the associated Multiple-Input Multiple-Output (MIMO) system theory and review the family of hard-decision and soft-decision based detection algorithms in the context of Spatial Division Multiplexing (SDM) systems. Our discussions culminate in the introduction of a range of powerful novel MIMO detectors, such as for example Markov Chain assisted Minimum Bit-Error Rate (MC-MBER) detectors, which are capable of reliably operating in the challenging high-importance rank-deficient scenarios, where there are more transmitters than receivers and hence the resultant channel-matrix becomes non-invertible. As a result, conventional detectors would exhibit a high residual error floor. We then invoke the Soft-Input Soft-Output (SISO) MIMO detectors for creating turbo-detected two- or three-stage concatenated SDM schemes and investigate their attainable performance in the light of their computational complexity. Finally, we introduce the powerful design tools of EXtrinsic Information Transfer (EXIT)-charts and characterize the achievable performance of the diverse near-capacity SISO detectors with the aid of EXIT charts.

SISO Detection Over Linear Channels With Linear Complexity in the Number of Interferers

We consider detection over linear channels impaired by additive white Gaussian noise. For this general model, which describes a large variety of scenarios, novel detection algorithms are derived by applying the sum-product algorithm to a suitably designed factor graph. Being soft-input soft-output (SISO) in nature, the proposed detectors can be adopted in turbo processing without additional modifications. Among various applications, we focus on channels with known intersymbol interference, on frequency-division-multiplexed systems where adjacent signals are allowed to overlap in frequency to increase the spectral efficiency, and on code division multiple access systems. When compared with the existing interference-cancellation algorithms, the proposed schemes result very appealing in terms of tradeoff between performance and computational complexity. Particularly, the proposed schemes can approach or even outperform the performance provided by much more complex algorithms.

ASIC Implementation of Soft-Input Soft-Output MIMO Detection Using MMSE Parallel Interference Cancellation

Multiple-input multiple-output (MIMO) technology is the key to meet the demands for data rate and link reliability of modern wireless communication systems, such as IEEE 802.11n or 3GPP-LTE. The full potential of MIMO systems can, however, only be achieved by means iterative MIMO decoding relying on soft-input soft-output (SISO) data detection. In this paper, we describe the first ASIC implementation of a SISO detector for iterative MIMO decoding. To this end, we propose a low-complexity minimum mean-squared error (MMSE) based parallel interference cancellation algorithm, develop a suitable VLSI architecture, and present a corresponding four-stream 1.5 mm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> detector chip in 90 nm CMOS technology. The fabricated ASIC includes all necessary preprocessing circuitry and exceeds the 600 Mb/s peak data-rate of IEEE 802.11n. A comparison with state-of-the-art MIMO-detector implementations demonstrates the performance benefits of our ASIC prototype in practical system-scenarios.

Soft–Input Soft–Output Single Tree-Search Sphere Decoding

Soft-input soft-output (SISO) detection algorithms form the basis for iterative decoding. The computational complexity of SISO detection often poses significant challenges for practical receiver implementations, in particular in the context of multiple-input multiple-output (MIMO) wireless communication systems. In this paper, we present a low-complexity SISO sphere-decoding algorithm, based on the single tree-search paradigm proposed originally for soft-output MIMO detection in Studer (“Soft-output sphere decoding: Algorithms and VLSI implementation,” IEEE J. Sel. Areas Commun., vol. 26, no. 2, pp. 290-300, Feb. 2008). The new algorithm incorporates clipping of the extrinsic log-likelihood ratios (LLRs) into the tree-search, which results in significant complexity savings and allows to cover a large performance/complexity tradeoff region by adjusting a single parameter. Furthermore, we propose a new method for correcting approximate LLRs - resulting from sub-optimal detectors - which (often significantly) improves detection performance at low additional computational complexity.

Low Complexity, Quasi-Optimal MIMO Detectors for Iterative Receivers

We propose a novel family of Soft-Input Soft-Output detectors for iterative, point-to-point, MIMO receivers. Compared to the optimal Maximum A Posteriori receiver, low complexity is achieved restricting the detector search to small subsets of the entire QAM hyper-symbol constellation, through simple criteria. These criteria are applied to an improved version of the non-iterative Layered ORthogonal lattice Detector. We show that, notwithstanding the suboptimal low-complexity implementation, this detector approaches the EXtrinsic Information Transfer of the MAP detector. Therefore, when included in an iterative receiver it delivers the same performance. Furthermore, the deterministic complexity and highly parallelizable structure of the proposed detector are well suited for HDL and ASIC implementation. To focus on a specific setting, we consider the indoor MIMO wireless LAN 802.11n standard, taking into account errors in Channel Estimation and a frequency selective, spatially correlated channel model.

Improved linear soft-input soft-output detection via soft feedback successive interference cancellation

We propose an improved minimum mean square error (MMSE) vertical Bell Labs layered space-time (V-BLAST) detection technique, called a soft input, soft output, and soft feedback (SIOF) V-BLAST detector, for turbo multi-input multioutput (turbo-MIMO) systems. We derive a symbol estimator by minimizing the power of the interference plus noise, given a priori probabilities of undetected layer symbols and a posteriori probabilities for past detected layer symbols. For a low-complexity implementation, an approximate SIOF algorithm is presented, which allows for a time-invariant realization of the symbol ordering and an MMSE filtering process. Another implementation, referred to as the iterative SIOF algorithm is introduced, which decides on symbol detection order based on a posteriori symbol probabilities to improve the detection performance. Simulations performed on a space-time bit-interleaved coded modulation (STBICM) architecture over quasi-static MIMO fading channels demonstrate that the SIOF V-BLAST detector provides performance gains over previous turbo-BLAST detectors, most notably when more transmit antennas are used.