Implementation aspects of list sphere decoder algorithms for MIMO-OFDM systems

We present a hybrid soft detector that has a good performance/complexity trade-off for a multiple-input multiple-output (MIMO) wireless communication system with known channel information. The new soft detector combines the merits of a simple unstructured least-squares (LS)-based soft detector and a list sphere decoder (LSD)-based soft detector for data bit detection. The former is computationally much more efficient than the latter at the cost of poorer performance. The poor performance of the former occurs mainly when the channel matrix is ill-conditioned. Whenever this happens, we use the LSD-based soft detector in the hybrid soft detector; otherwise, we use the LS-based one. Moreover, we provide a tight radius for a sphere decoder, a hard detector, via using the output of an LS-based hard detector. These two hard detectors are needed to determine if LS or LSD should be used in the hybrid soft detector. As an application example, we consider doubling the maximum data rate of the IEEE 802.11a conformable wireless local area networks by a MIMO system with two transmit and two receive antennas. For this application, the new soft detector is about 10 times faster than the LSD-based one and is about 10 times slower than the LS-based one. Yet the packet error rate due to using the new soft detector is quite close to that of using the LSD-based one.

The optimal detection for coded system requires the use of a maximum a posteriori (MAP) detection. A list sphere detector (LSD) can be used to approximate the MAP detector. Depending on the used list size, LSD provides a tradeoff between the performance and the computational complexity. The LSD output candidate list is used to calculate the approximation of the probability log-likelihood ratio (LLR) of each transmitted bit. The list should be large enough and it should include at least one candidate for both possible bits for good approximation. The use of a small list size causes inaccurate and, especially, very large LLRs that prevent the decoder from correcting the falsely detected signals and, thus, degrades performance. We study the effect of the LLR clipping to the performance and complexity of the LSD algorithm. We show that by limiting the dynamic range of the LLR the required LSD list size can be decreased, and, thus, the complexity of the algorithms is decreased. The optimal dynamic range values for LLR clipping are determined and the effect of the clipping to the complexity of the LSD algorithms is analyzed.

Polar codes, first achieving the capacity of symmetric binary-input discrete memoryless channels (B-DMCs), have been standardized for eMBB control channels. Since 5G cellular requires flexible architecture which is realized by the software defined networking paradigm, efficient polar decoder is anticipated. Though successive cancellation list (SCL) decoder achieves satisfactory performance, it requires a large amount of memory. For short control channel codes, sphere decoder (SD) is an alternative, but costs unbearable time complexity at low signal-to-noise ratio. List sphere decoder (LSD) abandons the radius and keeps a list of best paths to gain a fixed complexity. However, LSD needs a large list size L for satisfactory performance. In this paper, an efficient software LSD with path pruning and efficient sorting is proposed. We recall the radius as the bound to delete the paths out of the sphere at very early levels. Since L is dynamic, efficient sorting is proposed to reduce the copy operations. Implemented with C++, the proposed decoder can reduce up to 65.3% latency compared with the original LSD, with the same performance and lower complexity.

A soft iterative detection and decoding (IDD) scheme based on the sphere decoding technique for coded multiple-input multiple-output spatial multiplexing (MIMO-SM) systems is considered in this paper. We propose a new approach to approximate the maximum a-posteriori (MAP) cost function by a quadratic function such that the MAP search can be carried out by list sphere decoding (LSD). Performance of the coded MIMO-SM system with this approach is evaluated by simulation. It is shown that the proposed approach can achieve performance comparable to an existing approach.

Being the first codes achieving the capacity of symmetric binary-input discrete memoryless channels, polar codes have been favorable and standardized for enhanced mobile broadband (eMBB) control channels. In future mobile communications, the entire system is required to be flexible and adaptive to varying scenarios. Therefore, efficient software implementation of polar decoder is expected. Existing software successive cancellation list polar decoder can achieve good performance but with a good memory consumption. For short control channel codes, a more memory-efficient alternative is sphere decoder, but its latency gives rise to another issue. Equipped with a breadth-first search to keep a fixed complexity, list sphere decoder (LSD) is also considered. To improve the performance of LSD, a software LSD with synchronous determination is proposed in this paper. We precalculate the synchro sets to improve the decoding, which leads to a performance gain. Meanwhile, the decoding process is simplified due to the precalculation, which attains even lower complexity. Implemented with C++ , the proposed decoder can achieve up to 2 dB performance gain compared with the existing LSD.

A detection scheme built on a combination of a simplified branch metric based search and refined calculation is proposed in this work to reduce the computational complexity of the quasi-maximum-likelihood (QML) detectors, such as the QR-decomposition combined with M-algorithm (QRD-M), list sequential sphere decoder (LISS) and list sphere decoding (LSD), for multiple-input multiple-output (MIMO) multiplexing systems, while maintaining similar performance to the original methods. More specifically, the proposed method utilizes a multiplication-free accumulated branch metric to first identify the potential candidates with significantly reduced search complexity. The optimal solution is then determined by the standard squared Euclidean distance metric from the initial candidates. The key idea of the proposed method lies in the fact that the best candidate identified by the simplified branch metric coincides with that of which is based on the conventional one with a high probability for a properly designed parameter. Numerical results demonstrates that the QRD-M detector using the proposed method achieves significantly better performance than the conventional one with comparable (or even less) computational complexity.

Instead of using sphere decoding, list sphere decoding (LSD) has been introduced to increase the reliability of log-likelihood ratio (LLR) in recent soft decoding schemes employing iterative detection and decoding (IDD). Although LSD provides improved performance, it does not obtain complexity gain due to signal-to-noise ratio (SNR) increment as it detects large number of lattice points. Especially, its inefficient scenario arises when it has to search for lattice points which have small affect for obtaining LLR with high reliability. In this paper, we study an efficient algorithm to remove such lattice points, which results in complexity reduction based on radius optimization.

This paper examines near capacity performance of Markov Chain Monte Carlo (MCMC) detectors for multiple-input and multiple-output (MIMO) channels. The proposed MCMC detector (Log-MAP-tb b-MCMC) operates in a strictly bit-wise fashion and adopts Log-MAP algorithm with table look-up. When concatenated with an optimized low-density parity-check (LDPC) code, Log-MAP-tb b-MCMC can operate within 1.2-1.8 dB of the capacity of MIMO systems with 8 transmit/receive antennas at spectral efficiencies up to ¿ = 24 bits/channel use (b/ch). This result improves upon best performance achieved by turbo coded systems using list sphere decoding (LSD) detector by 2.3-3.8 dB, leading to nearly 50% reduction in the capacity gap. Detailed comparisons of the Log-MAP-tb b-MCMC with LSD based detectors demonstrate that MCMC detector is indeed the detector of choice for achieving channel capacity both in terms of performance and complexity.

A performance comparison between convolutional coded vertical Bell-lab layered space time (V-BLAST) and groupwise space time trellis coded (GSTTC) multiple-input multiple-output orthogonal frequency division multiplexing (MIMO-OFDM) systems is presented in this paper. Both systems have the same data rate and employ receivers with comparable complexity, which are zero-forcing, minimum mean square error (MMSE) and list sphere decoder (LSD) based turbo receivers. Simulation results show that V-BLAST significantly outperform the GSTTC systems when MMSE or LSD based turbo receiver is applied, while GSTTC perform similarly to or better than the V-BLAST systems when zero-forcing detection algorithm is applied.

Loosely-synchronized code division multiple access (LS-CDMA) technology is an excellent CDMA technology and very suitable to be applied in the future wireless communication systems. When the multiple input multiple output (MIMO) technique is integrated, better performance and system capacity can be achieved. But the computational complexity of classical detection algorithm based on exhaustive searching, such as maximum-likelihood (ML) rule, is too high and inconvenient to realisation. Although sphere-decoding (SD) algorithm is able to greatly decrease the detection complexity due to the sphere-constrained searching, the decoding complexity is very high especially when the constellation has a lot of points and the number of antennas is large. A modified detection algorithm based on SD method is proposed in this paper, for the sake of further decreasing the complexity. It decodes according to the signal-noise-ratio (SNR). The detector outputs the zero-forcing (ZF) detection results when the SNR is relatively high, otherwise it subtracts these decoded signals from the original receiving signals and then decodes them by SD algorithm. The simulation results shows that the performance of such modified algorithm has little difference as compared with that of SD algorithm.

Faster-than-Nyquist (FTN) signaling is a candidate non-orthonormal transmission technique to improve the spectral efficiency (SE) of future communication systems. However, such improvements of the SE are at the cost of additional computational complexity to remove the intentionally introduced intersymbol interference. In this paper, we investigate the use of deep learning (DL) to reduce the detection complexity of FTN signaling. To eliminate the need of having a noise whitening filter at the receiver, we first present an equivalent FTN signaling model based on using a set of orthonormal basis functions and identify its operation region. Second, we propose a DL-based list sphere decoding (DL-LSD) algorithm that selects and updates the initial radius of the original LSD to guarantee a pre-defined number N <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</inf> of lattice points inside the hypersphere. This is achieved by training a neural network to output an approximate initial radius that includes N <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</inf> lattice points. At the testing phase, if the hypersphere has more than N <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</inf> lattice points, we keep the N <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</inf> closest points to the point corresponding to the received FTN signal; however, if the hypersphere has less than N <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</inf> points, we increase the approximate initial radius by a value that depends on the standard deviation of the distribution of the output radii from the training phase. Then, the approximate value of the log-likelihood ratio (LLR) is calculated based on the obtained N <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</inf> points. Simulation results show that the computational complexity of the proposed DL-LSD is lower than its counterpart of the original LSD by orders of magnitude.

Since the first communication systems were developed, the scientific community has been witnessing attempts to increase the amount of information that can be transmitted. In the last 10--15 years there has been a tremendous amount of research towards developing multi-antenna systems which would hopefully provide high-data-rate transmissions. However, increasing the overall amount of transmitted information increases the complexity of the necessary signal processing. A large portion of this thesis deals with several important issues in signal processing of multi-antenna systems. In almost every particular case the goal is to develop a technique/algorithm so that the overall complexity of the signal processing is significantly decreased. In the first part of the thesis a very important problem of signal detection in MIMO (multiple-input multiple-output) systems is considered. The problem is analyzed in two different scenarios: when the transmission medium (channel) 1) is known and 2) is unknown at the receiver. The former case is often called coherent and the later non-coherent MIMO detection. Both cases usually amount to solving highly complex NP-hard combinatorial optimization problems. For the coherent case we develop a significant improvement of the traditional sphere decoder algorithm commonly used for this type of detection. An interesting connection between the new improved algorithm and the H-infinity estimation theory is established, and the performance improvement over the standard sphere decoder is demonstrated. For the non-coherent case we develop a counterpart to the standard sphere decoder, the so-called out-sphere decoder. The complexity of the algorithm is viewed as a random variable; its expected value is analyzed and shown to be significantly smaller than the one of the overall exhaustive search. In the non-coherent case, in addition to the complexity analysis of the exact out-sphere decoder, we analyze the performance loss of a suboptimal technique. We show that only a moderate loss of a few dbs in power required at the transmitter will occur if a polynomial algorithm based on the semi-definite relaxation is used in place of any exact technique (which of course is not known to be polynomial). In the second part of the thesis we consider a few problems that arise in wireless broadcast channels. Namely, we consider the problem of the information symbol vector design at the transmitter. A polynomial linear precoding technique is constructed. It enables achieving data rates very close to the ones achieved with DPC (dirty paper coding) technique. Additionally, for another suboptimal polynomial scheme (the so-called nulling and cancelling), we show that it asymptotically achieves the same data rate as the optimal, exponentially complex, DPC. In the last part of the thesis we consider a quantum counterpart of the signal detection from classical communication. In quantum systems the signals are quantum states and the quantum detection problem amounts to designing measurement operators which have to satisfy certain quantum mechanics laws. A specific type of quantum detection called unambiguous detection, which has numerous applications including quantum filtering, has recently attracted a lot of attention in the research community. We develop a general framework for numerically solving this problem using the tools from the convex optimization theory. Furthermore, in the special case where the two quantum states are of rank 2, we construct an explicit analytical solution for the measurement operators. At the end we would like to emphasize that the contribution of this thesis goes beyond the specific problems mentioned here. Most algorithmic optimization techniques developed in this paper are generally applicable. While it is a fact that our results were originally motivated by wireless and quantum communications applications, we believe that the developed techniques will find applications in many different areas where similar optimization problems appear.

In this paper, a new joint symbol detection and channel estimation algorithm is proposed for MIMO-OFDM systems over frequency-selective fading channels using the variational Bayesian expectation-maximization (VBEM) algorithm. Since the VBEM algorithm can provide distribution-estimates of the parameters, the statistical information about the channel uncertainty is exploited to improve the evaluation of the extrinsic information in the soft-input soft-output detector which identifies the significant symbol combinations via list sphere decoder. In addition, two channel estimators are derived based on the posterior distributions of the transmitted symbols which are obtained from the space-time detection. The VBEM iterations are embedded in the turbo-processing of the receiver. Simulation results demonstrate that the proposed VBEM algorithm has more robust performance over the conventional EM techniques.

A complete solution to joint channel tracking and symbol detection for bit-interleaved MIMO-OFDM systems in a time-varying frequency-selective fading environment is proposed in this research. In the training mode, the Rao-Blackwellised particle filter (RBPF) is used to estimate the phase offset (PO) and the carrier frequency offset (CFO). In the data mode, based on a recursive EM procedure in conjunction with soft decoding, we develop an iterative algorithm that performs the minimum mean squared error (MMSE) channel estimation and the maximum a posterior (MAP) probability symbol detection jointly. The soft decoding module is composed of the list sphere decoder (LSD) and the soft-in-soft-out (SISO) channel decoder based on the BCJR algorithm. The performance of the proposed algorithm is evaluated via simulation. It is demonstrated that the new algorithm has robust performance in the presence of phase noise and the carrier frequency offset.

This thesis is about feature-based mobile robot navigation in unknown environments. The work is focusing on solving the problem of Simultaneous Localization and Mapping (SLAM) including feature extraction, estimation and complete map building solution. The robot platforms used in this work have the encoders for odometry and several laser scanners for exteroperceptive sensors. Simulations, real experiments and existing well known datasets are used in order to verify the performance of the developed algorithms. The algorithms developed in this thesis are features based meaning that instead of directly using raw sensory data geometric features are first extracted. This allows the filtering of noise from the sensors and the dynamics of the environment. More importantly, feature based approaches can reduce the amount of data needed to process, enabling the algorithms to scale in large environments. Another advantage of using features is the characteristic of better isolating informative patterns so that by exploiting specific knowledge of the environment, specialized algorithms can be easily adopted with different types of features. Several geometric features (points, lines, planes) are considered in this work. In this thesis, the relative mapping approach is adopted for solving the SLAM problem. This approach has many advantages. First, the mapping is decoupled from the estimation of robot pose so that the map estimation is independent from odometry errors. In other words, odometry errors do not affect and accumulate to the map estimate as in the absolute mapping approach. Second, the estimation does not involve the dynamics model of the robot which is identity in a relative mapping algorithm, meaning that only the observation model is considered in the estimation. A relative map has extra consistency problem compared to an absolute map. It is subject to the geometrical consistency problem which may generate an inconsistent absolute map after an transformation. However, having only observation model in the estimation gives an insight to separating nonlinearities from the iterative part of the estimator and thus minimize the effects of linearization errors. In this work, these subjects are investigated and reported. For some service robotic applications, especially for indoor office-like environments, we would like to have a fast, robust and lightweight approach which is capable to perform real-time SLAM on minimal hardware platforms. By exploiting some known knowledge about the structure of the environment, we claim to be able to achieve that goal. Particularly, the OrthoSLAM algorithm has been developed for building 2D and 3D maps. The algorithm adopts the Orthogonality assumption (or constraint) on the environment. First, the complexity of the SLAM algorithm is significantly reduced. Second, the linearization error from the robot heading uncertainty is removed and thus the map consistency is greatly improved. Implementations of the developed algorithms are tested on simulated data, on existing real world datasets and on robot platforms. Existing algorithms used in this work have been also reimplemented. The performance of the algorithms are analysed and compared on well chosen criteria. Particularly, the issues on computational complexity, linearization error, map consistency, map precision, realtime capability are investigated.