Efficient Low Complexity Turbo Equalization with Soft Interference Cancellation in MIMO System

A novel Frequency Domain Turbo Equalization (FD-TE) is proposed in multiple input multiple output (MIMO) systems, in which equalization is executed on Single Frequency Tone (SFT). It is proposed that received data from all receive antennas on one frequency tone are considered jointly, and then minimum mean square error (MMSE) equalization is implemented. This algorithm can reduce the calculation complexity greatly, and has the same performance as the conventional algorithms. After equalization, data from one transmit antenna on all frequency tones are processed together and transformed into time domain. Later, extrinsic Log-likelihood ratio (LLR) is calculated and sent to Soft-In Soft-Out (SISO) decoder. Theoretical deduction and simulation prove that it can obtain the same performance with a low complexity.

This paper investigates iterative frequency domain techniques for the reception of spatially multiplexed single carrier signals transmitted over frequency-selective multiple input multiple output (MIMO) channels. The investigated equalizers are based on the soft-cancellation (SC) and minimum mean square error (MMSE) altering technique for turbo-coded single carrier point-to-point MIMO systems. We consider two different transmit antenna separation techniques in the frequency domain: (1) antenna-by-antenna (AA) and (2) joint over antenna techniques (JA). (1) aims to separate signals in different layers by MMSE filtering antenna-by-antenna, whereas (2) aims to detect the composite signal comprised of the signals transmitted from the multiple antennas. In (2) the composite received signal is decomposed by using the spatial maximum a posteriori probability (MAP) algorithm. We evaluate performances in terms of frame error rate (FER) and throughput in point-to-point MIMO frequency-selective fading channels. Impacts of spatial correlation on performance of the two detectors are also investigated in this paper.

In recent years, multiple-input multiple-output (MIMO) systems, which use several transmit and receive antennas, have attracted much attention for high performance radio systems. In MIMO systems, the channel estimation is important to distinguish transmit signals from multiple transmit antennas. While the space-alternating generalized expectation-maximization (SAGE) algorithm is known to offer good channel estimation and data detection. We proposed earlier the minimum mean square error (MMSE)-based SAGE algorithm for MIMO systems where the MMSE estimation is used for channel estimation. We showed that the proposed MMSE-based SAGE algorithm can achieve the better bit error rate (BER) than the maximum likelihood (ML) detection with training symbols. The MMSE channel estimation needs the knowledge of the maximum Doppler frequency F <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</sub> for deriving the covariance matrix of the channel and the variance sigma <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> of additive white Gaussian noise (AWGN). Additionally, the computation of the MMSE channel estimation requires O(L <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> ) operations where L is the transmitted frame length. Thus, its computational complexity is high. In this paper, we propose a zero-forcing (ZF)-based SAGE algorithm for channel estimation and data detection in MIMO systems that does not need the knowledge of Fd and sigma <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> . Since the computation of the proposed ZF-based SAGE algorithm requires O(N <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> ) operations where N is the number of transmit antennas, its computational complexity is low. We show that the proposed ZF-based tracking SAGE algorithm with less computational complexity can achieve almost the same BER as that of the MMSE-based tracking SAGE algorithm

Multiple-input multiple-output (MIMO) systems can achieve high data-rate and high capacity transmission. In MIMO systems, the scheme that weight substreams based on minimum mean square error (MMSE) criterion at the transmitter using feedback channel state information (CSI) achieves good performance (denoted hereafter as MMSE precoder). However, if the optimum number of substreams is not selected based on CSI and methods for reducing the performance degradation due to feedback delay is not used, MMSE precoder cannot achieve the full performance possible. In this paper, we propose an MMSE precoder with mode selection for MIMO systems, which selects both the number of substreams and the modulation scheme for each substream to minimize the average BER at a fixed rate. We evaluate the BER of the proposed MMSE precoder with two methods for reducing performance degradation due to feedback delay, channel prediction and receive weight robust to feedback delay. We also evaluate the BER of the proposed MMSE precoder with the method that combines channel prediction with receive weight robust to feedback delay. Simulation results show that the BER of the proposed MMSE precoder is improved compared to that of the conventional MMSE precoder using the fixed number of substreams. We also show that the method that combines channel prediction with receive weight robust to feedback delay can achieve good BER even when the large feedback delay exists.

This paper reports on investigations into the effects of spatial correlation on channel estimation and capacity of a multiple input multiple output (MIMO) system. Minimum mean square error (MMSE) method is applied for channel estimation under a correlated channel scenario. Simulation results for a 4 times 4 MIMO system with the Jakes model describing a channel between a base station and a mobile station demonstrate a trade-off between the effects of spatial correlation, channel estimation and capacity. For low values of signal to noise ratio (SNR), spatial correlation decreases channel estimation errors and improves capacity. For high values of SNR, spatial correlation has a less pronounced effect on improving channel estimation and thus the MIMO capacity is adversely affected by the decreased channel matrix rank.

This chapter is attempted to provide a survey of the advanced concepts and related issues involved in Multiple Input Multiple Output (MIMO) systems. MIMO system technology has been considered as a really significant foundation on which to build the next and future generations of wireless networks. The chapter addresses advanced MIMO techniques such as polarization diversity and antenna selection. We gradually provide an overview of the MIMO features from basic to more advanced topics. The first sections of this chapter start by introducing the key aspects of theMIMO theory. TheMIMO systemmodel is first presented in a genericway. Then, we proceed to describe diversity schemes used in MIMO systems. MIMO technology could exploit several diversity techniques beyond the spatial diversity. These techniques essentially cover frequency diversity, time diversity and polarization diversity. We further provide the reader with a geometrically based models for MIMO systems. The virtue of this channel modeling is to adopt realisticmethods for modeling the spatio-temporal channel statistics from a physical wave-propagation viewpoint. Two classes for MIMO channel modeling will be described. These models involve the Geometry-based Stochastic ChannelModels (GSCM) and the Stochastic channel models. Besides the listedMIMO channel models already described, we derive and discuss capacity formulas for transmission over MIMO systems. The achieved MIMO capacities highlight the potential of spatial diversity for improving the spectral efficiency of MIMO channels. When Channel State Information (CSI) is available at both ends of the transmission link, the MIMO system capacity is optimally derived by using adaptive power allocation based on water-filling technique. The chapter continues by examining the combining techniques for multiple antenna systems. Combining techniques are motivated for MIMO systems since they enable the signal to noise ratio (SNR) maximization at the combiner output. The fundamental combing techniques are the Maximal Ratio Combining (MRC), the Selection Combining (SC) and the Equal Gain Combining(EGC). Once the combining techniques are analyzed, the reader is introduced to the beamforming processing as an optimal strategy for combining. The use of multiple antennas significantly improves the channel spectral efficiency. Nevertheless, this induces higher system complexity of the communication system and the communication system performance is effected due to correlation between antennas that need to be deployed at the same terminal. As such, the antenna selection algorithm for MIMO systems is presented. To elaborate on this point, we introduce Space time coding techniques for MIMO systems and we evaluate by simulation the performance of the communication system. Next, we emphasis on multi polarization techniques for MIMO systems. As a background, we presume that the reader has a thorough understanding of antenna theory. We recall the basic antenna theory and concepts that are used throughout the rest of the chapter. We rigorously introduce the 3D channel model over the Non-Line of Sight (NLOS) propagation channel for MIMO system with polarized antennas. We treat the depolarization phenomena and we study its effect on MIMO system capacity. The last section of the chapter provides a scenario for collaborative sensor nodes performing distributed MIMO system model which is devoted to sensor node localization in Wireless Sensor Networks. The localization algorithm is based on beamforming processing and was tested by simulation. Our chapter provides the reader by simulation examples for almost all the topics that have been treated for MIMO system development and key issues affecting achieved performance.

In conventional ways of fast responding and high performing model predictive control using Field Programmable Gate Arrays (FPGA), the approaches developed are applicable only to Single Input Single Output System (SISO). Many real time systems are Multiple Input Multiple Output (MIMO) systems and loop interaction is a major concern and has to be reduced in control of MIMO systems. Also, direct digital control with ability to solve the Quadratic Programming (QP) problem online, which can be applied to complex systems with fast response time and/or embedded applications and with limited computational resource for supervisory control approach, is required in many complex industrial MIMO systems. A novel direct digital control of Model predictive controller with FPGA for a MIMO system which considers and reduces loop interaction and which can also be implemented with very less investment is proposed here. The system was modeled from first principles and then simulated in Labview environment for MIMO system. Implementation of the system and response was verified for a stirred tank system. The proposed system has good performance in terms of reduction in loop interaction which is a major concern in implementation of controller for MIMO systems. Also, direct digital control of MIMO system instead of supervisory control was accomplished.

This paper considers the design of a practical low-density parity check (LDPC)-coded multiple-input multiple-output (MIMO) system composed of M transmit and N receive antennas operating in a flat-fading environment where channel state information (CSI) is assumed to be unavailable both to the transmitter and the receiver. A soft iterative receiver structure is developed, which consists of three main blocks: a soft MIMO detector and two LDPC component soft decoders. We first propose at the component level several soft-input soft-output MIMO detectors whose performances are much better than the conventional minimal mean square error (MMSE)-based detectors. In particular, one optimal soft MIMO detector and two simplified suboptimal detectors are developed that do not require an explicit channel estimate and offer an effective tradeoff between complexity and performance. In addition, a modified expectation maximization (EM)-based MIMO detector is developed that completely removes positive feedback between input and output extrinsic information and provides much better performance compared with the direct EM-based detector that has strong correlations especially in fast-fading channels. At the structural level, the LDPC-coded MIMO receiver is constructed in an unconventional manner where the soft MIMO detector and LDPC variable node decoder form one super soft-decoding unit, and the LDPC check node decoder forms the other component of the iterative decoding scheme. By exploiting the proposed receiver structure, tractable extrinsic information transfer functions of the component soft decoders are obtained, which further lead to a simple and efficient LDPC code degree profile optimization algorithm with proven global optimality and guaranteed convergence from any initialization. Finally, numerical and simulation results are provided to confirm the advantages of the proposed design approach for the coded MIMO system.

The research work in this dissertation addresses reduced complexity equalization technique for multipath channels with large delay spread. This has been one of the key challenges for high data rate impulse radio based Ultra-Wideband (UWB) communication systems using low cost receiver design. Our research focus is on developing efficient and effective tap selection techniques for non-uniformly spaced Minimum Mean Squared Error (MMSE) equalization and applying it to UWB systems to achieve high performance with reduced receiver complexity. In this dissertation, a new class of tap selection techniques based on Order Recursive Least Squares (ORLS) and Matching Pursuit (MP) algorithms is proposed for UWB multipath channel equalization in the presence of Inter Symbol Interference (ISI) and unknown co-channel interference. The proposed tap selection techniques are directly implemented based on training symbol sequence under Least Squares (LS) criterion without the need for explicit channel estimation. In addition, Diagonal Loading (DL) technique is incorporated into the tap selection and MMSE equalization processes to insure system robustness given limited number of training symbols in the case of practical implementation. The proposed tap selection based equalizer is shown to outperform the conventional uniformly spaced linear equalizer and is with reduced computational complexity. The LS based technique proposed for equalizer tap selection is then extended to receive antenna selection for high data rate UWB systems with multiple receive antenna elements to achieve improved performance in the presence of Narrow Band Interference (NBI). Based on the LS criterion, antenna selection techniques for Multiple Input Multiple Output (MIMO) systems are also explored in our research work. Novel transmit and receive antenna selection techniques are proposed for MIMO spatial multiplexing systems with linear receivers under LS criterion. Unlike conventional approaches, xii

In this treatise, we study the error-rate results of turbo coded multi-carrier interleave division multiple access (MC-IDMA) using multiple-input multiple-output (MIMO) system for up-link (UL) communications. In a multi-user system, users experience multi user interference (MUI), multi-path effects and inter antenna interference (IAI). Further, the antenna correlation reflects in the system performance. We consider sub-optimal multi-user detection techniques based on zero-forcing maximum-a-posteriori probability (MAP) Multi-user detection (MUD) and minimum mean square error (MMSE) MAP MUD in order to mitigate the effects of above mentioned interferences for our system. Further, we realize multi-carrier modulation to obviate the effects of multi-path propagations. Specifically we analyze the effects of four types of delay-spread distributions pertaining to LTE and SUI channel models in the UL MIMO MC-IDMA. Our computer simulation reveals that coded MC-IDMA with the non-linear MMSE-MAP algorithm obtain better error-rate results performance with fewer signals to noise ratio by mitigating MUI and multi-path propagations.

Consider a multiple input multiple output (MIMO) system with pulse amplitude modulation (PAM), where each transmit antenna is allowed to choose a different transmission delay. (We refer to this system as a MIMO system with asynchronous PAM.) Such MIMO systems have been studied before for increasing diversity and avoiding unintentional beamforming. We quantify the capacity/outage capacity improvement due to asynchronism and the corresponding spectral leakage (if any) for MIMO point-to-point and MIMO broadcast channels. We show that under commonly used transmitter spectral mask constraints, the channel has unbounded degrees of freedom. Synchronous PAM exploits only a finite number of these degrees of freedom, and asynchronism helps to improve capacity. For most cases of interest, two distinct shifts attain most of the capacity improvement. These gains are robust to interference from adjacent carriers. Analysis of the spectrum of the asynchronous PAM suggests that optimal water-filling based schemes are useful for improving capacity only in directional links due to possible spectral leakage, while uniform power allocation leads to capacity improvement without any extra spectral leakage.

In this paper, an improved and low-complexity signal detection approach for large-scale multiple-input multiple-output (MIMO) systems has been proposed. This approach utilizes the preconditioning technique to accelerate the conventional detection algorithm based on Gauss-Seidel (GS) iterative method, and achieves a detection performance close to the minimum mean square error (MMSE) detection algorithm with relatively small iteration counts. It also outperforms the counterparts based on the Neumann series (NS) expansion and the conjugate gradient (CG) method in poor propagation environments, such as MIMO systems with large loading or correlated factors. The corresponding architecture is also proposed with both novelty and scalability. It takes advantage of the cyclic-shift property of the GS method, and therefore facilitates the hardware implementation. Both numerical results and complexity analysis demonstrate that the proposed detector is efficient and suitable for large-scale MIMO systems.

Model reference robust control (MRRC) is derived for MIMO systems that have a right Hermite normal form which is SPR and diagonal, and then for systems whose right Hermite normal form is diagonal but not SPR. It is shown that MRRC of multiple input multiple output (MIMO) systems is an extension of model reference control (MRC) of MIMO systems and MRRC of SISO systems. Unwanted coupling exists in many physical MIMO systems. The recursive backstepping procedure used in non-SPR SISO systems cannot be directly applied to diagonal MIMO non-SPR systems without the introduction of the augmented matrix or a precompensator. It is shown that MRRC decouples MIMO systems using only input and output measurements rather than state feedback.

The singular value decomposition (SVD) is a popular technique used in multiple-input multiple-output (MIMO) systems to remove inter-antennas interferences in order to achieve the best performance. As a result, the MIMO channel is decomposed into a number of independent singular-input singular-output (SISO) channels with different weightings. In order to improve the performance, bit- and power-allocation strategies are required due to the unequal weighting coefficients. In contrast, the geometric mean decomposition (GMD) decomposes the MIMO channel into a number of equally weighted SISO channels with remaining inter-antenna interference which can be removed by using dirty paper precoding at the transmit side. Having equally weighted layers, the computational complexity required to implement bit- and power-allocation strategies decreases and GMD-based MIMO systems seem to be an appropriate solution. This paper analyses and compares the performance of SVD- and GMD-based MIMO systems affected by antennas correlation where QAM constellations are transmitted along the transmit antennas, demonstrating that the GMD-based one is more robust against antennas correlation. Furthermore, optimal and suboptimal bit- and power-allocation strategies are compared. This investigation demonstrates that the suboptimal solution provides a performance close to that offered by the optimal one but with a reduced computational cost.

For iterative detection and decoding (IDD) in multiple-input multiple-output (MIMO) systems, the log-likelihood ratio (LLR) of each coded bit can be found by an optimal bit-wise maximum a posteriori probability (MAP) detector. However, since this MAP detector requires a prohibitively high computational complexity, low-complexity suboptimal detectors are desirable. In this paper, lattice reduction (LR)-based MIMO detection is investigated to derive a low-complexity detector that can achieve near MAP performance for IDD. In order to approximate LLR values incorporating the extrinsic information provided by a soft-input soft-output (SISO) decoder, bit-wise LR-based minimum mean square error (MMSE) filters are derived. Furthermore, in order to minimize the performance degradation due to quantization (or rounding) errors in the LR-based detection, a low-complexity integer perturbed list generation method is proposed, where no tree search is used by taking advantage of a near orthogonal channel basis obtained by LR. Through a complexity analysis and simulations, it is shown that the proposed approach achieves near optimal performance, while the complexity is comparable with that of the MMSE soft cancellation method, which is known to be computationally efficient. As a bit-wise detector, a parallel implementation of the proposed method would be straightforward, which lowers the detection delay.