Block-Diagonal Geometric Mean Decomposition (BD-GMD) for Multiuser MIMO Broadcast Channels

Tomlinson-Harashima precoding (THP) can be combined with geometric mean decomposition (GMD) to decouple a multiple-input multiple-output (MIMO) channel into multiple single-input single-output (SISO) subchannels with identical signal-to-noise ratios (SNRs). The combined system is called GMD-THP MIMO system. As all subchannels for this system have identical SNRs, it is more convenient to design modulation/demodulation and coding/decoding schemes than other MIMO systems that have different SNRs among the subchannels. In this paper, we consider low-density parity-check (LDPC) coded GMD-THP MIMO systems. Modulo operation at the receiver is needed for THP decoding but it may generate modulo errors. These modulo errors cause the log likelihood ratio (LLR) values provided by conventional soft demapper to be very inaccurate. We propose an expanded soft demapper scheme to reduce the inaccuracy of the LLR values, by which significant performance improvement can be achieved for LDPC decoding. Furthermore, THP introduces power loss and modulo loss into the system. These two losses are related to the size of the modulo boundaries and therefore we derive the expressions for these two losses as functions of the modulo size factor. With these expressions, we find the optimal modulo size factor which achieves the minimum combined losses through doing a tradeoff between power loss and modulo loss. Computer simulations are presented to show that the tradeoff indeed improves the performance of the LDPC coded GMD-THP systems.

Tomlinson-Harashima precoding (THP) can be combined with geometric mean decomposition (GMD) to decouple a multiple- input multiple-output (MIMO) channel into multiple single-input single-output (SISO) subchannels with identical signal-to-noise ratios (SNRs). The combined system is called GMD-THP MIMO system. In this system, there is an increase in the transmission power caused by the interferences cancellation at the transmitter. To bind the transmission power, a modulo operation is used at the transmitter. However, there is still an overall increase in transmission power and this loss is referred to as power loss. A corresponding modulo operation at the receiver to demap the signals will create modulo errors. Performance loss due to the modulo errors is referred to as modulo loss. In this paper, we do a tradeoff between the power loss and the modulo loss to obtain the minimum combined loss. This tradeoff is achieved by adjusting the modulo size of the modulo operation. Detailed theoretical analysis of the power loss and modulo loss are done and from the analysis, the optimum modulo size for the tradeoff is found. Simulations are carried out to confirm the theoretical analysis and to prove that tradeoff improves the BER performance of the GMD-THP MIMO systems.

In this paper, a cyclic-prefixed (CP) system with pulse amplitude modulation (PAM) for uplink transmission in light-fidelity (LiFi) is discussed. LiFi supports bi-directional transmission, i.e., downlink and uplink transmissions. However, there have been only a few studies on uplink LiFi despite the fact that the uplink traffic demand increases due to frequent use of, for example, video call and live streaming services. The uplink transmission is designed such that a transmitter has a low peak-to-average ratio as well as a lower computational complexity using a CP in conjunction with PAM. We investigate three different schemes, namely linear equalization (LE) where only a feedforward filter is applied, decision feedback equalization (DFE) where a feedback filter is added at the receiver and Tomlinson-Harashima precoder (THP) where a feedback filter is added at the transmitter. Both feedforward and feedback filters are jointly optimized. In addition, we consider an optical wireless channel with reflections, randomly-located and randomly-oriented user equipment, a human body acting as a reflector and a limited linear dynamic range of a light emitting diode. We conclude that a DFE system is suitable in a low spectral efficiency region, where, compared to an LE system, up to 4 dB gain is achieved. A THP system is suitable for a high spectral efficiency region, where up to 5 dB gain compared to the LE and DFE systems is achieved.

We investigate the equalization and channel identification for space-time block coded signals over a frequency-selective multiple-input multiple output (MIMO) channels. The equalization is considered by taking into account the cyclostationarity of space-time block coded signals. The minimum mean square error (MMSE) solutions are derived for linear and decision feedback (DF) equalizers. Due to the redundancy induced by space-time block coding, a blind estimation for MIMO channels is investigated by using the subspace method. Together with pilot symbols, the semi-blind channel estimation can be used and it can result in less (bit error rate) performance degradation of the MMSE linear and DF equalizers.

A subspace beamforming method is presented that decomposes a multiple-input multiple-output (MIMO) channel into multiple pairs of subchannels. The pairing is done based on singular values such that similar channel capacity is obtained between different subchannel pairs. This new capacity balancing concept is key to achieving high performance with low complexity. We apply the subspace idea to geometric mean decomposition (GMD) and maximum-likelihood (ML) detection. The proposed subspace GMD scheme requires only two layers of detection/decoding, regardless of the total number of subchannels, thus alleviating the latency issue associated with conventional GMD. We also show how the subspace concept makes the optimization of ML beamforming and ML detection itself feasible for any K timesK MIMO system. Simulation results show that subspace beamforming performs nearly as well as optimum GMD performance, and to within only a few decibels of the Shannon bound.

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.

This paper considers the decomposition of a complex matrix as the product of several sets of semi-unitary matrices and upper triangular matrices in iterative manner. The innermost triangular matrix has its diagonal elements equal to the geometric mean of the singular values of the complex matrix. This decomposition, generalized geometric mean decomposition (GGMD), has one order less complexity than the geometric mean decomposition (GMD) if the target matrix is a diagonal matrix. GGMD can be used to design the optimal decision feedback equalizer (DFE) MMSE transceiver for arbitrary multi-input-multi-output (MIMO) channels. The GGMD transceiver shares the same performance as the transceiver designed by using GMD. For the applications over cyclic prefix system, the GGMD transceiver has K/ log 2 (K) times lower complexity1 than the GMD transceiver, where K is the number of subchannels and is a power of 2.

In this paper, we design a zero-forcing (ZF) Tomlinson-Harashima precoding (THP) and a minimum mean square error (MMSE) THP for multiuser MIMO relay system with direct link. Based on these precoding structures, we propose the optimal combining weights of the ZF THP and the MMSE THP in half duplex relay system, and the sub-optimal weights of MMSE THP to reduce feedback channel state information (CSI). Through the Monte Carlo simulation, we verify that the optimal weights combining method outperforms the constant weights combining method. In addition, we confirm that the performance of the sub-optimal weights combining method is close to the optimal method, while reducing the feedback CSI simultaneously.

The combined Block Diagonalization and Geometric Mean Decomposition (BD-GMD) is a precoding scheme that is asymptotically optimal for downlink Multi-User Multiple-Input-Multiple-Output(MU-MIMO)systems. BD-GMD eliminate the interference between different user channels in MU-MIMO system under ideal condition, which leads to an improvement of the quality of users’ channel and brings a promotion of system throughput. In a downlink MU-MIMO system, there are a large number of users, the base station need to select a subset of users to serve for the reason that the number of simultaneously supportable users with BD-GMD is limited by the number of transmitting and receiving antennas. In the past, we paid our attention mostly on how to maximize the total throughput. However, the fairness is ignored may lead to “starvation”, which means that some subscribers are not able to get service in unacceptable long time. We introduce proportional fair scheduling schemes (PFS) into the system to guarantee the fairness, and also propose new schemes. The proposed algorithms update the adaptive parameters indicating past channel quality in each time slot. According to current and past channel information, we can make better multi-user scheduling and improve the system performance while maintaining the users’ fairness.

The faster-than-Nyquist (FTN) signaling is a bandwidth-efficient technology which has drawn attention in the bandwidth-starved world. Since the symbols appear too early, inter-symbol interference (ISI) cannot be avoided in the receiver. Decision feedback equalization (DFE) cancellation is an efficient interference cancellation and signal detection schemes for FTN based communication system. However, since the noise isn't considered, the DFE scheme performs badly at low E b /N 0 . In order to further improve the detection performance, firstly, the detector based on minimum mean square error (MMS E) is investigated to at low E b /No, and then the precoding scheme is introduced in FTN signaling, including: singular value decomposition (SVD), geometric mean decomposition (GMD). Simulation results show that the GMD precoding can perform better than DFE.

In this paper, robust transceiver design with Tomlinson-Harashima precoding (THP) for multi-hop amplify-and-forward (AF) multiple-input multiple-output (MIMO) relaying systems is investigated. At source node, THP is adopted to mitigate the spatial intersymbol interference. However, due to its nonlinear nature, THP is very sensitive to channel estimation errors. In order to reduce the effects of channel estimation errors, a joint Bayesian robust design of THP at source, linear forwarding matrices at relays and linear equalizer at destination is proposed. With novel applications of elegant characteristics of multiplicative convexity and matrix-monotone functions, the optimal structure of the nonlinear transceiver is first derived. Based on the derived structure, the transceiver design problem reduces to a much simpler one with only scalar variables which can be efficiently solved. Finally, the performance advantage of the proposed robust design over non-robust design is demonstrated by simulation results.

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.

A 2-D shooting-and-bouncing (SBR) ray-tracing method considering ray reflect, transmission and diffraction is used to analyze antenna spacing effect on capacity complementary cumulative distribution functions(CCDFS) of indoor non-line-of-sight (NLOS) MIMO channel and indoor multiple-input multiple-output (MIMO) channel with line-of-sight (LOS) path. The results show that the capacities of MIMO channel with LOS path are less than NLOS MIMO channel capacities in general. But whether in indoor MIMO channel with LOS path or in NLOS indoor MIMO channel, capacities CCDFS of indoor MIMO systems with antenna spacing of 5/spl times/ can reach the theoretical independent and identically distribution (i.i.d) Rayleigh capacities nearly fully. With the decrease of antenna spacing, the capacities dropped also. And the less antenna spacing, the more difference between indoor NLOS MIMO channel capacities and capacities of MIMO channel with LOS path.

The geometric mean of the eigenvalues of multiple-input multiple-output (MIMO) channels is a parameter occurring in a variety of instances, including MIMO transceiver design based on the so-called geometric mean decomposition (GMD), and MIMO mutual information at high SNR. In this paper, we derive the asymptotic geometric mean of MIMO channel eigenvalues in the case where the entries of the channel matrix are independent and identically distributed. We demonstrate that the result can be easily extended to channels with an exponential correlation model. As an application of the result, we provide an analytical expression for the asymptotic system capacity of GMD-based transceivers

In this paper, we present the error probability expressions for a wideband coherent spatially correlated Multiple Input Multiple Output (MIMO) channel in low signal to noise ratio (SNR) regimes. Prior works have depicted a decrease in performance due to spatial correlation in high SNR regimes. This work proves that in a power limited broadband MIMO system, spatial correlation across the channel fading matrix elements improves the probability of error performance. In other words, spatial correlation impacts the MIMO performance differently in high SNR compared to low SNR (wideband) regimes.