A Novel Optimal Precoder and Equalizer in $2\times 2$ MIMO VLC Systems for Vehicular Application

<p> Precoding is a technique which exploits transmission diversity by weighting the information stream, i.e. the transmitter sends the coded information to the receiver to achieve pre-knowledge of the channel. Visible light communication (VLC) channels inherently exhibit frequencyselective and multi-path fading effects that result in intersymbol interference (ISI) and thus reduces the data rate. To this end, optical multiple input multiple output (MIMO) can provide spatial diversity and thus achieve a high data rate. Inspired by these facts, we investigate different precoding and equalization schemes for 2 × 2 MIMO for the vehicle to vehicle (V2V-VLC) system. In this work, we consider three detection schemes, Zero Forcing (ZF), Maximum likelihood (ML), and Minimum Mean Squared Error (MMSE). Also, we consider flickering/dimming control and the nature of outdoor VLC channel as a frequency selective channel. Moreover, we investigate a transceiver considering perfect CSI based on different detection algorithms. Simulation results of the investigated transceiver demonstrate improvements in Bit Error Rate (BER) and Mean Squared Error (MSE) for the MMSE scheme </p>

The design of linear precoders or decoders for multiuser (MU) multiple-input multiple-output (MIMO) filterbank multicarrier (FBMC) modulations in the case of strong channel frequency selectivity is presented. The users and the base station (BS) communicate using space division multiple access (SDMA). The low complexity proposed solution is based on a single tap per-subcarrier precoding/decoding matrix at the base station (BS) in the downlink/uplink. As opposed to classical approaches that assume flat channel frequency selectivity at the subcarrier level, the BS does not make this assumption and takes into account the distortion caused by channel frequency selectivity. The expression of the FBMC asymptotic mean squared error (MSE) in the case of strong channel selectivity derived in earlier works is developed and extended. The linear precoders and decoders are found by optimizing the MSE formula under two design criteria, namely zero forcing (ZF) or minimum mean squared error (MMSE). Finally, simulation results demonstrate the performance of the optimized design. As long as the number of BS antennas is larger than the number of users, it is shown that those extra degrees of freedom can be used to compensate for the channel frequency selectivity.

In orthogonal frequency division multiplexing (OFDM), Fourier Transform (FT) is used as a modulation technique. To avoid inter-symbol interference (ISI) in OFDM by a time dispersive channel, a cyclic prefix (CP) is used which also reduces its spectral efficiency. wavelet packet transform (WPT) as a modulation scheme has been proposed for wireless communication. In this paper, WPT based OFDM is presented and proposed using minimum mean square error (MMSE) equalizer. Equalization is a major factor in wavelets. MMSE is proposed for wavelet based OFDM (WOFDM) based on WPT and compared with zero forcing equalizer (ZFE). The performance is measured for arbitrary magnitude finite impulse response (FIR) channels in the presence of additive white Gaussian noise (AWGN) and impulse noise. Simulation results show a clear improvement in bit error rate (BER) for MMSE over ZFE equalization technique in the presence of noise.

In a companion paper, we have studied the zero-forcing (ZF) transceiver with decision feedback equalizer (DFE) over slowly time-varying narrowband multiinput multioutput (MIMO) channels. The space-time generalized triangular decomposition (ST-GTD) was used for the design of ZF-DFE transceivers. The space-time geometric mean decomposition (ST-GMD) ZF transceiver minimizes both the arithmetic mean square error (MSE) at the feedback detector and the average uncoded bit error rate (BER) in moderate high signal-to-noise ratio (SNR). This paper addresses the design problem of DFE transceiver without zero-forcing constraint. In the first part, a channel independent temporal precoder is superimposed on the conventional block-wise GMD-based minimum mean square error (MMSE) DFE transceiver to take advantage of the temporal diversity. In the second part, ST-GTD is applied for the design of MMSE DFE transceivers. With accurate channel prediction and space-time powerloading, the proposed ST-GMD MMSE transceiver minimizes the arithmetic MSE at the feedack detector, and maximizes Gaussian mutual information. For practical applications, the ST-GTD MMSE transceiver which does not require channel prediction but shares the same asymptotic BER performance with the ST-GMD MMSE system is also developed. In the convex region, our analysis shows that the proposed MMSE transceivers has better BER performance than the conventional GMD-based MMSE transceiver; the average BERs of the proposed systems are nonincreasing functions of the ST-block size. The superior performance of ST-GMD MMSE transceiver over the ST-GMD ZF transceiver is also verified analytically.

Multi-user multiple-input multiple-output (MU-MIMO) systems in the indoor visible light communication (VLC) have attracted significant attention due to the use of the lighting-emitting diodes (LEDs) for illumination and communication. However, they experience performance degradation due to interference from multiple users and low modulation bandwidth requiring the development of mitigation techniques. This work proposes a joint transceiver design using the minimum mean square error (MMSE) to minimize interference for the VLC systems. The mean square error (MSE) is minimised assuming perfect channel state information (CSI) to suppress the interference. The developed results show the proposed transceiver design providing fair data transmission and improving the bit error rate (BER) over the zero-forcing (ZF) scheme. Moreover, the proposed transceiver design shows better convergence than the ZF scheme.

In this paper, linear precoding (LP) algorithm has been studied to improve the bit error rate (BER) performance of large scale multiple input multiple output (MIMO) system. A new technique of enhancing the BER performance of linear precoding algorithm without complexity in hardware and mathematical calculations is proposed and it is used on a traditional LP algorithms like a Maximum Ratio Transmission (MRT), a Zero-Forcing (ZF), a Regularized Zero-Forcing (RZF), and a Minimum Mean Square Error (MMSE) for Millimeter wave MU-MIMO communication system. A new technique is also used to mitigate the BER gab problem between (ZF, MMSE) and (RZF, MMSE) linear precoding algorithms. The result shows that with using the new technique, the BER performance of modified LP significantly outperform their traditional LP by 10−5 when using 4 element of BS antenna, 10−6 when using 16 element of BS antenna and mitigate the BER gab problem at different signal to noise ratio (SNR).

Visible Light Communication (VLC) has emerged as a powerful technique for wireless communication systems. Providing high data rate and increasing capacity are the major problems in VLC. Recent evidence suggests that Multiple Input Multiple Output (MIMO) technique can offers improved data rates and increased link range. This paper describes the design and implementation of visible light communication system in indoor environment exploring the benefits of MIMO. The specific objective of this research was to implement a 4×4 Multiple Input (LEDs) Multiple Output (photodetectors)-VLC communication system, where a 16 white power LEDs in four arrays are setting up at transmitter and four RX modules are setting up at receiver side without the need for additional power or bandwidth as well as analyze a mathematical model for a VLC- 4×4 MIMO with different modes such as the suitable angles to cover the entire room. The research designs practically an electronic circuit for the transmitter and receiver with inexpensive components. The power distribution of different propagation modes is calculated for Single Input Single Output (SISO) and MIMO channels in typical room dimensions. The results in this paper indicate that the power is distributed uniformly for entire room when implemented VLC-MIMO as compared to VLC-SISO. Furthermore, a 4×4 MIMO implementing VLC is compared in term of BER vs. SINR with SISO communication system for both Line of Sight (LOS) and Non Line of Sight (NLOS) propagation modes. Comparing the two results of LOS and NLOS, it can be seen that a 4×4 MIMO implementing VLC for LOS perform better than the same system with NLOS due to decreasing in the received power resulted from the multipath effect.

In orthogonal frequency-division multiplexing (OFDM) systems, it is generally assumed that the channel response is static in an OFDM symbol period. However, the assumption does not hold in high-mobility environments. As a result, intercarrier interference (ICI) is induced and the system performance is degraded. A simple remedy for this problem is the application of the zero-forcing (ZF) and minimum mean square error (MMSE) equalizers. Unfortunately, the direct ZF method requires the inversion of an NxN ICI matrix, where N is the number of subcarriers. When N is large, the computational complexity can become prohibitively high. As for the direct MMSE method, in addition to an NxN matrix inverse, it requires an extra NxN matrix multiplication, making the required computational complexity higher compared to the direct ZF method. In this dissertation, we first propose a low-complexity ZF method to solve the problem in single-input-single-output (SISO) OFDM systems. The main idea is to explore the special structure inherent in the ICI matrix and to apply Newton's iteration for matrix inversion. With our formulation, fast Fourier transforms (FFTs) can be used in the iterative process, reducing the complexity from O(N^3) to O(Nlog_2 N) . Also, the required number of the iteration is typically one or two. We also analyze the convergence behavior of the proposed method and derive the theoretical output signal-to-interference-noise-ratio (SINR). For the MMSE method, we first reformulate the MMSE solution in a way that the extra matrix multiplication can be avoided. Similar to the ZF method, we then exploit the structure of the ICI matrix and apply Newton's iteration to reduce the complexity of the matrix inversion. For a multiple-input-multiple-output (MIMO) OFDM system, the required complexity of the ZF and MMSE methods becomes more intractable. We then manage to extend the proposed ZF and MMSE methods for SISO-OFDM systems to MIMO-OFDM systems. It turns out that the computational complexity can be reduced even more significantly. Simulation results show that the performance of the proposed methods is almost as good as that of the direct ZF and MMSE methods, while the required computational complexity is reduced dramatically. Finally, we explore the application of the proposed methods in mobility-induced ICI mitigation for OFDM multiple access (OFDMA) systems, and in carrier frequency offset (CFO) induced ICI mitigation for OFDMA uplink systems. As that in OFDM systems, the proposed methods can reduce the required computational complexity, effectively.

Non orthogonal multiple access (NOMA) is used to maintain the throughput and fairness in communication system. It is also investigated in context of visible light communication (VLC). The bit-error-rate (BER) and channel performance like important parameters are improved by using equalizer. In this paper, NOMA multiple input multiple output (MIMO) based VLC system is analyzed using zero forcing equalizer with successive interface cancellation (ZF-SIC) and minimum mean square error (MMSE) equalizer with successive interface cancellation (MMSE-SIC) to enhance BER performance. Simulation results showed that MMSE-SIC improves BER by 3dB of signal-to-noise ratio (SNR).

This paper considers a cooperative wireless system with multiple antennas at the source. A multi-antenna relay equipped with a power splitter is introduced between the source and destination. It utilizes the energy from the received signal for amplification and transmit it to the destination. The linear precoding techniques such as zero forcing (ZF) and minimum mean square error (MMSE) are used to reduce the interference. We compare two antenna selection techniques viz. norm-based antenna selection (NBAS) and received signal-to-noise ratio (SNR) based antenna selection (RSBAS). It is analyzed that the NBAS and RSBAS antenna selection techniques offer improvement of 20% and 37% over random antenna selection technique. However, the antenna selection technique NBAS offers improvement in system bit error rate (BER) performance by 14% as compared to RSBAS at SNR value of 0 dB. We presented a scenario where the energy harvesting at relay node offers saving the battery power at the user node. Hence, the presented analysis is applicable in communication with remote sensors. This paper also analyses that the BER is improved with the reduction in the distance between source and relay for the given value of energy harvesting efficiency.

We investigate the use of the minimum mean-squared- error decision-feedback-equalizer (MMSE-DFE) as a preprocessor to reduce the computational complexity of symbol detection in frequency-selective multiple- input multiple-output (MIMO) channels. The preprocessor delays and focuses the received signal energy which reduces the effects of inter-symbol- interference and multiple-access-interference. This property of the MMSE-DFE preprocessor is exploited to order and to reduce the number of symbol candidates considered by an iterative maximum- likelihood (ML) detector. Simulations show that the proposed detection scheme can achieve lower bit- error-rates than existing reduced-complexity algorithms in overdetermined and underdetermined receive scenarios. Near-optimum performance is achieved when the number of symbol candidates is increased.

In this contribution, we consider the performance of multiple-input multiple-output (MIMO) code division multiple access (CDMA) system for digital image transmission over correlated Rayleigh fading channel. MIMO system employs multiple antennas both at the transmitter and receiver. In our work, we consider turbo coded system to investigate the performance of MIMO-CDMA system. We realize turbo code using parallel concatenated convolutional encoder and second convolutional encoder is preceded by random interleaver. Further the output of two convolutional encoder are punctured to get rate of ½. At the receiver, we employ iterative decoding algorithm to reduce the effect of multiple access interference (MAI) and Inter-Symbol-Interference (ISI) and median filters to reduce the effect of salt and pepper noise.. In particular, we evaluate the performance of coded MIMO-CDMA system using Zero forcing (ZF) - multi-user detection (MUD) and minimum mean square error (MMSE)-MUD detection technique to mitigate the effects of multi-stream interference (MSI). It is shown through the simulation study that our considered coded MIMO-CDMA system with MMSE algorithm achieves better picture quality with less signal-to-noise ratio (SNR) as compared to ZF MUD.

Wireless network is one of the most important things in the development of telecommunication. However, the existing wireless technology has not been able to efficiently create a very high data rate because it was very sensitive to fading. Therefore, Orthogonal Frequency Division Multiplexing (OFDM) technology combined with MIMO (Multiple Input Multiple Output) transceiver system was used to gain more diversity and bandwidth efficiency. The propagation performed on the OFDM MIMO system was multipath propagation. To reduce Intersymbol Interference (ISI) was used Zero Forcing (ZF) equalizer which works by combining channel response and equalizer response itself to eliminate ISI. This study aims to determine the effect of Zero Forcing Equalizer on OFDM MIMO system using rayleigh fading channel and compared the result with OFDM MIMO STBC system. The research method used was simulation using MatLab R2015a. The simulation results showed that the performance of OFDM MIMO ZF system was worse than OFDM MIMO STBC system i.e BER vs EbNo simulation, eye diagram simulation, and constellation diagram simulation. The OFDM MIMO ZF system was required an Eb / No value more than 25 dB to achieve BER 10-4 while the OFDM MIMO STBC system only required an Eb / No value of 10.5 dB to achieve BER 10-4. The eye pattern generated by the OFDM MIMO ZF system was more closed and the dispersion of constellation signals away from the ideal point while OFDM MIMO STBC system displayed a more open eye pattern and the dispersion of its constellation signal closer to the ideal point. It indicated more ISI occurs in the OFDM MIMO ZF system than that in OFDM MIMO STBC system.

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

Block data transmission is an efficient scheme to mitigate the inter-symbol interference (ISI) caused by dispersive channels. Recent research work attempt to obtain optimal designs of precoders given various linear and non-linear receivers. In this paper we focus on the systems with optimal precoder designs based on the minimization of bit error rate (BER) which is the more meaningful criterion in data communications. The linear receivers employed in these systems include zero-forcing (ZF) and minimum mean square error (MMSE) equalizers. Recently, block decision feedback equalization (DFE) has also been suggested to be used in the design of such block data transmission systems. We also revisit the jointly optimum designs of the precoder coupled with the DFE receivers. First we derive the block-data error rate for all of these different systems with their corresponding optimal precoders. Then we rank their performance accordingly. Simulation results are also obtained to verify our analysis. Later, we evaluate the computational complexity on the various systems and draw some conclusions on their relative merits. Finally, we derive the lower and upper bounds of bit error rate (BER) considering error propagation for systems employing nonlinear equalizers.