Low Complexity High-Performance Precoding Algorithms for mm-Wave MU-MIMO Communication System

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.

Capacity maximizing in massive MIMO with linear precoding for SSF and LSF channel with perfect CSI

In this paper, a new signal detection scheme for overloaded multiple-input multiple output (MIMO) systems is proposed. In MIMO signal detection with belief propagation (BP), a factor graph consists of many loops that arise high complexity and cause performance degradation due to outliers. Various schemes have been proposed to overcome these issues. In BP with maximal ratio combining (MRC) and minimum mean square error (MMSE) pre-cancellation, a conventional scheme applies MRC on received signals in advance to obtain diversity gain to improve bit error rate (BER) performance as compared with BP using only MMSE pre-cancellation. To achieve further performance improvement, BP using a combined channel matrix is proposed in this paper. In the proposed scheme, the number of observation nodes is increased by combining a part of an original channel matrix to the channel matrix with MRC and MMSE pre-cancellation to enhance diversity gain. Numerical results obtained through computer simulation show that the BER performance of the proposed scheme is superior to that of BP or BP with MRC and MMSE pre-cancellation. The proposed scheme improves BER performance by about 3.1 dB at a BER of 10<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−3</sup> as compared with the BP withMRC and MMSE pre-cancellation. The computational complexity of the proposed scheme increases as the number of rows of the additional channel submatrix. It is in the same order of magnitude as that of the original BP based MIMO detection scheme.

In this paper, precoding and receive filter matrices are designed such that minimum mean square error (MMSE) is achieved for interference alignment using 3-symbol extension in the multiple-input multiple-output (MIMO) X channels which comprise two transmitter-receiver pairs with M antennas at each transmitter/receiver. The performance of the proposed algorithm is demonstrated through numerical simulation and compared with the conventional scheme where the precoding matrices are randomly generated and the respective linear equalizers are employed at the receivers. The bit-error-rate (BER) performance of the proposed algorithm is superior compared with that of the conventional scheme across all signal-to-noise ratio (SNRs). Its BER improves with the iterative procedure to refine the precoding and receive filter matrices. Moreover, only a small number of iterations is required to achieve significant improvement in the BER performance.

This work proposes a new adaptive pilot pattern used for pilot arrangement at the mobile station and a new channel estimation at the base station. It addresses the bit error rate (BER) performance optimization of wireless channel estimation in massive multiple-input multiple-output systems. First, we propose a new adaptive pilot pattern (APP) that offers a lower BER than the conventional pilot patterns. Then, we suggest a new channel estimation algorithm based on the APP. It is called the shifted APP-channel estimation (SACE). As a result, APP guarantees an optimal BER performance for the different system configurations, channel models, and carrier frequencies. It offers better BER performance than conventional pilot patterns, such as the long-term evolution (LTE) pilot pattern. Moreover, the shifted APP-based channel estimation algorithm solves the error floor caused by the usage of multiple subcarriers. It also offers a signal-to-noise ratio (SNR) improvement that reaches 17 dB at BER $= 10^{-2}$ compared to the conventional minimum mean square error (MMSE) channel estimation.

An asymptotically minimum bit error rate (BER) linear block precoder is determined for block-by-block communication systems employing linear minimum mean square error (MMSE) equalisation and disjoint detection. The problem is solved by a two-stage optimisation procedure in which a lower bound on the BER is first minimised, and then it is shown how this minimised lower bound can be achieved. Simulation results show that the BER performance of the proposed scheme is superior to the standard MMSE precoder and several other conventional systems such as orthogonal frequency division multiplexing. At reasonable BERs, the signal-to-noise ratio (SNR) gain can be of the order of several decibels.

Equalisation is one of the most important algorithms to improve the Bit-Error-Rate (BER) performance in communication systems. In general, equalisation can be classified into two categories: linear and non-linear equalisation. The linear equalisers include Zero Forcing (ZF), and Minimum Mean Square Error (MMSE) equalisers. The non-linear equalisers include ZF and MMSE equalisers that are based on Successive Interference Cancellation (SIC). The ZF equaliser suffers from noise enhancement. The MMSE equaliser can mitigate the noise enhancement using the estimated Signal-to-Noise Ratio (SNR). The ZF-SIC and MMSE-SIC equalisers suffer from error propagation, and high computational complexity, respectively. In this paper, the Orthogonal Frequency Division Multiplexing (OFDM) system is modulated and demodulated using Inverse Discrete Wavelet Transform (IDWT), and DWT instead of Inverse Discrete Fourier Transform (IDFT) and DFT, respectively. Also, we propose a Joint Low-complexity Regularised ZF-SIC (JLRZF-SIC) equaliser that jointly performs the equalisation, and Carrier Frequency Offset (CFO) compensation with lower complexity using banded matrix approximation. The proposed JLRZF-SIC equaliser can accomplish the equalisation, and CFO compensation processes with low-complexity compared to the corresponding MMSE-SIC equaliser. Simulation results show that the proposed JLRZF-SIC equaliser outperforms different linearand non-linear equalisers.

Frequency-domain equalization (FDE) based on the minimum mean square error (MMSE) criterion can significantly improve the downlink bit error rate (BER) performance of DS-CDMA in a frequency-selective fading channel. However, the uplink BER performance degrades due to a strong multi-user interference (MUI). We have proposed frequency-interleaved single-carrier spread spectrum multi-access (SC-SSMA) with MMSE-FDE, in which the subcarrier components of each user's signal are interleaved onto a wider bandwidth. Since frequency-interleaving patterns assigned to different users are orthogonal to each other, frequency-interleaved SC-SSMA can avoid the MUI completely while achieving frequency diversity gain with MMSE-FDE. In this paper, transmit/receive antenna diversity is applied to frequency-interleaved SC-SSMA with MMSE-FDE to further improve the BER performance. Its conditional BER is derived for the given set of channel gains. The average BER performance is numerically evaluated using the derived conditional BER and is confirmed by computer simulation.

Beamforming (BF) with multiple receiving antennas significantly improves the bit error rate (BER) performance for a DS-CDMA system in a flat Rayleigh fading environment. However, BF fails to suppress multiple access interference (MAI) completely, which results in an irreducible BER floor. Furthermore, soft-decision Viterbi decoding (VD) with BF further lowers the BER floor. The BER performance difference between the minimum mean square error (MMSE) linear multiuser detector (MUD) and zero forcing (ZF) MUD increases with the eigenvalue spread of the code correlation matrix. BF with MUD performs better than MUD alone, and BF+VD is much more effective at combating MAI than MUD+VD for low to moderate SNRs. In this regime, the performance of BF+VD approaches that of BF+MUD+VD, which clearly offers the best performance for all SNRs.

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.

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.

A turbo receiver combined with CFO compensation in frequency-domain for OFDMA uplink

This paper presents some experimental results on both the channel estimation based minimum mean square error Turbo equalizer (CE MMSE-TEQ) and the direct-adaptation turbo equalizer (DA-TEQ) in single-input single-output (SISO) underwater acoustic (UWA) channels. For CE MMSE-TEQ, we compare the soft-decision feedback Turbo equalizer (SDFE), the bidirectional soft-decision feedback Turbo equalizer (Bi-SDFE) and the classic linear Minimum Mean Square Error (MMSE) Turbo equalizer in terms of bit error rate (BER) performance. For DA-TEQ, the recently proposed soft-decision direct-adaptation TEQ (Soft DA-TEQ) is evaluated with the same set of experimental data. Both QPSK and multilevel modulations (8PSK and 16QAM) have been tested with the symbol rate of 9.77 ksymbols/s. Experimental results show that the CE-TEQs are more robust in SISO underwater acoustic transmission under harsh channel conditions. Especially, with low pilot overheads, the recently proposed Bi-SDFE achieved low BER performance in all cases.

Minimum mean square error (MMSE) linear detector has been considered as one of the potential detection algorithm for uplink multi-user massive MIMO systems, because it can achieve the near-optimal bit error rate (BER) performance. However, it involves matrix inversion with high complexity. Thus, the conventional Gauss-Seidel (GS) method has been applied for obtain a low-complexity MMSE detector without employing the computationally intensive matrix inversion. In this paper, we propose a refinement for the conventional GS method based on band matrix concept in order to accelerate the convergence rate, that means reduce the number of iterations and consequently the complexity, guaranteeing the near-optimal BER performance. Analytical and numerical results show the efficiency of the proposed method in comparison to the conventional GS method.

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.