Adaptive Beamforming Assisted ReceiverAdaptive Beamforming

Adaptive channel equalization is a signal processing technique to mitigate inter-symbol interference in a time dispersive channel. For adaptive equalization, minimum mean square error (MMSE) criterion-based reproducing kernel Hilbert spaces (RKHS) approaches such as the kernel least mean squares (KLMS) algorithm and its variants have been suggested in the literature for nonlinear channels. Another optimality criterion, based on minimum bit/symbol error rate (MBER/MSER), is a better choice for adapting an equalizer as compared to MMSE criterion. A kernel-based minimum symbol error rate (KMSER) equalization algorithm combines minimum symbol error rate (MSER)-based approaches with RKHS techniques. However, most algorithms in RKHS such as KMSER/KLMS require infinite storage requirement and hence cannot be practically implemented. To curtail the infinite memory requirement, and make adaptive algorithm suitable for implementation with finite memory and processing power, we propose quantized KMSER (QKMSER) and fixed-budget quantized KMSER (FBQKMSER)-based equalizers in this paper. In this paper, we derive the dynamical equation for MSE evolution of the QKMSER and FBQKMSER and find their performance to be asymptotically close to the MSE behavior of the KMSER. Also, it is found via simulations that the tracking performance of FBQKMSER is better than all the compared algorithms in this paper which is particularly useful for non-stationary channels.

Adaptive beamforming for binary phase shift keying communication systems

The existence of phase noise in virtually every digital communications system poses a serious challenge to system designers especially as system complexity increases. Communication system complexity could be attributed to the modulation techniques adopted and the circuitry employed in achieving such modulations. This work investigates the impact of phase noise on the Symbol Error Rate (SER) of the different Quadrature Amplitude Modulation (QAM) schemes. MATLAB simulation technique is adopted for the work and the results of the simulations show that as the phase noise is increased negatively, all the QAM schemes investigated show a reduction in SER and at a point, records a zero error. The value at which the schemes record this zero symbol error rate increases as the complexity of the scheme increases. So, higher order QAM schemes accommodate more symbol errors than the lower orders. The results also show that hard decision decoding has the worst performance index, irrespective of the QAM scheme, when compared with soft decision decoding.

This paper presents a relay selection for decode-and-forward based on network coding (DF-NC) and analog-NC protocols in general scheme of cellular network system. In the propose scheme the two source node simultaneously transmit their own information to all the relays as well as the destination node, and then, a single relay i.e. best with a minimum symbol error rate (SER) will be selected to forward the new version of the received signal. Simulation results show that, the DF-NC scheme with considerable performance has exactness over analog-NC scheme. To improve the system performance, optimal power allocation between the two sources and the best relay is determined based on the asymptotic SER. By increasing the number of relays node, the optimum power allocation achieve better performance than asymptotic SER.

An ultra-reliable and low latency communications assisted modulation based non-orthogonal multiple access scheme

Sparse decision feedback equalization for underwater acoustic channel based on minimum symbol error rate

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.

In this paper we study the performance of space-time bit-interleaved coded modulation (ST-BICM) over block-fading multi-input multi-output (MIMO) channels with iterative receivers based on minimum mean square error (MMSE) detection. We show how full diversity can be achieved with a special class of space-time precoders. Performance in terms of symbol error rate (SER) and word error rate (WER), obtained via Monte Carlo simulations, is shown.

Optimal receiver diversity combining employing linear channel estimation is examined. Based on the statistical properties of least-squares (LS) and minimum mean square error (MMSE) channel estimation, an optimal diversity receiver for wireless systems employing practical linear channel estimation on Rician fading channels is proposed. The new receiver structure includes the conventional maximal ratio combining receiver as a special case. Exact analytical expressions for the symbol error rates (SERs) of LS and MMSE channel estimation aided optimal diversity combining are derived. It is shown that, if an optimal detector is used, an MPSK wireless system with MMSE channel estimation has the same SER when the MMSE channel estimation is replaced by LS estimation. This is an interesting counterexample to the common perception that channel estimation with smaller mean square error leads to smaller SER. Extensive simulation results validate the theoretical results.

SummaryIn this work, a deep learning (DL)‐based massive multiple‐input multiple‐output (mMIMO) orthogonal frequency division multiplexing (OFDM) system is investigated over the tapped delay line type C (TDL‐C) model with a Rayleigh fading distribution at frequencies ranging from 0.5 to 100 GHz. The proposed bi‐directional long short‐term memory (Bi‐LSTM) channel state information (CSI) estimator uses online learning during training and offline learning during the practical implementation phase. The design of the estimator takes into account situations in which prior knowledge of channel statistics is limited and targets excellent performance, even with limited pilot symbols (PS). Three separate loss functions (mean square logarithmic error [MSLE], Huber, and Kullback–Leibler Distance [KLD]) are assessed in three classification layers. The symbol error rate (SER) and outage probability performance of the proposed estimator are evaluated using a number of optimization techniques, such as stochastic gradient descent (SGD), momentum, and the adaptive gradient (AdaGrad) algorithm. The Bi‐LSTM‐based CSI estimator is trained considering a specific number of PS. It can be readily seen that by incorporating a cyclic prefix (CP), the system becomes more resilient to channel impairments, resulting in a lower SER. Simulations show that the SGD optimization approach and Huber loss function‐trained Bi‐LSTM‐based CSI estimator have the lowest SER and very high estimation accuracy. By using deep neural networks (DNNs), the Bi‐LSTM method for CSI estimation achieves a superior channel capacity (in bps/Hz) at 10 dB than long short‐term memory (LSTM) and other conventional CSI estimators, such as minimum mean square error (MMSE) and least squares (LS). The simulation results validate the analytical results in the study.

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.

To approach the potential MIMO capacity while optimizing the system bit error rate (BER) performance, the joint transmit and receive minimum mean squared error (MMSE) design has been proposed. It is the optimal linear scheme for spatial multiplexing MIMO systems, assuming a fixed number of spatial streams p as well as a fixed modulation and coding across these spatial streams. However, state-of-the-art designs arbitrarily choose and fix the value of the number of spatial streams p, which may lead to an inefficient power allocation strategy and a poor BER performance. We have previously proposed to relax the constraint of fixed number of streams p and to optimize this value under the constraints of fixed average total transmit power and fixed spectral efficiency, which we referred to as spatial-mode selection. Our previous selection criterion was the minimization of the system sum MMSE. In the present contribution, we introduce a new and better spatial-mode selection criterion that targets the minimization of the system BER. We also provide a detailed performance analysis, over flat-fading channels, that confirms that our proposed spatial-mode selection significantely outperforms state-of-the-art joint Tx/Rx MMSE designs for both uncoded and coded systems, thanks to its better exploitation of the MIMO spatial diversity and more efficient power allocation.

For the code division multiple access (CDMA) downlink channel, the chip-level equalization has been considered in this paper. There is no interference after despreading if all spreading codes are orthogonal, as in IS-95. However, it cannot be true for a frequency-selective fading channel. In this case, the chip-level equalization can be applied to restore the orthogonality. We investigate the chip-level equalization using finite impulse response (FIR) equalizers for the mobile station with multiple receive antennas. A blind approach and the minimum mean square error (MMSE) approach with code-multiplexed pilot are considered. A generalized MMSE equalization, which combines the MMSE and blind approaches together, is also investigated. It is shown that the generalized MMSE equalizer can effectively increase the number of samples to track the variation of channel and thereby performs better when the coherence time is small. In addition, we derive closed-form solutions of the blind, MMSE, and generalized MMSE equalizers for given channels.

The zero-forcing (ZF) and minimum mean square error (MMSE) based detectors can approach optimal performance in the uplink of massive multiple-input multiple-output (MIMO) systems. However, they require inverting a matrix whose complexity is cubic in relation to the matrix dimension. This can lead to the high computational effort, especially in massive MIMO systems. To mitigate this, several iterative methods have been proposed in the literature. In this paper, we consider accelerated Chebyshev SOR (AC-SOR) and accelerated Chebyshev AOR (AC-AOR) algorithms, which improve the detection performance of conventional Successive Over-Relaxation (SOR) and Accelerated Over-Relaxation (AOR) methods, respectively. Additionally, we propose using a deep unfolding network (DUN) to optimize the parameters of the iterative AC-SOR and AC-AOR algorithms, leading to the AC-AORNet and AC-SORNet methods, respectively. The proposed DUN-based method leads to significant performance improvements compared to conventional iterative detectors for various massive MIMO channels. The results demonstrate that the AC-AORNet and AC-SORNet are effective, outperforming other state-of-the-art algorithms. Furthermore, they are highly effective, particularly for high-order modulations such as 256-QAM (Quadrature Amplitude Modulation). Moreover, the proposed AC-AORNet and AC-SORNet require almost the same number of computations as AC-AOR and AC-SOR methods, respectively, since the use of deep unfolding has a negligible impact on the system’s detection complexity. Furthermore, the proposed DUN features a fast and stable training scheme due to its smaller number of trainable parameters.

In this paper, we consider an algorithm of detecting a signal with quadrature amplitude modulation (QAM) in a multiple inputs and multiple outputs (MIMO) communication system. The algorithm consists of two steps: soft-decision decoder using Kalman filtering and hard-decision decoder using criterion of the minimum distance between soft decision vectors and possible information symbols at each receiving antenna. The Kalman filter estimates symbols at the i-th time point during K iterations. The comparison of the noise immunity of QAM signal reception was performed using the Zero Forcing equalizer, the minimum mean square error (MMSE) algorithm, and the recurrent Kalman filtering. Signal processing takes place under conditions of Rayleigh fading multipath channel with Doppler spectrum spreading. Two cases were considered: the channel matrix is known precisely and the second when it is estimated by the least squares method (LS) using a first-order polynomial approximation for the elements of the channel matrix. The channel matrix contains not only signal distortions due to the multipath channel, but also distortions of the direct conversion receiver, such as amplitude and phase imbalance between signal in-phase and quadrature components, frequency offset due to non-ideal detection algorithm, as well as direct current offset (DC offset). In addition, the computational complexity of the detector based on the Kalman filtering is analyzed.