Minimum Mean Square Error Equalizer Research Articles

Doubly selective channel estimation and equalization based on ICI/ISI mitigation for OQAM-FBMC systems

Over a doubly selective channel, broadband transmission systems face challenges in channel estimation and equalization. High mobility causes inter-carrier interference (ICI), while multipath transmission induces inter-symbol interference (ISI). In this paper, we present a mitigation method of ICI/ISI for the offset quadrature amplitude-modulated filter bank multi-carrier (OQAM-FBMC) system. It features low inherent imaginary interference (IMI) sensitivity and high efficiency. Specifically, a pilot indices optimization algorithm and a sparse adaptive orthogonal subspace pursuit (SAOSP) algorithm are presented based on the 2-D channel modeling scheme. The guard pilots are first added to mitigate the effect of ICI. Then the index optimization and SAOSP algorithms are applied to achieve a high-accuracy estimation of sparse channel coefficients. In addition, a threshold judgment suboptimal minimum mean square error (MMSE) equalization method is presented based on the variability of the interference power. The method uses normalized interference power thresholds to estimate the ISI dimension and reduce the equalization data, thus mitigating the effect of ISI and achieving efficient equalization. To verify the above methods, single-input-single-output (SISO) and multiple-input-multiple-output (MIMO) models are built. Simulation results indicate a 3-5 dB improvement in channel estimation accuracy. The suboptimal MMSE equalization results are close to the optimal MMSE with about four orders of magnitude reduction in complexity.

Performance Analysis of Turbo Codes, LDPC Codes, and Polar Codes over an AWGN Channel in the Presence of Inter Symbol Interference.

This paper discusses the results of simulations relating to the performances of turbo codes, low density parity check (LDPC) codes, and polar codes over an additive white Gaussian noise (AWGN) channel in the presence of inter symbol interference, denoting the disturbances that altered the original signal. To eliminate the negative effects of inter symbol interference (ISI), an equalizer was used at the level of the receiver. Practically, two types of equalizers were used: zero forcing (ZF) and minimum mean square error (MMSE), considering the case of perfect channel estimation and the case of estimation using the least square algorithm. The performance measure used was the modification of the bit error rate compared to a given signal to noise ratio; in this sense, the MMSE equalizer offered a higher performance than the ZF equalizer. The aspect of channel equalization considered here is not novel, but there have been very few works that dealt with equalization in the context of the use of turbo codes, especially LDPC codes and polar codes for channel coding. In this respect, this research can be considered a contribution to the field of digital communications.

BER performance analysis of OTFS systems with power allocation

Orthogonal time frequency space (OTFS), as a novel 2-D modulation technique, has been proposed to achieve better BER performances over delay-Doppler channels. In this paper, we propose two different power allocation (PA) algorithms in OTFS systems with zero forcing (ZF) or minimum mean square error (MMSE) equalization, where general formulas with PA are derived in advance under the condition of minimum BER (MBER) criterion. On one hand, a suboptimal MBER power allocation method is put forward to achieve better BER performances, and then analytical BER expressions are derived with proposed PA strategy. Considering the case of MMSE equalization, a combined subsymbol allocation (SA) and PA strategy is raised, where some subsymbols may be abandoned due to worse channel conditions, and then it is proven effectively to improve BER performances through theoretical and simulation results. Furthermore, BER performances with proposed joint SA and PA strategy are also investigated in delay-Doppler channels, where an improved message passing (MP) receiver based on equivalent channel matrix with PA is given.

Parallel minimum mean square error equalization for reduced‐zero‐padding orthogonal time frequency space with the aid of unitary precoding

AbstractThis work studies the equalization method for the reduced‐prefix version of the orthogonal time frequency space (OTFS) modulation in which one zero‐padding (ZP) is inserted in each frame. We focus on applications in low data rate scenarios such as the Internet of Things, and will consider the case where the number of subcarriers and time slots are small. The idea of this work is to retain the large singular values of the channel matrix through linear transformations, while discarding the remaining small singular values. This makes it possible to avoid performance degradation due to small singular values when inverting the matrix in the minimum mean square error (MMSE) equalization. Specifically, a joint unitary precoding and signal linear transformation method is proposed for the reduced‐ZP OTFS modulation which decomposes the whole system into parallel subsystems. Then, the receiver can perform parallel MMSE equalization, where the singular values of each branch are not small. Simulation results show that the proposed method can achieve better bit error rate performance than the state‐of‐the‐art methods like message passing, unitary approximate message passing, and variational unitary approximate message passing.

Efficient Fast-Convolution Based Hybrid Carrier System

The weighted-type fractional Fourier transform (WFRFT)-based hybrid carrier (HC) system has been proposed to bridge the gap between orthogonal frequency division multiplexing (OFDM) system and single-carrier system with frequency domain equalization (SC-FDE). In this paper, we propose a novel HC system based on efficient fast-convolution (FC) without a cyclic prefix to meet the requirements of complex scenarios towards future communications. The proposed system can achieve flexible optimization of system performance, such as minimizing out-of-band emission (OOBE), peak to average power ratio (PAPR) and bit error rate (BER). This efficient FC based hybrid carrier (FCHC) system is among the most competitive waveforms. The closed-form BER expressions are derived and analyzed over additive white Gaussian noise (AWGN) and frequency-selective fading channels. A modified equalizer over frequency-selective channels is also provided to resist the inter-block interference (IBI). Moreover, the banded minimum mean-square error (MMSE) equalization based on FC can be embedded in the proposed system over doubly-selective channels, and then the interference caused by fading channels can be further suppressed through the combination of FC and HC. The simulation results demonstrate the superiority of the proposed system over the conventional HC system in terms of OOBE, PAPR and BER. The significant flexibility and combined performance advantages make the proposed system a potential scheme for future communications.

Adaptive Transmission With Frequency-Domain Precoding and Linear Equalization Over Fast Fading Channels

In this paper, the emerging orthogonal time frequency space (OTFS) modulation is firstly restructured as a precoded orthogonal frequency division multiplexing (OFDM) system, so that the well-established frequency-domain approach can be applied to perform signal in fast fading channels. Then a frequency-domain minimum mean squared error (MMSE) equalizer for OTFS is introduced and its performance is analyzed based on the eigenvalue decomposition of the channel matrix. Inspired by the frequency-domain precoding structure, an adaptive transmission scheme with frequency-domain precoding matrix composed of the eigenvectors of the channel matrix is proposed to improve the system performance under MMSE equalization, and its optimized performance is derived with simple expression. Finally, considering two extreme channel conditions, the lower and upper bounds for the diversity performance of the adaptive transmission scheme are derived. Simulation results show that the proposed adaptive transmission achieves significantly better performance for short signal frames and can work well with imperfect channel state information (CSI). The derived performance bounds can serve as benchmarks for OTFS and other precoded OFDM systems.

CE-OFDM-CDMA Phase Modulation for 5G System

In the present work, we propose a novel modulation scheme for 5G wireless communication system. Our contribution is to combine PM-OFDM (Phase Modulation Orthogonal Frequency Division Multiplexing) and CDMA (Code Division Multiple Access) to exploit their distinctive advantages. On the one hand, PM-OFDM is an effective technique to combat multipath fading effects. On the other hand, CDMA can serve multiple users who are using the same resources of time/frequency. The aim is to make a combination of PM-OFDM and CDMA techniques. In this paper, the OFDM-CDMA scheme and its PAPR (Peak-to-Average Power Ratio) statistics are reviewed. In this paper, the proposed scheme PM-OFDM-CDMA is described and its performances in terms of PAPR, power spectral density, and BER (Bit Error Rate) are analyzed. Moreover, MMSE (Minimum Mean Square Error) equalizer is used to avoid multipath and noise effects simultaneously. The simulation through AWGN (Additive white Gaussian noise) and Rayleigh channels is performed using MATLAB. From the simulation results, we observed that PM-OFDM-CDMA is an efficient technique in terms of energy consumption (PAPR = 0dB). Besides, CE-OFDM-CDMA offers high spectral efficiency with low BER due to its low PAPR. In CE-OFDM-CDMA method, the shape of the spectrum varies according to the value of the modulation index h. The band occupied by the spectrum increases with the value of h. Therefore, CE-OFDM-CDMA could be considered as a suitable technique for 5G applications.

Iterative turbo receiver design for superposition coding based downlink underwater acoustic OFDM communication system

Superposition coding (SC) with successive interference cancellation (SIC) is considered a promising non-orthogonal multiple access (NOMA) technique for improving spectral efficiency recently. In contrast, the residual interference after SIC at the receiver severely degrades the BER performance when applied in underwater acoustic (UWA) channels. In this paper, we propose a receiver that combined SIC and turbo equalization for superposition coding based downlink UWA orthogonal frequency-division multiplexing (OFDM) system, where a near-far user pair is mainly considered. We design an SC signal detector based on the minimum mean square error (MMSE) algorithm and eliminate the far user information with high power after detection. After SIC, the turbo equalization composed of an MMSE equalizer and LDPC decoder is adopted for the near user symbols with residual interference from the SIC process. Simulation results and recorded data from the Yellow Sea, China, show that the proposed receiver has a performance gain of at least 1 dB under different modulation pairs compared with traditional SIC receiver based on maximum a posteriori probability principle (MAP SIC). The error-free two-user downlink communication result shows a maximum sum-rate of 8kbps over the horizontal range of downlink 3.55km has been achieved in the Yellow Sea test.

A Low-Complexity Pilot-Based Frequency-Domain Channel Estimation for ICI Mitigation in OFDM Systems

A low-complexity pilot pattern and a frequency-domain channel estimation method for Inter-Carrier Interference (ICI) mitigation is proposed for Orthogonal Frequency Division Multiple Access (OFDM) systems. The proposed method exploits the band structure of the coupling matrix to perform an ICI-free channel estimation in the frequency domain. This ICI-free estimation relies on some conditions imposed over the pilot pattern that simplify the complexity of channel estimation significantly, since its complexity is the same as classical least squares (LS) channel estimation used in low mobility scenarios. Then, the ICI is removed by using a modified version of Minimum Mean Square Error (MMSE) equalization, which reduces the computational complexity considerably. This modified MMSE equalization relies on the sparse and banded structure of the coupling matrix and on a low complexity variant of the Cholesky decomposition, which is named LDLH factorization. It is shown that the proposed method greatly improves the Bit Error Rate (BER) in the high Signal-to-Noise Ratio (SNR) regime.

Frequency Domain Analysis and Equalization for Molecular Communication

Molecular Communication (MC) is a promising micro-scale technology that enables wireless connectivity in electromagnetically challenged conditions. The signal processing approaches in MC are different from conventional wireless communications as molecular signals suffer from severe inter-symbol interference (ISI) and signal-dependent counting noise due to the stochastic diffusion process of the information molecules. One of the main challenges in MC is the high computational complexity of the existing time-domain ISI mitigation schemes that display a third-order polynomial or even exponential growth with the ISI length, which is further exasperated under the high symbol rate case. For the first time, we develop a frequency-domain equalization (FDE) with lower complexity, capable of achieving independence from the ISI effects. This innovation is grounded in our characterization of the channel frequency response of diffusion signals, facilitating the design of receiver sampling strategies. However, the perfect counting noise power is unavailable in the optimal minimum mean square error (MMSE) equalizer. We address this issue by exploiting the statistical information of the transmit signal and decision feedback for noise power estimation, designing novel MMSE equalizers with low complexity. The FDE for MC is successfully developed with its immunity to ISI effects, and its signal processing cost has only a logarithmic growth with symbol length in each block.

Time Domain Channel Estimation and Equalization of CP-OTFS Under Multiple Fractional Dopplers and Residual Synchronization Errors

In the last few years, orthogonal time frequency space (OTFS) modulation has received significant attention as an alternative to OFDM especially for high mobilty scenarios. In this work, we develop a delay-Doppler domain embedded pilot based time domain channel estimation for cyclic prefix (CP)-OTFS in the presence of residual frame timing offset, carrier frequency offset and fractional multiple Doppler. One of the reasons for time domain processing is that the time domain channel representation is relatively more sparse as compared to its delay Doppler domain representation in the presence of residual synchronization errors. We also describe a time domain low complexity linear minimum mean square error (MMSE) equalization and successive interference cancellation (SIC) receiver for LDPC (low density parity check) coded CP-OTFS in this work. We further show the impact of residual frame timing offset, carrier frequency offset and fractional multiple Doppler on OTFS symbols. It is seen from the extensive Monte Carlo simulation results that the estimation and compensation methods presented here provide necessary resilience properties to OTFS. We bring out the tolerance of OTFS to such residual synchronization errors. It is further observed that the SIC is able to improve the performance of the system such that it almost matches that of the ideal knowledge based MMSE equalization. We also show the performance of RCP (reduced CP)-OTFS when used with the developed channel estimation and equalization algorithms. A unified signal processing flow for OTFS and orthogonal frequency division multiplexing (OFDM) is also described in this work to motivate studies on coexistence between the two as well as to encourage investigations on a seamless transition between OFDM and OTFS based systems for future adaptive air interface design.

Mode-Dependent Loss and Gain Estimation in SDM Transmission Based on MMSE Equalizers

The capacity in space division multiplexing (SDM) systems with coupled channels is fundamentally limited by mode-dependent loss (MDL) and mode-dependent gain (MDG) generated in components and amplifiers. In these systems, MDL/MDG must be accurately estimated for performance analysis and troubleshooting. Most recent demonstrations of SDM with coupled channels perform MDL/MDG estimation by digital signal processing (DSP) techniques based on the coefficients of multiple-input multiple-output (MIMO) adaptive equalizers. Although these methods provide a valid indication of the order of magnitude of the accumulated MDL/MDG over the link, MIMO equalizers are usually updated according to the minimum mean square error (MMSE) criterion, which is known to depend on the channel signal-to-noise ratio (SNR). Therefore, MDL/MDG estimation techniques based on the adaptive filter coefficients are also impaired by noise. In this paper, we model analytically the influence of the SNR on DSP-based MDL/MDG estimation, and show that the technique is prone to errors. Based on the transfer function of MIMO MMSE equalizers, and assuming a known SNR, we calculate a correction factor that improves the estimation process in moderate levels of MDL/MDG and SNR. The correction factor is validated by simulation of a 6-mode long-haul transmission link, and experimentally using a 3-mode transmission link. The results confirm the limitations of the standard estimation method in scenarios of high additive noise and MDL/MDG, and indicate the correction factor as a possible solution in practical SDM scenarios.

Finite-Order Source and Relay Filtering Design for Wideband Full-Duplex Amplify-and-Forward Relaying Networks

Compared with half-duplex relaying, the full-duplex relay (FDR) system provides higher spectral efficiency due to the concurrent transmission and reception at the relay node. As known, the full-duplex operation will introduce the self-interference (SI) that significantly degrades the system performance. Conventionally, SI is treated as a harmful signal that needs to be removed from the system as completely as possible. The conventional design concept, however, may not be efficient since SI is in fact a delayed version of the desired signal. Specifically, it is possible to have further performance improvement if SI can be exploited appropriately. In this paper, we will investigate the source/relay filter design problem where the source and relay are considered as finite impulse response (FIR) and infinite impulse response (IIR) filters, respectively. The design goal is to optimize the end-to-end performance for the linear minimum mean-square error (MMSE) and nonlinear MMSE decision-feedback equalizers. To reduce the implementation cost, we further propose a finite-order filter design for the source and relay precoders. Simulations demonstrate that our designs outperform the conventional ones.

Finite-Alphabet MMSE Equalization for All-Digital Massive MU-MIMO mmWave Communication

We propose finite-alphabet equalization, a new paradigm that restricts the entries of the spatial equalization matrix to low-resolution numbers, enabling high-throughput, low-power, and low-cost hardware equalizers. To minimize the performance loss of this paradigm, we introduce FAME, short for finite-alphabet minimum mean-square error (MMSE) equalization, which is able to significantly outperform a naive quantization of the linear MMSE matrix. We develop efficient algorithms to approximately solve the NP-hard FAME problem and showcase that near-optimal performance can be achieved with equalization coefficients quantized to only 1-3 bits for massive multi-user multiple-input multiple-output (MU-MIMO) millimeter-wave (mmWave) systems. We provide very-large scale integration (VLSI) results that demonstrate a reduction in equalization power and area by at least a factor of 3.9× and 5.8×, respectively.

Non-linear equalisation and CFO compensation for MIMO-OFDM communication systems based on DWT

ABSTRACT 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.

Modeling and mitigation of spectral crosstalk in OFDM WDM-VLC system

The present work deals with the thorough modeling of the wavelength division multiplexing (WDM) associated with orthogonal frequency division multiplexing (OFDM) in visible light communication (VLC) systems to evaluate and mitigate the spectral crosstalk (SC). The SC generated by the spectral overlap can degrade the performance of the WDM-VLC system since the adjacent WDM channels can generate considerable interference in the channel of interest. The system is fully modeled with the dual optical diversity (DOD) considering red–green–blue (RGB) color commercial LEDs, their respective color filters, photodiodes and other components of the system from the measurement of its optical quantities and also considering standard features from its datasheets. In the models, the non-ideal behaviors of these components were considered, such as the responsiveness curve of the photodiodes. A more realistic model for the transmittance of optical filters is also proposed. The parameters of WDM channels are estimated by the proposed SC mitigation scheme, allowing the suppression of substantial part of the SC at the receiver side by subtracting interfering signals deploying an zero-forcing (ZF) and a minimum mean-squared error (MMSE) equalizers. The proposed system was simulated whose results demonstrate its effectiveness by evaluating the bit error rate (BER).

Time-Varying Channel Equalization in Underwater Acoustic OFDM Communication System

In this paper, three time-varying channel equalization schemes are studied in the underwater acoustic (UWA) Orthogonal Frequency Division Multiplexing (OFDM) communication system. The equalization algorithms are the zero-forcing (ZF) equalization algorithm, and the minimum mean square error equalization (MMSE) algorithm and the serial interference cancellation (SIC) equalization algorithm. Among the schemes, there is a problem of needing a large amount of operation when obtaining the inversion of the channel matrix. Then, to reduce the computation complexity of channel matrix inversion, the band approximation of the channel matrix, the serial equalization and the LDLH decomposition are also studied. To evaluate the efficacy of the algorithms studied in this paper, numerical simulation and the field experiment are both conducted. The simulation results proof that each equalization algorithm can work appropriately under different time-varying conditions, and valid the reliability of each simplified algorithm under the same Doppler factor. The results of two sets of field experiment also prove that the simplified algorithm eliminates the influence of the residual narrow band Doppler to a certain extent, and a better effect is obtained while a channel estimation algorithm with higher accuracy is combined.

Nonorthogonal Multiple Access With Orthogonal Time–Frequency Space Signal Transmission

Orthogonal time frequency space (OTFS) is being pursued in recent times as a suitable wireless transmission technology for use in high mobility scenarios. In this work, we propose nonorthogonal multiple acess (NOMA) based OTFS which may be called NOMA-OTFS system and evaluate its performance from system level and link level perspective. The challenge lies in the fact that while OTFS transmission technology is known for its resilience to high mobility conditions, while NOMA is known to yield high spectral efficiency in low mobility scenarios in comparison to orthogonal multiple access (OMA). We present a minimum mean square error (MMSE)- successive interference cancellation (SIC) based receiver for NOMA-OTFS, for which we derive expression for symbol-wise post-processing SINR in order to evaluate system sum spectral efficiency (SE). We develop power allocation schemes to maximize the sum SE in the high-mobility version of NOMA. We further design a realizable codeword level SIC (CWIC) receiver using LDPC codes along with MMSE equalization for evaluating link level performance of such practical NOMA-OTFS system. The system level and link level performance of the proposed NOMA-OTFS system are compared against benchmark OMA-OTFS, OMA-orthogonal frequency division multiplexing (OMA-OFDM) and NOMA-OFDM schemes. From system-level performance evaluation, we observe interestingly that NOMA-OTFS provides higher sum SE than OMA-OTFS. When compared to NOMA-OFDM, we find that outage SE of NOMA-OTFS is improved at the cost of decrease in mean SE. Whereas link-level results show that the developed CWIC based NOMA-OTFS receiver performs significantly better than NOMA-OFDM in terms of block error rate (BLER), goodput and throughput.

Performance enhancement of OFDM systems with lower-complexity using DST based on successive interference cancellation

Equalization is the most important algorithm to improve the Bit-Error-Rate (BER) performance in wireless communication systems. The Zero Forcing (ZF) equalizer, and the Minimum Mean Square Error (MMSE) equalizer suffer from noise enhancement, and high complexity, respectively. The ZF, and MMSE equalizers based on Successive Interference Cancellation (SIC) also suffer from error propagation, and high complexity, respectively. On the other hand, the MMSE, and the MMSE-SIC need the estimation of the Signal-to-Noise Ratio (SNR) to work properly. The Orthogonal Frequency Division Multiplexing (OFDM) systems are very sensitive to Carrier Frequency Offset (CFO) at the receiver side. In this paper, we propose a Joint Low-complexity Regularized ZF (JLRZF) equalizer based on SIC for the OFDM system that depends on the Discrete Sine Transform (DST). The proposed JLRZF-SIC scheme jointly performs the equalization and CFO compensation processes with low complexity using banded-matrix approximation. Simulation results show that the proposed JLRZF-SIC scheme improves the BER performance compared to other equalization algorithms.

Joint equalization and CFO compensation for performance enhancement of MIMO-OFDM communication systems using different transforms with banded-matrix approximation

The conventional Zero Forcing (ZF), and Minimum Mean Square Error (MMSE) equalizers suffer from noise enhancement, and high complexity, respectively. Moreover, the MMSE equalizer needs the estimation of the Signal-to-Noise Ratio (SNR) to work properly. In this paper, we propose Joint Low-Complexity Regularized ZF (JLCRZF) equalizers based on Successive Interference Cancellation (SIC) for Orthogonal Frequency Division Multiplexing (OFDM). The Bit-Error-Rate (BER) performance of the OFDM system model is tested using different transforms such as Discrete Fourier Transform (DFT), Discrete Sine Transform (DST), Discrete Cosine Transform (DCT), and Discrete Wavelet Transform (DWT). The proposed JLCRZF-SIC equalizers jointly perform the equalization and Carrier Frequency Offset (CFO) compensation processes with lower complexity using banded-matrix approximation. Simulation results prove that the proposed JLCRZF-SIC equalizers outperform different linear, and non-linear equalizers, especially in the presence of estimation errors.