Zero-forcing Equalizer Research Articles

Signal detection of M-MIMO-orthogonal time frequency space modulation using hybrid algorithms: ZFE + MMSE and ZFE + MF

Orthogonal Time Frequency Space (OTFS) modulation, coupled with Massive Multiple Input Multiple Output (Massive-MIMO) technology, presents a promising avenue for enhancing the efficiency and reliability of fifth-generation (5G) and beyond fifth-generation (B5G) systems. OTFS modulation offers robust communication in high-mobility environments by converting signals into the delay-Doppler domain, ensuring better performance over fading channels. MIMO enhances wireless networks by using large antenna arrays to boost capacity, spectral efficiency, and reliability, making both technologies vital for next-generation radio systems. In this study, we explore the detection of (8 × 8, 16 × 16, 64 × 64, and 256 × 256) Massive-MIMO-OTFS signals utilizing two prominent detection algorithms: zero forcing equalization (ZFE) with matched filter (MF) known as (ZFE + MF) and Zero Forcing with minimum mean square error (MMSE) known as (ZFE + MMSE). The combination of Massive MIMO and OTFS offers improved spectral efficiency, robustness against fading, and enhanced spatial multiplexing capabilities. The parameters such as bit error rate (BER) and power spectral density (PSD) are analyzed and estimated for the proposed hybrid and conventional algorithms. The proposed algorithms obtained the SNR and PSD gain of 3.2 dB, 3.2 dB, 4.8 dB, and 6.1 dB gain, respectively, for 8 × 8, 16 × 16, 64 × 54, and 256 × 256 MIMO systems. Further, the PSD gain of -390 is obtained for the 256 × 256 system, resulting in high spectral efficiency.

A hybrid detection algorithm for 5G OTFS waveform for 64 and 256 QAM with Rayleigh and Rician channels

Abstract Signal detection in orthogonal time frequency space modulation is one of the critical aspects for enhancing the throughput of the beyond fifth-generation framework, especially in challenging environments characterized by high mobility and multipath propagation. In this work, we proposed a hybrid detection algorithm by combining zero-forcing equalization (ZFE) and minimum square error equalization (MMSE), also known as ZFE–MMSE, with Rician and Rayleigh channels for 64 and 256 quadrature amplitude modulation. The combination of ZFE and MMSE allows for a more comprehensive approach to equalization. ZFE addresses channel-induced distortions, while MMSE tackles the impact of noise. Together, they enhance the overall performance of the equalization process, resulting in improved signal detection accuracy. The analysis and comparison of the simulation parameters with traditional detection systems include bit error rate, power spectral density (PSD), and complexity. The projected algorithms achieve a signal-to-noise ratio and a PSD gain of 2 dB and −800, respectively, outperforming the traditional detection techniques.

Performance enhancement of 5G uplink MIMO over fading-shadowing, path losses, and ISI using LZF equalize

The challenges of the 5G mobile wireless communication systems transmission channels have been changed continuously because of the signal transfer path characteristics such as real-time applications, path loss, multiple users, reflected rays, channel Rayleigh-fading, shadowing, noise, and inter symbol interference (ISI). These challenges have been treated to reach the minimum bit error rate (BER) value of the received data and maximum data rate of high-speed wireless mobile communication systems. In this paper, the linear zero-forcing (LZF) equalizer with uplink multi-input multi-output (MIMO) system has been proposed to enhancement the BER, which is caused by the ISI, Rayleigh fading, shadowing, path losses, and additive white gaussian noise (AWGN). Furthermore, the proposed approach is applied to a different number of antennas constellation to show the effect of increasing the number of antennas on the BER. The results show that the proposed LZF equalizer-MIMO system model has reached lower BER values, and high performance with an increase in the receiver to 8×14, 8×16 and 8×18 antennas constellation at 8, 10, 12, 14, 16, and 18 dB signal to noise ratio (SNR).

Reliability performance analysis for OTFS modulation based integrated sensing and communication

In this paper, we develop an orthogonal time frequency space (OTFS) modulation based integrated (radar) sensing and communication (ISAC) technique, namely OTFS-ISAC, for the high mobility multiuser system. In particular, at the transmitter, it can alternate the modes between sensing and communication using time division multiplexing so that it takes advantage of radar assistance to design the OTFS frame structure for reducing the overhead of guard symbols. At the receiver, based on the embedded pilot-aided channel estimation, it employs zero-forcing (ZF) equalization. For performance analysis, we derive the error probability of channel estimation based on radar sensing, and find the outage probability of downlink communication. Then, we introduce an adaptive power allocation scheme at the transmitter to optimize the outage probability of the communication link. Our simulations show that, by properly selecting N, M, and the pilot symbol strength, the proposed OTFS-ISAC scheme can reduce the overhead of guard symbols while achieving promising reliability performance of the downlink transmission with relative low channel estimation error.

Nonlinear Equalization for Performance Enhancement of FBMC Systems Using Walsh Transform

The Filter Bank Multi-Carrier (FBMC) is an interesting recent technology for next-generation wireless radio communication systems. Equalization is a fundamental technique for enhancing Bit Error Rate (BER) performance. The traditional Linear Zero Forcing (LZF) and Linear Minimum Mean Square Error (LMMSE) equalizers have large noise amplification and high complexity, respectively. As the estimated error of the Signal-to-Noise Ratio (SNR) grows, the BER performance of the LMMSE equalizer degrades. In this paper, we present a Joint Low Complexity Optimized ZF-Successive Interference Cancellation (JLCOZF-SIC) equalizer for FBMC communication systems that are based on the Walsh–Hadamard Transform (WHT) rather than the Fast Fourier Transform (FFT). As in the MMSE-Successive Interference Cancellation (MMSE-SIC) equalizer, the proposed equalizer avoids the estimating error induced by average power per symbol estimation. The simulation results show that the proposed algorithm improves the system performance more than the existing algorithms. Furthermore, the proposed equalization provides stability in the BER performance at high levels of the co-Carrier Frequency Offset (co-CFO). In terms of computational complexity, the proposed scheme has a lower computational complexity than traditional schemes.

GFDM Zero Forcing Equalizer for Large Doppler Shift in Correlated Double Ring Channel Models

The nature of wireless communication channels evolves throughout time. Depending on the channel model, wireless communication channels can also be affected by a number of key factors. In the Correlated Double Ring (CDR) wireless channel model, the channel gain parameters are affected by the movement of vehicles on the transmitter and receiver sides as well as the amount of scatterers surrounding the transmitter and receiver. When bits are transmitted across the CDR channel using a Generalized Frequency Division Multiplexing (GFDM) multi-carrier system, the received bit will be degraded as a result of Doppler shift and multipath. To circumvent this, we use a Zero Forcing (ZF) equalizer to correct the erroneous bits on the receive side. In this study, we simulate data bits transmitted via a CDR channel at various speeds, ranging from low speed to high speed, using a GFDM multicarrier system. The ZF equalization method that we propose to overcome the higher Doppler frequency on a high-speed CDR channel of 95 m/s with the scatterer of 8 has been demonstrated to increase Bit Error Rate (BER) performance in comparison to the emergence of a ZF equalization scheme. In order to counteract the vast number of up to 16 multipaths on CDR channels, the ZF equalization approach can improve the BER performance at 95 m/s when compared to when it is not employed. On the Rician CDR channel, the ZF equalization algorithm can efficiently overcome the highly significant Doppler effect and multipath fading.

Supervised identification and equalization of transmission channel using reproducing kernel Hilbert space

The subject matter of the article is to identify and equalize the parameters of telecommunication channels. The goal is to develop a new mathematical approach based on positive definite kernels on a Hilbert space. The tasks to be solved are: (a) to formulate a mathematical procedure based on a kernel; a kernel is a function that maps pairs of data points to a scalar value, and positive definite kernels are widely used in machine learning and signal processing applications; (b) to identify the channel parameters using the proposed method; and (c) to apply the Zero Forcing and MMSE equalizer to measure the performance of the proposed system. This article introduces a new method to address the problem of supervised identification of transmission channel parameters based on the positive definite kernel on Hilbert space, which implements Gaussian kernels. The input sequence, used as an input for a system or process, is assumed to be independent, have a zero mean, a non-Gaussian distribution, and be identically distributed. These assumptions are made to simplify the analysis and modeling. The proposed method for estimating the parameters of the channel impulse response yields promising results, indicating that the estimated parameters are close to the measured parameters of the model for various channels. The convergence of the estimated parameters toward the measured parameters of the model is particularly noticeable for BRAN A (indoor) and BRAN E (outdoor) channels. The method has been tested with different channel models, and the results remain consistent. Overall, the proposed method appears to be a reliable and effective approach for estimating channel impulse response parameters. The accuracy of the estimated parameters is particularly noteworthy considering the challenges inherent in modeling wireless channels, which can be influenced by various factors such as obstacles and interference. These findings have important implications for the design and optimization of wireless communication systems. Accurate estimates of channel impulse response parameters are essential for predicting and mitigating the effects of channel distortion and interference, and the proposed method represents a promising tool for achieving this goal. Further research and testing are needed to validate and refine the method and to explore its potential applications in different settings and scenarios. We evaluated the performance of the system using the estimated parameters obtained from the proposed method. Two equalizers, MMSE and ZF, were used, and the results show that MMSE outperforms ZF. Both equalizers produced highly satisfactory outcomes.

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.

Global Estimation and Compensation of Linear Effects in Coherent Optical Systems Based on Nonlinear Least Squares

This article proposes a new estimation and compensation approach to mitigate several linear and widely linear effects in coherent optical systems using digital signal processing (DSP) algorithms. Compared to most of the available strategies that employ local estimation and/or compensation algorithms, this approach performs a global impairments estimation and compensation based on nonlinear least squares. The proposed method estimates and compensates for the chromatic dispersion (CD), carrier frequency offset (CFO), in-phase/quadrature (IQ) imbalance, and laser phase noise in two steps. First, it estimates the quasi-static parameters related to the CD, CFO, and both transmitter and receiver IQ imbalance. Second, it estimates both transmitter and receiver lasers’ phases and compensates for all the imperfections by using a zero-forcing equalizer. Simulations show the effectiveness of the approach in terms of statistical performance and computational time. The estimation performance is assessed by computing the Cramér–Rao lower bound, while the detection performance is compared to a modified clairvoyant equalizer.

A Novel Blind High-Order Modulation Classifier Using Accumulated Constellation Temporal Convolution for OSTBC-OFDM Systems

Deep learning (DL)-based blind modulation classification (BMC) has flourished in the single carrier system for low-order modulation signals. However, the research of DL-based BMC has not been well explored in the OSTBC-OFDM system (Orthogonal Space-Time Block Coded-Orthogonal Frequency Division Multiplexing), especially high-order modulation types. This brief proposes a novel BMC algorithm for high-order modulation signals (e.g., 4096QAM), which is based on reconstruction processing and accumulation constellation temporal convolution BMC network (ACTC-BMCNet). First, we employ the blind zero-forcing (ZF) equalization algorithm to reconstruct the damaged signal and enhance the signal representation power. Then, the constellation accumulation strategy is executed on the raw constellation diagram (CD) to generate the accumulated CD (ACD) image for reducing constellation dispersion. After that, instead of traditional 2D convolution, the constellation temporal convolution enabled in ACTC-BMCNet is leveraged to reduce computational overhead and extract the more discriminative feature. Monte-Carlo experiments are performed on fourteen modulation signals, and results indicate that the proposed ACTC-BMCNet possesses a superior classification accuracy and a faster recognition speed than the DL-based benchmark classifiers.

Robust Frequency-Domain Timing Offset Estimation for DCO-OFDM Systems

Optical wireless communication (OWC) systems suffer inter-symbol interference (ISI) in time domain due to light emitting diode (LED)’s limited bandwidth at transmitter. As intensity modulation and direct detection (IM/DD) is used, the transmitted signals are unipolar and real-valued rather than bipolar and complex-valued as in radio frequency (RF). Thus, it is challenging to employ the RF-based timing offset estimation for OWC. Also, there is no carrier frequency offset (CFO) like in RF. It is possible to estimate timing offset in frequency domain for two reasons. First, the effect of ISI in time domain is mitigated in frequency domain with correct timing offset estimation, robust against LED’s limited bandwidth. Second, the correlation between frequency-domain signals are high, as signals are bipolar and complex-valued in frequency domain rather than unipolar and real-valued in time domain. Therefore, we propose an effective frequency-domain timing offset estimation approach for direct current biased optical-orthogonal frequency division multiplexing (DCO-OFDM) OWC systems, where a small number of pilots are applied on few DCO-OFDM subcarriers, leading to very low spectral overhead. The property of no CFO is utilized to formulate an error function, by exploring the correlation between received signals and pilots. We propose a squared error function (SEF)-based timing offset estimation approach, conducted by maximizing the ratio of two successive variances of squared errors. Simulation results show that, with a very low training overhead of 0.48%, the proposed SEF-based approach provides a bit error ratio (BER) performance close to ideal case with perfect timing offset estimation, perfect channel state information and zero-forcing (ZF) equalization.

Coded-GFDM for Reliable Communication in Underwater Acoustic Channels.

The performance of the coded generalized frequency division multiplexing (GFDM) transceiver has been evaluated in a shallow underwater acoustic channel (UAC). Acoustic transmission is the scheme of choice for communication in UAC since radio waves suffer from absorption and light waves scatter. Although orthogonal frequency division multiplexing (OFDM) has found its ground for multicarrier acoustic underwater communication, it suffers from high peak to average power ratio (PAPR) and out of band (OOB) emissions. We propose a coded-GFDM based multicarrier system since GFDM has a higher spectral efficiency compared to a traditional OFDM system. In doing so, we assess two block codes, namely Bose, Chaudari, and Hocquenghem (BCH) codes, Reed-Solomon (RS) codes, and several convolutional codes. We present the error performances of these codes when used with GFDM. Furthermore, we evaluate the performance of the proposed system using two equalizers: Matched Filter (MF) and Zero-Forcing (ZF). Simulation results show that among the various block coding schemes that we tested, BCH (31,6) and RS (15,3) give the best error performance. Among the convolutional codes that we tested, rate 1/4 convolutional codes give the best performance. However, the performance of BCH and RS codes is much better than the convolutional codes. Moreover, the performance of the ZF equalizer is marginally better than the MF equalizer. In conclusion, using the channel coding schemes with GFDM improves error performance manifolds thereby increasing the reliability of the GFDM system despite slightly higher complexity.

Clustering-based data detection for spectral signature multiplexing in multispectral camera communication.

Optical camera communication (OCC) is a promising technology to be used in future wireless communication systems. In this work, a cluster-based data detection procedure is applied to enhance the performance of an OCC system. A multispectral camera is employed to capture the spectral variations in light-emitting diodes (LEDs) caused by temperature. This strategy's system performance is compared with a system that uses traditional linear methods, such as zero-forcing (ZF) and minimum mean square error (MMSE) equalizers. The findings of this study indicate that an improvement in the bit error rate (BER) can be achieved by applying a clustering approach.

Pilot-Assisted OFDM for Underwater Acoustic Communication

Multicarrier techniques have made it possible to wirelessly transmit data at higher rates for underwater acoustic (UWA) communication. Several multicarrier techniques have been explored in the past for wireless data transmission. OFDM is known to fight off inter-symbol interference due to the orthogonality of its subcarriers. However, due to time variations, OFDM suffers from intercarrier interference. As the UWA channel is both a time and frequency variant, channel estimation becomes complex. We propose a pilot-based channel estimation technique and explore two equalizers for improving the error performance of an OFDM-based UWA system. Both the equalizers employ pilot subcarriers to estimate the UWA channel. One equalizer is a least squares (LS) equalizer and the other is a zero forcing (ZF) equalizer. Using computer simulations, it is observed that, for an acceptable error performance, the number of pilots should be one-fourth the number of subcarriers. Moreover, if the energy of the pilots is increased without changing the overall symbol energy, the error performance degrades. It is also noted that both the LS and ZF equalizers give an acceptable error performance with the ZF performing marginally better than the LS. Furthermore, the error performance of the proposed system is evaluated as a function of the transmitter-receiver distance and an acceptable error performance is observed even at 1250 m.

A Microwave Quantum-Defined Millivolt Source

We demonstrate a tenfold increase in the amplitude of microwave-frequency waveforms generated by a quantum-defined superconducting voltage source, with an open-circuit signal of 17.56 mV rms at 1.005 GHz. The voltage source is an RF Josephson arbitrary waveform synthesizer (RF-JAWS) that utilizes a circuit that is cooled to 4 K and is composed of an array of 4500 Josephson junctions. These junctions are connected in series along the center conductor of a 50- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\Omega $ </tex-math></inline-formula> superconducting coplanar waveguide transmission line. We introduce a new zero-forcing equalization technique for reducing distortion in drive current pulse patterns. This technique allows an increase in the amplitude of the quantum-based voltage waveforms while suppressing parasitic feedthrough signals to −75 dBc. Synthesizing a two-tone delta–sigma waveform, we monitor an audio-frequency 10-kHz tone of less than 100- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mu \text{V}$ </tex-math></inline-formula> rms amplitude while simultaneously measuring the 1.005-GHz tone of −28.12-dBm power in a 50- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\Omega $ </tex-math></inline-formula> environment. The two-tone synthesis allows simultaneous verification of correct operation of the voltage source using time-efficient low-frequency measurement techniques as well as slower microwave measurements.

Joint Blind Channel Estimation, Channel Equalization, and Data Detection for Underwater Visible Light Communication Systems

In this letter, we jointly consider the problems of blind channel estimation (BCE), channel equalization and data detection in underwater visible light communication (UVLC) systems. Specifically, we propose to solve them with a model-driven deep learning (DL) approach. Inspired by the module-based signal processing methodology and communication theory, we devise a new blind receiver architecture called blind detection network (BDNet), which consists of three modules corresponding to BCE, channel equalization, and symbol demapping, respectively. Different from existing BCE schemes, the BDNet does not directly estimate the channel itself, but instead estimates the inverse channel regardless of the scalar ambiguity issue by learning the latent channel features from the received signal only. The UVLC channel effects can then be partially compensated by the zero-forcing equalization module of BDNet. Finally, the symbol demapping module recovers the transmitted symbols with the aid of the learned decision thresholds. Simulation results show the competitive bit error rate performance of BDNet in comparison to conventional pilot-aided schemes.

BER Analysis for Downlink MIMO-NOMA Systems over Rayleigh Fading Channels

The Multiple-input multiple-output (MIMO) technique combined with non-orthogonal multiple access (NOMA) has been considered to enhance total system performance. This paper studies the bit error rate of two-user power-domain NOMA systems using successive interference cancellation receivers, with zeroforcing equalization over quasi-static Rayleigh fading channels. Successive interference cancellation technique at NOMA receivers has been the popular research topic due to its simple implementation, despite its vulnerability to error propagation. Closed-form expressions are derived for downlink NOMA in single-input single-output and uncorrelated quasi-static MIMO Rayleigh fading channel. Analytical results are consolidated with Monte Carlo simulation.

On Analyzing Beamforming Implementation in O-RAN 5G

The open radio access network (O-RAN) concept is changing the landscape of mobile networks (5G deployment and 6G research). O-RAN Alliance’s suggestions that O-RAN can offer openness and intelligence to the traditional RAN vendors will enable the capability for multi-vendors to re-shape the RAN structure and optimize the network. This paper positions the main research challenges of the O-RAN approach in regards to the implementation of beamforming. We investigate the O-RAN architecture and the configurations of the interfaces between O-RAN units and present the split options between the radio and distributing units in terms of O-RAN specification and 3GPP standards. From this point, we discuss the beamforming methods in O-RAN, addressing challenges and potential solutions, and suggest the introduction of the zero-forcing equalizer as a precoding vector in the channel-information-based beamforming method. This may be one of the solutions for achieving flexibility in a high-traffic communication environment while reducing the radio unit interferences caused by implanting the precoding in the open radio unit.

Fractional weighted ZF equalizer: A novel approach for channel equalization in MIMO-OFDM system under impulse noise environment

Impulse noise is the major factor degrading the performance of the wireless system, imposing the need for the impulse noise mitigation strategy. Mainly, in the multiple-input multiple-output (MIMO) and orthogonal frequency-division multiplexing (OFDM) system contaminated with the impulse noise creates a major impact in the performance as the conventional zero-forcing (ZF) equalizer as there is no satisfactory results. Thus, the paper concentrates on the impulse noise mitigation strategy based on the fractional weighed zero-forcing (FWZF) equalizer, which is the integration of the fractional concept in the Zero-Forcing equalizer. The noise impacts in the MIMO-OFDM system are minimized and the performance is enhanced due to the usage of the fractional theory in the ZF equalizer as the equalization values of the previous instances are interpreted for the formulation of the effective equalization value in the current instance of the ZF equalizer. The performance of the methods is done based on the valuation metrics, Bit Error Rate (BER), Mean Square Error (MSE), and Symbol Error Rate (SER) with respect to the Signal-to-Noise Ratio (SNR) and dissimilar antenna array size. It is found that the proposed Fractional Weighed Zero-Forcing equalizer outperformed the existing methods with a minimal BER and SER of 0.063, and 0.1038 while analyzing the methods in the Rayleigh environment.

Experimental Demonstration of 3 × 3 MIMO LED-to-LED Communication Using RGB Colors.

Optical wireless communication (OWC) is one of the promising candidates for beyond fifth-generation communication (B5G). Depending on the type of transmitters, receivers, and information carriers applied in the system, OWC can be categorized into visible light communication, light fidelity, free-space optical communication, optical camera communication, etc. In addition to these OWC subcategories, this paper proposes light-emitting diode (LED)-to-LED communication as another subcategory of OWC technique. Furthermore, we show an experimental demonstration of the multiple-input multiple-output (MIMO) LED-to-LED communication system using red, green, and blue colored LEDs. We believe that LED-to-LED communication is an effective solution to resolve the communication burden arising from massive connectivity in B5G internet of things. Along with the measurement results of the transmitter LED, receiver LED, and the channel properties, it is shown that the MIMO LED-to-LED system is able to successfully recover the transmitted signal with low inter-channel interferences due to the receiver LED’s unique characteristics. Finally, the bit error rate (BER) performance of the MIMO LED-to-LED system is shown in comparison with the BER performance of the single-input single-output (SISO) LED-to-LED system. We successfully implemented the 3 × 3 MIMO LED-to-LED communication system using RGB colors at a data rate of 30.62 kbps over a 10 cm transmission distance along with direct current biased optical orthogonal frequency division multiplexing (DCO-OFDM) modulation and zero-forcing (ZF) equalizer.