Semi-blind adaptive spatial equalisation for MIMO systems with high-order QAM signalling

This contribution investigates semi-blind adaptive spatial filtering or equalisation for multiple-input multiple-output (MIMO) systems that employ high-throughput quadrature amplitude modulation (QAM) signalling. A minimum number of training symbols, equal to the number of receivers (we assume that the number of transmitters is no more than that of receivers), are first utilized to provide a rough least squares channel estimate of the system's MIMO channel matrix for the initialization of the spatial equalizers' weight vectors. A constant modulus algorithm aided soft decision-directed blind algorithm, originally derived for blind equalization of single-input single-output and single-input multiple-output systems employing high-order QAM signalling, is then extended to adapt the spatial equalizers for MIMO systems. This semi-blind scheme has a low computational complexity, and our simulation results demonstrate that it converges fast to the minimum mean-square-error spatial equalization solution

A Novel QAM Technique for High Order QAM Signaling

The paper proposes a novel spread quadrature amplitude modulation (S-QAM) technique with high SNR improvement for high-order QAM channels. Simulated and experimental bit error rate (BER) performance analyses of the proposed technique in blind and non-blind equalizers are obtained by using single carrier (SC) WiMAX (IEEE 802.16-2004) radio. Instead of using any one particular type of channel profile, this study concentrates on true frequency selective Rayleigh fading channels in the real-time WiMAX radio environment around 3.5 GHz. The Constant Modulus Algorithm (CMA) blind equalizer has been compared with the popular non-blind equalizers, Recursive Least Squares (RLS) and Least Mean Squares (LMS) algorithm, as benchmarks. It has been proven in experimental and simulated channels that CMA blind equalizer, using the proposed technique, can be considered as a low complexity, spectrum efficient and high performance time domain equalizations to be embedded in a transceiver for the next generation communications. Furthermore the proposed technique has also reduced approximately till 5 dB and 7.5 dB performance differences between non-blind and blind equalizers for 16-QAM and 64-QAM, respectively. The simulation results have demonstrated that the simulated and experimental studies of the proposed technique are compatible with each other and extremely satisfying

Blind equalization based on spatial and temporal diversity in block coded modulations

Linear block codes can be applied in spatial and/or temporal diversity receivers in order to develop high performance schemes for blind equalization in mobile communications. The proposed technique uses the structure of the encoded transmitted information (with redundancy) to achieve equalization schemes based on a deterministic criterion. Simulations show that the proposed technique is more efficient than other schemes that follow similar equalizer structures. The result is an algorithm that provides the design of blind channel equalizers in low EbNo scenarios.Peer ReviewedPostprint (published version

Diversity in mobile communications for blind detection of block-coded modulations

Spatial, temporal, and frequency diversity structures are analyzed to address the blind equalization problem in the presence of time-variant frequency selective channels. The aim of the paper is to present equalization schemes useful in front of fast changing channel responses. The best solution is a deterministic blind criterion that allows direct channel equalization and symbol detection. The main contribution of this paper is to present deterministic blind equalization schemes in CDMA systems (frequency diversity) to reduce the impact of the time-variant frequency selective channel.Peer ReviewedPostprint (published version

A new family of blind adaptive equalization algorithms

Published versio

Diversity techniques for blind channel equalization in mobile communications

A blind algorithm for channel distortion compensation is presented which can be employed in spatial or temporal diversity receivers. The proposed technique can be used in frequency selective and frequency flat fading mobile channels, using burst transmission schemes in the first case and OFDM modulation in the second one. The algorithm is base on a deterministic criteria and is suited for estimation when short sets of data are available.Peer ReviewedPostprint (published version

Fractional biorthogonal partners in channel equalization and signal interpolation

The concept of biorthogonal partners has been introduced recently by the authors. The work presented here is an extension of some of these results to the case where the upsampling and downsampling ratios are not integers but rational numbers, hence, the name fractional biorthogonal partners. The conditions for the existence of stable and of finite impulse response (FIR) fractional biorthogonal partners are derived. It is also shown that the FIR solutions (when they exist) are not unique. This property is further explored in one of the applications of fractional biorthogonal partners, namely, the fractionally spaced equalization in digital communications. The goal is to construct zero-forcing equalizers (ZFEs) that also combat the channel noise. The performance of these equalizers is assessed through computer simulations. Another application considered is the all-FIR interpolation technique with the minimum amount of oversampling required in the input signal. We also consider the extension of the least squares approximation problem to the setting of fractional biorthogonal partners

Blind Equalization and Channel Estimation in Coherent Optical Communications Using Variational Autoencoders

We investigate the potential of adaptive blind equalizers based on variational inference for carrier recovery in optical communications. These equalizers are based on a low-complexity approximation of maximum likelihood channel estimation. We generalize the concept of variational autoencoder (VAE) equalizers to higher order modulation formats encompassing probabilistic constellation shaping (PCS), ubiquitous in optical communications, oversampling at the receiver, and dual-polarization transmission. Besides black-box equalizers based on convolutional neural networks, we propose a model-based equalizer based on a linear butterfly filter and train the filter coefficients using the variational inference paradigm. As a byproduct, the VAE also provides a reliable channel estimation. We analyze the VAE in terms of performance and flexibility over a classical additive white Gaussian noise (AWGN) channel with inter-symbol interference (ISI) and over a dispersive linear optical dual-polarization channel. We show that it can extend the application range of blind adaptive equalizers by outperforming the state-of-the-art constant-modulus algorithm (CMA) for PCS for both fixed but also time-varying channels. The evaluation is accompanied with a hyperparameter analysis.Comment: Published (Open Access) in IEEE Journal on Selected Areas in Communications, Sep 202

A Closed-Form Approximated Expression for the Residual ISI Obtained by Blind Adaptive Equalizers with Gain Equal or Less than One

In this paper we propose for the real and two independent quadrature carrier case, a closed-form approximated expression for the achievable residual Inter-Symbol Interference (ISI) that depends on the step-size parameter, equalizer’s tap length, equalized output gain, input signal statistics, channel power and SNR. This expression is valid for blind adaptive equalizers, where the error that is fed into the adaptive mechanism which updates the equalizer‘s taps can be expressed as a polynomial function of order three of the equalized output and where the gain between the input and equalized output signal is less than or equal to one, as is in the case of Godard (gain = 1) and WNEW (gain < 1) algorithm. Since the channel power is measurable or can be calculated if the channel coefficients are given, there is no need to carry out simulation with various step-size parameters in order to reach the required residual ISI. In addition, we show two new equalization methods (gain dependent), which have shown to have improved equalization performance compared to Godard and WNEW