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Simplified Robust Adaptive Detection and Beamforming for Wireless Communications

Ayman Elnashar

Emirates Integrated Telecommunications Company (EITC)
Dubai
UAE

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Dedication

This book is dedicated to the memory of my parents (God bless their souls). They gave me the strong foundation and unconditional love, which remains the source of motivation and is the guiding light of my life.

Also, this book is dedicated to my PhD supervisors, Prof. Said Elnoubi from Alexandria University and Prof. Hamdi Elmikati from Mansoura University. They have guided and encouraged me during my PhD thesis and inspired me to author this book.

To my dearest wife, your encouragement and patience has strengthened me always.

To my beloved children Noursin, Amira, Yousef, and Yasmina. You are the inspiration!

Finally, I acknowledge the contribution of Tamer Samir from mobily for chapter 8.

– Ayman Elnashar, PhD

About the Author

Ayman Elnashar, PhD, has 20+ years of experience in telecoms industry including 2G/3G/LTE/WiFi/IoT/5G. He was part of three major start‐up telecom operators in MENA region (Orange/Egypt, Mobily/KSA, and du/UAE). Currently, he is Vice President and Head of Infrastructure Planning ‐ ICT and Cloud with the Emirates Integrated Telecommunications Co. “du”, UAE. He is the founder of the Terminal Innovation Lab and UAE 5G innovation Gate (U5GIG). Prior to this, he was Sr. Director – Wireless Networks, Terminals and IoT where he managed and directed the evolution, evaluation, and introduction of du wireless networks including LTE/LTE‐A, HSPA+, WiFi, NB‐IoT and currently working towards deploying 5G network in UAE. Prior to this, he was with Mobily, Saudi Arabia, from June 2005 to Jan 2008 as Head of Projects. He played key role in contributing to the success of the mobile broadband network of Mobily/KSA. From March 2000 to June 2005, he was with Orange Egypt.

He published 30+ papers in wireless communications arena in highly ranked journals and international conferences. He is the author of “Design, Deployment, and Performance of 4G‐LTE Networks: A Practical Approach” published by Wiley & Sons, and “Practical Guide to LTE‐A, VoLTE and IoT: Paving the way towards 5G” to be published in May 2018. His research interests include practical performance analysis, planning and optimization of wireless networks (3G/4G/WiFi/IoT/5G), digital signal processing for wireless communications, multiuser detection, smart antennas, massive MIMO, and robust adaptive detection and beamforming.

About the Companion Website

This book is accompanied by a companion website:

flastg001

www.wiley.com/go/elnashar49

The website include:

  • Matlab scripts

1
Introduction

1.1 Motivation

This book presents alternative and simplified approaches for the robust adaptive detection and beamforming in wireless communications. The book adopts several system models, including:

  • DS/CDMA, with and without antenna array
  • MIMO‐OFDM with antenna array
  • general smart antenna array model.

Recently developed detection and beamforming algorithms are presented and analyzed with an emphasis on robustness. In addition, simplified and efficient robust adaptive detection and beamforming techniques are developed and compared with existing techniques. The robust detectors and beamformers are implemented using well‐known algorithms including, but not limited to:

  • least‐mean‐square
  • recursive least‐squares (RLS)
  • inverse QR decomposition RLS (IQRD‐RLS)
  • fast recursive steepest descent (RSD)
  • block‐Shanno constant modulus (BSCMA)
  • conjugate gradient (CG)
  • steepest descent (SD).

The robust detection and beamforming methods are derived from existing detectors/beamformers including, but not limited to:

  • the robust minimum output energy (MOE) detector
  • partition linear interference canceller (PLIC) detector
  • linearly constrained constant modulus (CM) algorithm (LCCMA),
  • linearly constrained minimum variance (LCMV) beamforming with single constraint,
  • minimum variance distortionless response (MVDR) beamformer with multiple constraint
  • block Shanno constant modulus algorithm (BSCMA) based detector/beamformer
  • adaptive minimum bit error rate (BER) based detectors.

The adopted cost functions include the mean square error (MSE), BER, CM, MV and the signal‐to‐noise or signal‐to‐interference‐plus‐noise ratios (SINR/SNR). The presented robust adaptive techniques include:

  • quadratic inequality constraint (QIC)
  • diagonal loading techniques
  • single and multiple worst‐case (WC) constraint(s)
  • ellipsoidal constraint
  • joint constraints

Detailed performance analysis in terms of MSE, SINR, BER, computational complexity, and robustness are conducted for all the presented detectors and beamformers. Practical examples based on the above system models are provided to exemplify the developed detectors and beamforming algorithms. Moreover, the developed techniques are implemented using Matlab and the relevant Matlab scripts are provided to allow the readers to develop and analyze the presented algorithms. The developed algorithms will be presented in the context of DS/CDMA, MIMO‐OFDM, and smart antenna arrays, but they can be easily extended to other domains and other applications. Figure 1.1 provides a high‐level description of the book.

Schematic illustration of the summary of the book.

Figure 1.1 Summary of the book.

Recently, robust adaptive detection/beamforming has become a hot topic. Researchers seek to provide robustness against uncertainty in the direction of arrival (DOA) or the signature waveform, accuracy errors, calibration errors, small sample sizes, mutual coupling in antenna arrays, and so on. The major concern with the robust algorithms is the compromises involving robustness, complexity, and optimality. This book is aims to efficiently address this concern by presenting alternative and simplified approaches for robust adaptive detection and beamforming in wireless communications systems. The presented algorithms have low computational complexity while offering optimal or close‐to‐optimal performance and can be practically implemented. Wireless communication applications using DS/CDMA, MIMO‐OFDM, and smart antenna systems are presented to demonstrate their robustness and to compare their complexity with established techniques and optimal detectors/beamformers.

The book presents and addresses current hot topics in adaptive signal processing: robustness and simplified adaptive implementation. It presents simplified approaches that add robustness to adaptive signal processing algorithms, with less computational complexity, while maintaining optimality. In addition, the presented algorithms are illustrated with practical examples and simulation results for major wireless communications systems, including DS/CDMA, MIMO‐OFDM, and smart antenna systems. Moreover, Matlab scripts are provided for further analysis and development. The reader can easily extend the techniques and approaches in this book to other areas and to different applications.

With the growth of mobile communication subscribers, the introduction of high data‐rate services, and the overall increase in user traffic, new ways are needed to increase the capacity of wireless networks. Smart antennae, MIMO and beamforming are some of the most promising technologies now being exploited to enhance the capacity of the cellular system. In wireless networks, the traditional omni and directional antennae of a base‐station cause higher interference than necessary. Additionally, they are wasteful, as most transmitted signals will not be received by the target user. Adaptive antennas are a multidiscipline technology area that has exhibited growth steadily over the last four decades, primarily due to the impressive advances in the field of digital processing. Exploiting the spatial dimension using adaptive antennae promises impressive increases in system performance in terms of capacity, coverage, and signal quality. This will ultimately lead to increased spectral efficiency and extended coverage, especially for higher‐frequency bands, such as millimetre waves (mmWave), that will be adopted for 5G evolution.

1.2 Book Overview

In Chapter 1, the mathematical models of DS/CDMA and MIMO‐OFDM systems are presented. These form the foundation for the robust adaptive detection and beamforming algorithms that will be presented and/or developed in this book. DS/CDMA and OFDM are used in 3GPP 3G and 4G systems respectively. The 5G system under development by 3GPP will use evolved versions of MIMO‐OFDM. The algorithms presented in this book may fit any of these systems and may also be extended to other systems. The focus of the 3G and 4G evolutions were on mobile broadband, as a result of widespread smartphone adoption. The internet of things (IoT) evolution will lead to billions of devices being connected to the internet and this has directed the 3GPP and mobile communications industry towards narrowband technologies. 3GPP has modified the LTE system to meet the IoT requirements by introducing NB‐IoT. Other proprietary technologies, such as low‐power wide‐area networks, have used narrowband or ultra‐narrowband technologies such as chirp spread spectrum. The focus of this book is not on certain technologies and readers will need to expend some effort in order to apply the detection and beamforming algorithms outlined here to specific systems. The focus of the book is the development and comparative analysis of robust adaptive detection and beamforming algorithms based on simplified system models. All the results in the book are simulated using Matlab and the developed scripts are provided along with the book. The reader may need to slightly modify the scripts depending on the Matlab version. In addition, some algorithms developed by other authors are provided as part of the software package with this book for the purpose of comparative analysis.

In Chapter 3, we will provide a survey of adaptive detection algorithms based on the DS/CDMA model. However, the adaptive techniques that are summarized in this survey can be easily extended to MIMO‐OFDM and smart antenna arrays. The DS/CDMA model is the most complicated system model, because of its need for multiuser interference cancellation and since the channel is frequency selective, as explained in Chapter 2. Despite the various advantages of the DS/CDMA system, it is interference limited due to multiuser interference and it cannot be easily extended to ultra‐broadband systems. A conventional DS/CDMA receiver treats each user separately as a signal, with other users considered as noise or multiple access interference (MAI). A major drawback of such conventional DS/CDMA systems is the near–far problem: degradation in performance due to the sensitivity to the power of the desired user against the power of the interference. A reliable demodulation is impossible unless tight power control algorithms are exercised. The near–far problem can significantly reduce the capacity. Multiuser detection (MUD) algorithms can give dramatically higher capacity than conventional single‐user detection techniques. MUD considers signals from all users, which leads to joint detection. MUD reduces interference and hence leads to a capacity increase, alleviating the near–far problem. Power control algorithms can be used but are not necessary.

Linear receiver design by minimization of some inverse filtering criterion is explained in Chapter 4. Appropriate constraints are used to avoid the trivial all‐zero solution. A well‐known cost function for the constrained optimization problem is the variance or the power of the output signal. An MOE detector for multiuser detection is developed, based on the constrained optimization approach. In an additive white Gaussian environment with no multipath, this detector provides a blind solution with MMSE performance. In Chapter 4, linearly constrained IQRD‐RLS algorithms with multiple constraints are developed and implemented for MUD in DS/CDMA systems. As explained above, the same algorithms can be extended to MVDR beamforming algorithms. Two approaches are considered, the first with a constant constrained vector and the other with an optimized constrained vector. Three IQRD‐based detectors are developed as follows:

  • a direct form MOE detector based on the IQRD update method with fixed constraints
  • a MOE detector in the PLIC structure based also on the IQRD‐RLS algorithm
  • an optimal MOE algorithm built using the IQRD update method and a subspace tracking algorithm for tracking the channel vector.

The constrained vector (estimated channel vector) is obtained using the max/min approach with IQRD‐RLS based subspace tracking algorithms that are analyzed and tested for channel vector tracking.

The recently developed subspace tracking algorithms are tested and analyzed for channel estimation in Chapter 4. These are the fast orthogonal projection approximation subspace tracking (OPAST) algorithm and the normalized orthogonal Oja (NOOja) algorithm. In addition, a fast subspace tracking algorithm based on the Lagrange multiplier methodology and the IQRD algorithm will be developed and adopted for channel vector estimation and tracking. Moreover, a new strategy for combining the max/min channel estimation technique with the robust quadratic constraint technique is proposed anchored in the direct form algorithm. Specifically, a robust MOE detector is developed, based on the max/min approach and QIC on the weight vector norm to overcome noise enhancement at low SNR. A direct form solution is introduced for the quadratically constraint detector with a variable loading (VL) technique employed to satisfy the QIC. Thus, the IQRD algorithm acts as a core to the proposed receivers, which facilitate real‐time implementation through systolic implementation. However, the same algorithms can be easily implemented using fast and robust RLS‐based algorithms.

A robust low‐complexity blind detector is presented in Chapter 5. This is based on a recursive steepest descent (RSD) adaptive algorithm rather than the RLS algorithm and a QIC on the weight vector norm. The QIC is employed to manage the residual signal mismatch and other random perturbations errors. In addition, the QIC will make the noise constituent in the output SINR constant and hence overcome noise enhancement at low SNR. Quadratic constraints have been used in adaptive beamforming for a variety of purposes, such as improving robustness against mismatch and modeling errors, controlling mainlobe response, and enhancing interference cancellation capability. The quadratic constraint will be analyzed along with beamforming algorithms in Chapter 7.

Analogous to the recursive conjugate gradient (RCG) algorithm, a fast RSD algorithm is developed in Chapter 5. A low‐computational complexity recursive update equation for the gradient vector is derived. Furthermore, a variable step‐size approach is introduced for the step‐size update of the RSD algorithm based on an optimum step‐size calculation. The RSD algorithm is exploited to update the adaptive weight vector of the PLIC structure to suppress MAI. The same technique will be extended to MVDR beamforming in Chapter 7. From this similarity, the reader can easily extend the algorithms in this book to other systems and even beyond the realm of wireless communications. From this it can be seen that we have simplified the deployment of the robust techniques, such as quadratic constraints, uncertainty constraints, worst‐case constraint optimization, and constrained optimization.

The drawbacks of diagonal loading techniques are tackled in Chapter 5. An alternative way of robust adaptive detection based on the RSD adaptive algorithm is presented. This involves an accurate technique for precisely computing the diagonal loading level without approximation or eigendecomposition. We combined the QIC with the RSD algorithm to produce a robust recursive implementation with O(N2) complexity. A new optimal VL technique is developed and integrated into the RSD adaptive algorithm. In addition, the diagonal loading term is optimally computed, with O(N) complexity, using a simple quadratic equation. Geometrical interpretations of the scaled projection (SP) and VL techniques, along with RLS and RSD algorithms, are illustrated and analyzed. The performance of the robust detectors is compared with traditional detectors and the former are shown to be more accurate and more robust against signal mismatch and random perturbations. Finally, the presented approach can be reformulated to handle an uncertainty constraint – imposed on the signature waveform in MUD, or on a steering vector in beamforming – such as the ellipsoidal constraint. It can also be exploited with any of the robust approaches to produce a simple recursive implementation.

In Chapter 6, the quadratic inequality constraint is imposed on the weight vector norm of the LCCMA and BSCMA algorithms in order to enhance their performance. The weight norm constraint will control the gradient vector norm, meaning that there is no need to check the gradient vector norm increase in BSCMA. Additionally, the iteration inside the block can continue without affecting algorithm stability due to the weight vector norm constraint. We will investigate the effect of adding a quadratic inequality constraint on the LCCMA and BSCMA algorithms. The proposed VL technique in Chapter 5 is exploited to estimate the optimum diagonal loading value. The LCCMA and BSCMA algorithms are used to update the adaptive vector of the PLIC structure. The PLIC structure with multiple constraints is employed to identify the MAI and hence help in avoiding interference capture. Moreover, the different forms of BS‐CMA algorithms – the block‐conjugate gradient CMA algorithm (BCGCMA) and block gradient descent constant modulus algorithm (BGDCMA) – are investigated as well. The resistance of BSCMA‐based algorithms against the near–far effect is discussed and evaluated.

In Chapter 7, we will present four approaches for robust adaptive beamforming as follows:

  • Improved recursive realization for robust LCMV beamforming We first develop an improved recursive realization for robust LCMV beamforming. This includes an ellipsoidal uncertainty constraint on the steering vector. The robust recursive implementation presented here is based on a combination of the ellipsoidal constraint formulation and the variable diagonal loading technique demonstrated in Chapter 5. As a consequence, an accurate technique for computing the diagonal loading level without eigendecomposition or SOCP is developed. The geometrical interpretation of the diagonal loading technique is demonstrated and compared with eigendecomposition approach. Note that this approach adopts a spherical constraint on the steering vector to optimize the beamformer output power. Unfortunately, the adaptive beamformer developed here is apt to noise enhancement at low SNR and an additional constraint is required to bolster the ellipsoidal constraint.
  • Joint constraint approach for a joint robustness beamformer The second approach is the development of a joint constraint approach for a joint robustness beamformer. A joint constraint approach is presented for joint robustness against steering vector mismatch and unstationarity of interferers. An alternative approach involves imposing an ellipsoidal uncertainty constraint and a quadratic constraint on the steering vector and the beamformer weights, respectively. We introduce a new simple approach to get the corresponding diagonal loading value. The quadratic constraint is invoked as a cooperative constraint to overcome noise enhancement at low SNR. The performance of the robust adaptive schemes developed and other robust approaches are demonstrated in scenarios with steering vector mismatch and several moving jammers.
  • Beamformer with a single WC constraint In the third approach, a robust MVDR beamformer with a single WC constraint is implemented using an iterative gradient minimization algorithm. This involves a simple technique to estimate the Lagrange multiplier instead of a Newton‐like algorithm. This algorithm exhibits several merits, including simplicity, low computational load, and no need for either sample‐matrix inversion or eigendecomposition. A geometric interpretation of the robust MVDR beamformer is demonstrated to supplement the theoretical analysis.
  • LCMV beamformer with MBWC constraints In the last approach, a robust LCMV beamformer with multiple‐beam WC (MBWC) constraints is developed using a novel multiple‐WC constraints formulation. The optimization problem entails solving a set of nonlinear equations. As a consequence, a Newton‐like method is mandatory to solve the system of nonlinear equations, which yields a vector of Lagrange multipliers. The Lagrange method is used to give the solution.

The traditional MMSE detector is the most popular technique for beamforming. An adaptive implementation of the MMSE can be achieved by minimizing the MSE between the desired output and the actual array output. The LCMV and MVDR beamformers in Chapter 7 are different forms of MMSE detectors. For a practical communication system, it is the BER or block BER, not the MSE performance, that really matter. Ideally, the system design should be based directly on minimizing the BER rather than the MSE. For application in single‐user channel equalization, multiuser detection, and beamforming, it has been shown that the MMSE solution can, in certain situations, be distinctly inferior to the minimum BER (MBER) solution. However, the BER cost function is not a linear function of the detector or the beamformer, making it difficult to minimize. Several adaptive MBER beamformer/detectors implementations are developed in the literature.

It must be stated here that the cost function of the MMSE criterion has a circular shape. This means that we have one global minimum. Hence, convergence can be easily achieved. In contrast, the cost function of the BER is highly nonlinear. This means that during minimization steps we may converge to a local minimum. The MMSE and MBER solutions lead to very different detector weight vectors. Clearly, the MBER design is more intelligent in utilizing the detector's resources. However, special attention is mandatory with the minimization algorithm in order to avoid convergence to a local minimum, and hence the algorithm diverging rather than converging.

Beamforming is a key technology in smart antenna systems, and can increase capacity and coverage and mitigate multipath propagation in mobile radio communication systems. The most popular criterion for linear beamforming is MMSE. However, the MSE cost function is not optimal in terms of the bit error probability performance of the system. In Chapter 8, a class of adaptive beamforming algorithms using direct minimization of the BER cost function is presented. Unfortunately, the popular least minimum BER stochastic beamforming algorithm suffers from low convergence speeds. Gradient Newton algorithms are presented as an alternative. These speed up the convergence rate and enhance performance but only at the expense of complexity. In Chapter 8, a block processing objective function for the MBER is formulated, and a nonlinear optimization strategy that produces the so‐called ‘block‐Shanno MBER’ is developed. A complete consideration of the complexity calculations of the proposed algorithm is given. Simulation scenarios are carried out in a multipath Rayleigh‐fading DS‐CDMA system to explore the performance of the proposed algorithm. Simulation results show that the proposed algorithm offers good performance in terms of convergence speed, steady‐state performance, and even system capacity, compared to other MBER‐ and MSE‐based algorithms.

Finally, we will extend the adaptive filtering algorithms using the concept of spatial multiuser detection in a MIMO‐OFDM system model rather than beamforming in a DS‐CDMA model. As stated above, a fundamental goal in any digital communications system is to directly minimize the BER. Wiener solution based algorithms indirectly minimize the BER by optimizing other cost functions (SNR, SINR, or MSE), which may result in suboptimal BER performance.