Machine learning based approaches are being increasingly used for designing decoders for next generation communication systems. One widely used framework is neural belief propagation (NBP), which unfolds the belief propagation (BP) iterations into a deep neural network and the parameters are trained in a data-driven manner. NBP decoders have been shown to improve upon classical decoding algorithms. In this paper, we investigate the generalization capabilities of NBP decoders. Specifically, the generalization gap of a decoder is the difference between empirical and expected bit-error-rate(s). We present new theoretical results which bound this gap and show the dependence on thedecoder complexity, in terms of code parameters (blocklength, message length, variable/check node degrees), decoding iterations, and the training dataset size. Results are presented for both regular and irregular parity-check matrices. To the best of our knowledge, this is the first set of theoretical results on generalization performance of neural network based decoders. We present experimental results to show the dependence of generalization gap on the training dataset size, and decoding iterations for different codes.

Machine learning based approaches are being increasingly used for designing decoders for next generation communication systems. One widely used framework is neural belief propagation (NBP), which unfolds the belief propagation (BP) iterations into a deep neural network and the parameters are trained in a data-driven manner. NBP decoders have been shown to improve upon classical decoding algorithms. In this paper, we investigate the generalization capabilities of NBP decoders. Specifically, the generalization gap of a decoder is the difference between empirical and expected bit-error-rate(s). We present new theoretical results which bound this gap and show the dependence on the decoder complexity, in terms of code parameters (blocklength, message length, variable/check node degrees), decoding iterations, and the training dataset size. Results are presented for both regular and irregular parity-check matrices. To the best of our knowledge, this is the first set of theoretical results on generalization performance of neural network based decoders. We present experimental results to show the dependence of generalization gap on the training dataset size, and decoding iterations for different codes.

We provide unsupervised machine learning (ML) schemes based on autoencoders for unconstrained beamforming (BF) and hybrid BF in millimeter-waves (mmWaves). An autoencoder is a powerful unsupervised ML model, and it is used to reconstruct the input with a minimal error by finding a low-dimensional representation of the input. In this paper, we present a linear autoencoder for finding the beamformers at the transmitter (Tx) and receiver (Rx), which maximize the achieved rates over the mmWave channel. Since the autoencoder has a close relationship with the singular value decomposition (SVD), we first study autoencoders for unconstrained BF based on SVD. In hybrid BF, beamformers are designed by using finite-precision phase shifters in the radio frequency (RF) domain along with power constraints. Therefore, we propose a hybrid BF algorithm based on autoencoders, which incorporates these constraints. We present our simulation results for both unconstrained BF as well as hybrid BF, and compare their performance with state-of-the-art. By using the stochastic and NYUSIM channel models, we achieve 30 - 40% and 60 - 70% gains in rates with the proposed autoencoder based approach compared to the supervised hybrid BF with the stochastic and NYUSIM channel models, respectively.

Utilization of multiple-input multiple-output (MIMO) systems as a means of increasing channel capacity has been an area of increasing consideration in radio communications. However, less study has been devoted to MIMO in the high-frequency band. This research is important because high-frequency communication using MIMO allows for international communication at long distances using lower power consumption than many other approaches. The inter-symbol interference caused by the selective fading of multiple received signals and the randomness of the ionospheric conditions means there is a need for a novel solution. The purpose of this research is to introduce two machine learning approaches that can adaptively apply equalization algorithms to address fading and optimize equalization parameters. The novelty of our approach lies in two main factors. The first is that our approach allows for a software-defined radio to switch equalization algorithms depending on conditions during run-time. The second is that we optimize this selected algorithm further by using two machine-learning approaches. The first proposed cognitive engine model, which utilizes a genetic algorithm, demonstrates the validity and advantage of using a cognitive engine to select optimal equalization parameters at the receiver under the problems created by utilizing the high-frequency band. This approach acts as a comparison for our second. We then propose a second cognitive engine, the adaptive manipulator, which optimizes not only by selecting equalization parameters but also continually changes the equalization algorithm. Finally, we compare the performance of the proposed cognitive engine models with state-of-the-art algorithms.

Hybrid beamforming (BF), which divides BF operation into radio frequency (RF) and baseband (BB) domains, will play a critical role in MIMO communication at millimeter-wave (mmW) frequencies. In principle, we can obtain unconstrained (optimum) beamformers of a transceiver, which approach the maximum achievable data rates, through its singular value decomposition (SVD). Due to the use of finite-precision phase shifters, combined with power constraints, additional challenges are imposed on the problem of designing hybrid beamformers. Motivated by the recent success of machine learning (ML) techniques, particularly in areas such as computer vision and speech recognition, we explore if ML techniques can be effectively used for SVD and hybrid BF. To this end, we first present a data-driven approach to compute the SVD. We propose three deep neural network (DNN) architectures to approximate the SVD, with varying levels of complexity. The methodology for training these DNN architectures is inspired by the fundamental property of SVD, i.e., it can be used to obtain low-rank approximations. We next explicitly take the constraints of hybrid BF into account (such as quantized phase shifters, power constraints), and propose a novel DNN based approach for the design of hybrid BF systems. To validate the DNN based approach, we present simulation results for both approximating the SVD as well as for hybrid BF. Our results show that DNNs can be an attractive and efficient solution for estimating SVD in a data-driven manner. For the simulations of hybrid BF, we first consider the geometric channel model. We show that the DNN based hybrid BF improves rates by up to 50 - 70% compared to conventional hybrid BF algorithms and achieves 10 - 30% gain in rates compared with the state-of-art ML-aided hybrid BF algorithms. We also discuss the impact of the choice of hyperparameters, such as the number of hidden layers, mini-batch size, and training iterations on the accuracy of DNNs. Furthermore, we provide time complexity and memory requirement analyses for the proposed approach and state-of-the-art approaches.

A sliding window technique for vision-based autonomous navigation applications is a common approach to path mapping from extracted features. Mapping a path inside a captured image requires finding a series of waypoints representing the path. Previous approaches find these points by sliding a window along the path in fixed increments across one image dimension. After each slide, the center of the window in the other dimension is adjusted so that the window maximally covers the path in that area. These approaches, however, fails to map paths that experience sharp curvature since the windows slide along only one dimension. The method proposed herein uses a pseudo-derivative approach to sliding windows that improves upon the traditional technique by dynamically adjusting the windows along both image dimensions during each slide. In this method, the directional components of a vector representing the previous slide are used as a naive estimation to perform the current slide. If this fails to map the path, the vector direction is used to enlarge the window dimensions. The method was tested in the domain of autonomous vehicles for lane- following based on lane-markings. The algorithm proved to be successful with lanes possessing sharp curvature and discontinuities as compared to previous sliding window approaches.

The radio frequency spectrum is occupied with authorized and unauthorized user activities which might include noise and interference. Detection of signals-of-interest (SOI) and differentiation from non-signals-of-interest (NSOI) are therefore crucial for frequency use management. There is a wide variety of signals in a desired radio spectrum band, which leads to the application of Signal Intelligence (SIGINT) to detect and identify signals in real-time. In this paper, we study the problem of non-Gaussian signal detection when the receivers are configured with a large number of antennas (or the massive antenna regime). First, we investigate the performance of signal detection with massive MIMO when the transmitted signals are generated from a Gaussian distribution. For the detection of Gaussian signals, we consider the Neyman-Pearson (NP) detector. Then, we focus on the performance of non-Gaussian signal detection with massive MIMO, which is one of the main objectives of this paper. We show that the NP detector gives poor performance for non-Gaussian signals in low signal-to- noise-ratio (SNR). Therefore, we propose to use a bispectrum detector, which contains the Gaussian noise and reveals the non-Gaussian information that exists in the signal. We present the theoretical analysis for asymptotic behavior of Probability of False Alarm (PFA) and Probability of Detection (PD) when the transmitter sends Gaussian and non-Gaussian signals. We show the performance of signal detection (for both Gaussian and non-Gaussian signals) as a function of the number of antennas and sampling rate. We also obtain the scaling behavior of the performance in the massive antenna regime.

Automatic Modulation Classification is a key technology in Cognitive Radio Networks. Blind identification of the modulation scheme of an unknown detected signal has various commercial and military applications. Performance of Automatic Modulation Classifiers degrades severely under low Signal-to-Noise ratios and fading channel scenarios. Cooperative classification is presented as a means to enhance the classification performance as well as to relax the computational constraints on individual nodes. In this work, the performance of cooperative cumulants-based modulation classification is studied under flat Rayleigh fading channels. The degradation in performance of a single node under flat Rayleigh fading is first presented in comparison to Additive White Gaussian Noise channels. Next, performance improvement obtained through cooperative combining of classification data from several nodes is presented. Analytical results as well as simulations show that cooperation will improve the overall performance of modulation classifiers, overcoming the performance loss due to fading and reaching classification results comparable to the AWGN scenario.

In this paper, we provide an overview of how cognitive radio (CR) technology is making its way into the current wireless standards, and we discuss further opportunities for more CR-oriented standardization efforts. Specifically, we discuss how a cognitive engine (CE) can be potentially standardized, and we offer our latest innovations on metacognitive engine (meta-CE) design. The intelligent techniques of a CR are implemented in an agent commonly referred to as a CE. A CE manages the CR's operation. Typically, a CE is based on a primary learning and optimization algorithm that is utilized within the CE. Each of these algorithms has its own strengths and deficiencies depending on the operating scenario that makes some of them more appropriate for specific operating conditions. A meta-CE is an engine that learns which CE is more appropriate to provide the adaptation needed for the operating conditions. To make a meta-CE possible, first, we need a method for characterizing the CE algorithm's performance. Second, we should classify the operating conditions based on the CE algorithm's characteristics in order to determine the most appropriate operating condition. Our results show that, when we use meta-CE techniques, we have about 30% increase in performance compared with using the best individual CE.

Automatic Modulation Classification (AMC) is an important component in Cognitive Radio (CR) Networks. Multiuser AMC classifies the modulation schemes of simultaneous multiple unknown transmitters. In addition, cooperation among multiple CR receivers for modulation classification offers significant improvements in classification performance and overcomes the detrimental channel effects that degrades the single CR classifier performance. In this paper, a novel centralized soft-combining data fusion algorithm based on the joint probability distribution of fourth order cumulants is presented for cooperative modulation classification. Fourth order cumulants of the received signals are calculated as discriminating features for different modulation schemes at each CR node and sent to a centralized data Fusion Center (FC). The FC chooses the modulation scheme that maximizes the joint probability of the estimated cumulants. As compared to independent receiver classification, cooperative classification results are significantly improved under the same multi-path environment.

In this paper we consider spectrum sharing between a communication system, modeled as MIMO interference channel (MIMO IFC), and MIMO radar. We first derive a zero-forcing precoder to eliminate the interference at the communication receivers. We show that this precoder is equivalent to orthogonal projection matrix onto the null space of an effective interference channel and show that this choice of precoder will degrade the radar target direction estimation performance. We show that the radar performance can be improved at the cost of non-zero interference at communication users by projecting the radar signal onto a subspace which is an expanded version of the aforementioned null space. We propose two approaches to smoothly expand the projected subspace and study the tradeoff between radar performance and interference at the communication users through simulation.

In practice, computational complexity is an important consideration of an adaptive signal processing system. A well-known approach to controlling computational complexity is applying partial update (PU) adaptive filters. In this paper, a partial update Euclidean Direction Search (EDS) algorithm is employed. The theoretical analyses of mean and mean-square performance are presented. The simulation results of different PU EDS are shown.

Wireless distributed computing has several unique problems compared with currently well investigated wireless sensor networks. These problems include the impact of channel variation on power allocation, different traffic pattern with higher utilization, and more restricted delay constraints. This paper investigates the impact of communication channel condition on the average execution time of the computing task within wireless distributed computing networks (WDCN). It has been found that the delay performance of wireless distributed computing is influenced by both the average channel condition and the variation of channels. In addition, the impact of channel heterogeneity is also investigated to show the possibility of the optimal workload distribution for energy saving and robustness. Finally, a workload distribution approach combined with a power allocation scheme exploiting the spatial heterogeneity of the channel condition is proposed to balance energy efficiency and robustness.

Advanced wireless applications such as sensor networks involve a close interaction between the communication and computation processes that deliver the services under stringent power constraints. Wireless network distributed computing (WNDC) is a potential solution to reducing the power consumption per node as well as that of the network. In WNDC, a computational task is executed among a network of collaborative nodes in a distributed manner as against performing the same task on a single node. In addition to providing power savings, WNDC enables power demand-supply matching that allows for system operation under a constrained power supply such as solar power. This paper presents fundamental power efficiency analysis of WNDC. The conditions for achieving power demand-supply matching and positive network power savings under power and computational latency constraints are derived. The results show the impact of non-linearity in the computational system characteristics and the communication overhead on the power savings.

When adaptive filtering algorithms are implemented in a finite wordlength processor, quantization effects are inevitable. In this paper, the Euclidean Direction Search (EDS) filtering algorithm is analyzed for quantization effects. A mathematical analysis is performed for both transient and steady state behavior of the algorithm. A new energy conservation identity and an expression for the steady state error are obtained for the quantized system. Computer simulations are given to support the theoretical results.

This paper considers the problem of blind adaptive equalization of single-input multiple-output IIR channels without requiring the channel diversity condition. That is, the parallel sub-channels in the fractionally sampled model can have common factors. We develop an equalizer based on IIR prediction of the received signal. The predictor parameters are estimated by using the recursive extended least squares (RELS) algorithm. It is proved that the adaptive equalizer is globally stable and the prediction error converges in a Cesaro sense almost sure (a.s.) (with probability one) towards a scalar multiple of the input symbol sequence

The paper develops an extension of the adaptive RLS-type algorithm proposed by X.-L. Zhu and X.-D. Zhang (see IEEE Sig. Process. Lett., vol.9, no.12, p.432-5, 2002). Their work uses the matrix inversion lemma to solve iteratively the equation obtained from the natural gradient of the nonlinear principle component analysis problem. We reduce the complexity of the solution by applying the Euclidean direction search concept in place of the matrix inversion lemma. The simulations performed show that the convergence rate is comparable, albeit slower, but with reduced complexity per iteration.

We introduce a genetic algorithm (GA)-based method for structural optimization of multiplicative general parameter (MGP) finite impulse response (FIR) filters. These computationally efficient reduced-rank adaptive filters are robust, suitable for predictive configurations, and they have numerous applications in 50/60 Hz power systems instrumentation. The design process of such filters has three independent stages: Lagrange multipliers-based optimization of the sinusoid-predictive basis filter, genetic algorithm-based search of optimal FIR tap cross-connections and, finally, the online MGP-adaptation phase guided by variations in signal statistics. Thus, our multi-stage design procedure is a complementary fusion of hard computing (HC) and soft computing (SC) methodologies. Such advantageous fusion (or symbiosis) thinking is emerging among researchers and practicing engineers, and it can potentially lead to competitive combinations of individual HC and SC methods.

The stability of two-dimensional (2-D) periodically shift varying (PSV) filters formulated as the Givone-Roesser (GR) model is considered. The GR model is embedded into the 2ndmodel of Fornasini-Marchesisni (FM) and the stability of this embedded model is then studied. Several sufficient conditions and one necessary condition are obtained.

The stability of two-dimensional (2D) periodically shift varying (PSV) filters is considered. These filters have applications in filtering video signals with cyclostationary noise, image and video scrambling, and design of multiplierless filters. The considered system is represented in state space by the first model of Fornasini-Marchesini with periodic coefficients. The stability of this model is then studied. Two necessary conditions and two sufficient conditions are established for asymptotic stability. The conditions are easy to use and computationally simple.

The use of median and averaging filters is fairly routine in signal processing applications. One problem in using such algorithms is the lack of objective criteria by which to decide whether an averager or a median filter is more appropriate. We formulate an L/sub p/ (1/spl les/p/spl les/2) normed filter where p is chosen as a function of the kurtosis of the residual vector; we restrict attention in this work to a mean filter (p=2) and a median filter (p=1). In order to highlight the effectiveness of this filtering algorithm we demonstrate reduced sum squared error by adaptively filtering a sinusoid and a test image in the presence of both additive white Gaussian noise and an impulsive noise component.

Subband adaptive filters have been used extensively in system modeling configurations to model unknown systems with large impulse responses. This paper illustrates the advantages of a non-uniform subband adaptive filter over a uniform subband adaptive filter while giving insight to subband bandwidth allocations for system modeling configurations. By implementing small subbands which isolate the transition regions in the unknown system, while using larger subbands for other, more spectrally flat regions, one can minimize convergence time and lower misadjustment.

A mathematical analysis is performed on a previously reported gradient-based adaptive algorithm named the Euclidean direction set (EDS) method. It has been shown that the EDS algorithm has a computational complexity of O(N) for each system update, and a rate of convergence (based on computer simulations) comparable to the RLS algorithm. The stability of the EDS method is studied and it is shown that the algorithm converges to the true solution. It is also proved that the convergence rate of the EDS method is superior to that of the steepest descent method.

Normal form digital filters are attractive due to their desirable properties when implemented in finite wordlength arithmetic. These filters are free from all overflow limit cycles and quantization limit cycles when magnitude truncation is used. However, when two's complement truncation (TCT) quantization is used, limit cycles can still exist. It is shown that when block structures are used, normal form digital filters can be made free of limit cycles due to TCT quantization. It is shown that this can be done with a small block size. An algorithm is also presented to find the minimum block size required for a given filter. Some examples are given to illustrate the results.

A new recursive conjugate gradient (RCG) algorithm is developed for two-dimensional (2-D) adaptive differential pulse code modulation (ADPCM). This algorithm is based on the conjugate gradient method of optimization and therefore has a fast convergence characteristic. The RCG operates on samples of data rather than blocks, and is computationally simpler than the recursive least square (RLS) algorithm. Simulation results illustrate the efficiency of the method in ADPCM encoding of images.

Two-dimensional (2-D) periodically shift variant (PSV) digital filters are considered. These filters have potential applications in processing video signals with cyclostationary noise, scrambling of digital images, and in 2-D multirate signal processing. The filters are formulated in the form of the Fornasini-Marchesini (FM) state-space model with periodic coefficients. This PSV model is then represented as a new shift-invariant system which is named the "Kiok-Neon" model. This model has several advantages that include ease of analysis and reduced computations compared to the existing state-space models. An algorithm is developed that transforms any given 2-D PSV FM system to its equivalent "Kiok-Neon" model. Invertibility of this model is an important consideration, especially in image scrambling applications. A condition is established for the invertibility of the "Kiok-Neon" model of the 2-D PSV system. Also, the inverse system can be easily computed from the original. It is established that the 2-D PSV system is asymptotically stable if an equivalent shift-invariant FM system is asymptotically stable. The established results are illustrated with examples.

Two-dimensional (2-D) periodically shift variant (PSV) digital filters are considered. The filters are formulated in the form of the Fornasini-Marchesini (FM) state-space model with periodic coefficients. This PSV model is then represented as a new shift-invariant system which is named the "Kiok-Neon" model. This model has several advantages that include ease of analysis and reduced computations compared to the existing state-space models. An algorithm is developed that transforms any given 2-D PSV FM system to its equivalent "Kiok-Neon" model. Invertibility of this model is an important consideration, especially in image scrambling applications. A condition is established for the invertibility of the "Kiok-Neon" model of the 2-D PSV system. Also, the inverse system can be easily computed from the original.

A new class of nonlinear discrete-time systems is formulated and called the "Generalized Bilinear System (GBLS)". The well known bilinear system is a special class of this system, and hence the reason for the name. The GBLS is investigated for bounded input bounded output (BIBO) stability. It is shown that the GBLS is a special class of linear shift variant (LSV) systems. Three different sufficient conditions are established for the stability of LSV systems. Two of these conditions can be used in a very straightforward manner for monitoring the stability of a GBLS used as an adaptive filter.>

Normal-form digital filters are investigated for limit cycles due to two's complement truncation quantization. Regions in the parameter plane of a coupled-form filter are obtained where various types of period-one limit cycles are possible. A sufficient condition is established for the global asymptotic stability of a quantized coupled-form digital filter. A bound on the amplitude of limit cycles is obtained. This is used to develop an algorithm to check whether or not limit cycles are possible in a given filter. If possible, the algorithm produces all the initial conditions and periods for all possible limit cycles.>

Necessary and sufficient conditions are established for the existence of limit cycles due to two's complement truncation quantization in state-space digital filters. Accessibility of limit cycles is investigated, and a set of sufficient conditions is derived for the existence of period-one limit cycles with a specified access time. It is also established that if the system matrix has an inverse, then all possible limit cycles are accessible. The results are illustrated with examples.>

The bounded-input bounded-output (BIBO) stability of shift-variant digital filters is investigated. Periodically shift-variant digital filters are considered and a Floquet-type solution is established. This is used to investigate the BIBO stability of a general periodically shift-variant digital system.