Adversarial training (AT) incurs significant computational overhead, leading to growing interest in designing inherently robust architectures. We demonstrate that a carefully designed first layer of the neural network can serve as an implicit adversarial noise filter (ANF). This filter is created using a combination of large kernel size, increased convolution filters, and a maxpool operation. We show that integrating this filter as the first layer in architectures such as ResNet, VGG, and EfficientNet results in adversarially robust networks. Our approach achieves higher adversarial accuracies than existing natively robust architectures without AT and is competitive with adversarial-trained architectures across a wide range of datasets. Supporting our findings, we show that (a) the decision regions for our method have better margins, (b) the visualized loss surfaces are smoother, (c) the modified peak signal-to-noise ratio (mPSNR) values at the output of the ANF are higher, (d) high-frequency components are more attenuated, and (e) architectures incorporating ANF exhibit better denoising in Gaussian noise compared to baseline architectures.

Our objective is to derive the range and velocity of multiple targets from the delay-Doppler domain for radar sensing using orthogonal time frequency space (OTFS) signaling. Noise contamination affects the performance of OTFS signals in real-world environments, making radar sensing challenging. This work introduces a two-stage approach to tackle this issue. In the first stage, we use a generative adversarial network to denoise the corrupted OTFS samples, significantly improving data quality. Following this, the denoised signals are passed to a convolutional neural network model to predict the values of the velocities and ranges of multiple targets. The proposed two-stage approach can predict the range and velocity of multiple targets, even in very low signal-to-noise ratio scenarios, with high accuracy and outperforms existing methods.

Learning rate is a crucial parameter in training of neural networks. A properly tuned learning rate leads to faster training and higher test accuracy. In this paper, we propose a Lipschitz bandit-driven approach for tuning the learning rate of neural networks. The proposed approach is compared with the popular HyperOpt technique used extensively for hyperparameter optimization and the recently developed bandit-based algorithm BLiE. The results for multiple neural network architectures indicate that our method finds a better learning rate using a) fewer evaluations and b) lesser number of epochs per evaluation, when compared to both HyperOpt and BLiE. Thus, the proposed approach enables more efficient training of neural networks, leading to less training time and less computational cost.

Designing a cognitive radar system capable of adapting its parameters is challenging, particularly when tasked with tracking a ballistic missile throughout its entire flight. In this work, we focus on proposing adaptive algorithms that select waveform parameters in an online fashion. Our novelty lies in formulating the learning problem using domain knowledge derived from the characteristics of ballistic trajectories. We propose three reinforcement learning algorithms: bandwidth scaling, Q-learning, and Q-learning lookahead. These algorithms dynamically choose the bandwidth for each transmission based on received feedback. Through experiments on synthetically generated ballistic trajectories, we demonstrate that our proposed algorithms achieve the dual objectives of minimizing range error and maintaining continuous tracking without losing the target.

The performance of (OR-PCA) technique heavily depends on the optimum tuning of the explicit regularizers. This tuning is dataset-sensitive and often impractical to optimize in real-world scenarios. We aim to remove the dependency on these tuning parameters by using implicit regularization. To this end, we develop an approach that integrates implicit regularization properties of various gradient descent methods to estimate sparse outliers and low-dimensional representations in a streaming setting—a non-trivial extension of existing techniques. A key novelty lies in the design of a new parameterization for matrix estimation in OR-PCA. Our method incorporates three different versions of modified gradient descent that separate but naturally encourage sparsity and low-rank structures in the data. Experimental results on synthetic and real-world video datasets demonstrate that the proposed method, namely, OR-PCA (TF-ORPCA), outperforms existing OR-PCA methods. TF-ORPCA makes it more scalable for large datasets.

Conventionally, in a differentially private additive noise mechanism, independent and identically distributed (i.i.d.) noise samples are added to each coordinate of the response. In this work, we formally present the addition of noise that is independent but not identically distributed (i.n.i.d.) across the coordinates to achieve tighter privacy-accuracy trade-off by exploiting coordinate-wise disparity in privacy leakage. In particular, we study the i.n.i.d. Gaussian and Laplace mechanisms and obtain the conditions under which these mechanisms guarantee privacy. The optimal choice of parameters that ensure these conditions are derived considering (weighted) mean squared and$\ell _{ p}^{ p}$-errors as measures of accuracy. Theoretical analyses and numerical simulations demonstrate that the i.n.i.d. mechanisms achieve higher utility for the given privacy requirements compared to their i.i.d. counterparts. One of the interesting observations is that the Laplace mechanism outperforms Gaussian even in high dimensions, as opposed to the popular belief, if the irregularity in coordinate-wise sensitivities is exploited. We also demonstrate how the i.n.i.d. noise can improve the performance in private (a) coordinate descent, (b) principal component analysis, and (c) deep learning with group clipping.

We propose a deep reinforcement learning (DRL) approach for a full-duplex (FD) transmission that predicts the phase shifts of the reconfigurable intelligent surface (RIS), base station (BS) active beamformers, and the transmit powers to maximize the weighted sum rate of uplink and downlink users. Existing methods require channel state information (CSI) and residual self-interference (SI) knowledge to calculate exact active beamformers or the DRL rewards, which typically fail without CSI or residual SI. Especially for time-varying channels, estimating and signaling CSI to the DRL agent is required at each time step and is costly. We propose a two-stage DRL framework with minimal signaling overhead to address this. The first stage uses the least squares method to initiate learning by partially canceling the residual SI. The second stage uses DRL to achieve performance comparable to existing CSI-based methods without requiring the CSI or the exact residual SI. Further, the proposed DRL framework for quantized RIS phase shifts reduces the signaling from BS to the RISs using 32 times fewer bits than the continuous version. The quantized methods reduce action space, resulting in faster convergence and 7.1% and 22.28% better UL and DL rates, respectively than the continuous method.

Reconfigurable intelligent surfaces (RIS) can be crucial in next-generation communication systems. However, designing the RIS phases according to the instantaneous channel state information (CSI) can be challenging in practice due to the short coherent time of the channel. In this regard, we propose a novel algorithm based on the channel statistics of massive multiple input multiple output systems rather than the instantaneous CSI. The beamforming at the base station (BS), power allocation of the users, and phase shifts at the RIS elements are optimized to maximize the minimum signal-to-interference and noise ratio (SINR), guaranteeing fair operation among various users. In particular, we design the RIS phases by leveraging the asymptotic deterministic equivalent of the minimum SINR that depends only on the channel statistics. This significantly reduces the computational complexity and the amount of controlling data between the BS and RIS for updating the phases. This setup is also useful for electromagnetic fields (EMF)-aware systems with constraints on the maximum user’s exposure to EMF. The numerical results show that the proposed algorithms achieve more than 100 % gain in terms of minimum SINR, compared to a system with random RIS phase shifts, when 40 RIS elements, 20 antennas at the BS and 10 users, are considered.

The framework of differential privacy protects an individual’s privacy while publishing query responses on congregated data. In this work, a new noise addition mechanism for differential privacy is introduced where the noise added is sampled from a hybrid density that resembles Laplace in the centre and Gaussian in the tail. With a sharper centre and light, sub-Gaussian tail, this density has the best characteristics of both distributions. We theoretically analyze the proposed mechanism, and we derive the necessary and sufficient condition in one dimension and a sufficient condition in high dimensions for the mechanism to guarantee (ϵ, δ)-differential privacy. Numerical simulations corroborate the efficacy of the proposed mechanism compared to other existing mechanisms in achieving a better trade-off between privacy and accuracy.

In this work, we study the outage probability (OP) at the destination of an intelligent reflecting surface (IRS) assisted communication system in a$\kappa -\mu $fading environment. A practical system model that takes into account the presence of phase error due to quantization at the IRS when a) source-destination (SD) link is present and b) SD link is absent is considered. First, an exact expression is derived, and then we derive three simple approximations for the OP using the following approaches: (i) uni-variate dimension reduction, (ii) moment matching and, (iii) Kullback–Leibler (KL) divergence minimization. The resulting expressions for OP are simple to evaluate and quite tight even in the tail region. The validity of these approximations is demonstrated using extensive Monte Carlo simulations. We also study the impact of the number of bits available for quantization, the position of IRS with respect to the source and destination and the number of IRS elements on the OP for systems with and without an SD link. We also demonstrate how the method of moment matching and KL divergence minimization can be used to analyze systems experiencing spatial correlation between the IRS elements.

In this paper, we propose a scheme for the joint optimization of the user transmit power and the antenna selection at the access points (AP)s of a user-centric cell-free massive multiple-input-multiple-output (UC CF-mMIMO) system. We derive an approximate expression for the achievable uplink rate of the users in a UC CF-mMIMO system in the presence of a mixed analog-to-digital converter (ADC) resolution profile at the APs. Using the derived approximation, we propose to maximize the uplink sum-rate of UC CF-mMIMO systems subject to energy constraints at the APs. An alternating-optimization solution is proposed using binary particle swarm optimization (BPSO) and successive convex approximation (SCA). We also propose a complete meta-heuristic-based solution that can be used as an alternative solution for applications where latency is the critical metric. Along with this, we used a genetic algorithm (GA)-based approach to compare the performance of the proposed algorithm. We study the impact of various system parameters on the performance of the system.

This paper derives the asymptotic distribution of the normalized$k$-th maximum order statistics of a sequence of non-central chi-square random variables with non-identical non-centrality parameters. We demonstrate the utility of these results in characterizing the signal-to-noise ratio in three different applications in wireless communication systems where the statistics of the$k$-th maximum channel power over Rician fading links are of interest. Furthermore, we derive simple expressions for the asymptotic outage probability, average throughput, achievable throughput, and average bit error probability. The proposed results are validated via extensive Monte Carlo simulations.

Directional beamforming is a crucial component for realizing robust wireless millimeter wave (mmWave) communication systems. Beam alignment using brute-force search introduces time overhead, and the location aided blind beam alignment adds additional hardware requirements to the system. In this paper, we propose a blind beam alignment method based on the radio frequency (RF) fingerprints of the user equipment obtained from the base stations. The proposed system performs blind beam alignment using deep reinforcement learning on a multiple-base station cellular environment with multiple mobile users. We present a novel neural network architecture that can handle a mix of both continuous and discrete actions and use policy gradient methods to train the model. Our results show that the proposed method can achieve a data rate of up to four times the data rate of the traditional method without any overheads.

This paper derives the distribution of the maximum end-to-end (e2e) signal to noise ratio (SNR) in an opportunistic relay selection based cooperative relaying network having a large number of non-identical relay links. The source is simultaneous wireless information and power transfer enabled, and the relays are capable of both time splitting (TS) and power splitting (PS) based energy harvesting (EH). Contrary to the majority of literature in communication, which uses extreme value theory (EVT) to derive the statistics of extremes of sequences of independent and identically distributed random variables (RVs), we demonstrate how EVT can be used to derive the maximum statistics of sequences of independent and non-identically distributed normalised SNR and hence the distribution of the maximum SNR. Using these results, we derive simple expressions for evaluating the outage capacity, and achievable throughput at the destination. Finally, we present the utility of the results for deciding the optimum TS and PS factors of the hybrid EH relays that maximise outage capacity, and achievable throughput at the destination. Furthermore, we establish the stochastic ordering of the e2e SNR, which in turn allows the characterisation of the variations in the e2e performance with respect to the variations in different system parameters.

Millimeter wave communication is eminently suitable for high-rate wireless systems, which may be beneficially amalgamated with intelligent reflecting surfaces (IRS), while relying on beam-index modulation. Explicitly, we propose three different architectures based on IRSs for beam-index modulation in millimeter wave communication. Our schemes are capable of eliminating the detrimental line-of-sight blockage of millimeter wave frequencies.The schemes are termed as single-symbol beam index modulation, multi-symbol beam-index modulation and maximum-SNR single-symbol beam index modulation. The principle behind these is to embed the information both in classic QAM/PSK symbols and in the transmitter beam-pattern. Explicitly, we proposed to use a twin-IRS structure to construct a low-cost beam-index modulation scheme. We conceive both the optimal maximum likelihood detector and a low-complexity compressed sensing detector for the proposed schemes. Finally, the schemes designed are evaluated through extensive simulations and the results are compared to our analytical bounds.

This paper determines the optimum secondary user (SU) power allocation and ergodic multicast rate of point-to-multipoint communication in a cognitive radio network (CRN) in the presence of various quality of service (QoS) constraints for the primary users (PUs). Using tools from extreme value theory (EVT), it is first proved that the limiting distribution of the minimum of independent and identically distributed (i.i.d.) signal-to-interference ratio (SIR) random variables (RVs) is a Weibull distribution, when the user signal and the interferer signals undergo independent and non-identically distributed (i.n.i.d.) κ-μ shadowed fading. Also, the rate of convergence of the actual minimum distribution to the Weibull distribution is derived. This limiting distribution is then used for determining the optimum transmit power of a secondary network in an underlay CRN subject to three different QoS constraints at the primary network in a generalized fading scenario. Furthermore, the optimum transmit power and the asymptotic ergodic multicast rate of SUs is analyzed for varying channel fading parameters.

Using tools from extreme value theory (EVT), it is proved that when the user signal and the interferer signals undergo independent and non-identically distributed (i.n.i.d.) κ-μ shadowed fading, the limiting distribution of the maximum of L independent and identically distributed (i.i.d.) signal-to-interference ratio (SIR) random variables (RVs) is a Frechet distribution. It is observed that this limiting distribution is close to the true distribution of maximum for maximum SIR evaluated over moderate L. Furthermore, moments of the maximum RV is shown to converge to the moments of the Frechet RV. In addition, the rate of convergence of the actual distribution of the maximum to the Frechet distribution is derived and analyzed for different κ and μ parameters. Finally, results from the stochastic ordering are used to analyze the variation in the limiting distribution with respect to the variation in source fading parameters. These results are then used to derive upper bound for the rate in full array selection (FAS) schemes for the antenna selection and the asymptotic outage probability and the ergodic rate in maximum-sum-capacity (MSC) scheduling systems.

Orthogonal matching pursuit (OMP) is a widely used algorithm for recovering sparse high dimensional vectors in linear regression models. The optimal performance of OMP requires a priori knowledge of either the sparsity of regression vector or noise statistics. Both these statistics are rarely known a priori and are very difficult to estimate. In this paper, we present a novel technique called residual ratio thresholding (RRT) to operate OMP without any a priori knowledge of sparsity and noise statistics and establish finite sample and large sample support recovery guarantees for the same. Both analytical results and numerical simulations in real and synthetic data sets indicate that RRT has a performance comparable to OMP with a priori knowledge of sparsity and noise statistics.

In this paper, we derive the data-aided error vector magnitude (EVM) in an interference limited system when both the desired channel and interferers experience independent and nonidentically distributed κ-μ shadowed fading. Then, it is analytically shown that the EVM is equal to the square root of number of interferers when the desired channel and interferers do not experience fading. Furthermore, the EVM is derived in the presence of interference and noise, when the desired channel experiences κ-μ shadowed fading and the interferers experience independent and identical Nakagami fading. Moreover, using the properties of the special functions, the derived EVM expressions are also simplified for various special cases.

New expressions for symbol error probability (SEP) in the presence of peak-to-average-power-ratio/clipping are derived from the orthogonal frequency division multiplexing systems. These expressions are significantly tighter than the expression in the existing literature, since we model the peak behavior using a peak over threshold approach. An adaptive back-off scheme is also proposed and its SEP is derived. It is shown that with negligible SEP degradation, the adaptive back-off scheme saves power.

The κ-μ shadowed fading model is a very general fading model as it includes both κ-μ and η-μ as special cases. In this paper, we derive the expression for outage probability when the signal-of-interest (SoI) and interferers both experience κ-μ shadowed fading in an interference limited scenario. The derived expression is valid for arbitrary SoI parameters, arbitrary κ, and μ parameters for all interferers and any value of the parameter m for the interferers excepting the limiting value of m → ∞. The expression can be expressed in terms of Pochhammer integral, where the integrands of integral only contains elementary functions. The outage probability expression is then simplified for various special cases, especially when SoI experiences η-μ or κ-μ fading. Furthermore, the rate expression is derived when the SoI experiences κ-μ shadowed fading with the integer values of μ, and the interferers experience κ-μ shadowed fading with arbitrary parameters. The rate expression can be expressed in terms of sum of Lauricella's function of the fourth kind. The utility of our results is demonstrated by using the derived expression to study and compare fractional frequency reuse and soft frequency reuse in the presence of κ-μ shadowed fading. Extensive simulation results are provided and these further validate our theoretical results.

Sparse channel estimation (SCE) in orthogonal frequency division multiplexing (OFDM) systems with large number of virtual sub-carriers and regularly spaced pilots is studied in this paper. Such OFDM systems are present in wireless standards like long term evolution (LTE). We numerically evaluate the performance of popular compressive sensing (CS) algorithms and shows that low complexity CS algorithms like OMP, subspace pursuit etc performs badly in these OFDM systems. We also provide analytical reasoning for this suboptimal performance. This paper points to the need of developing new low complexity CS algorithms for SCE in OFDM systems with large number of virtual sub-carriers and equispaced pilots.

Device-to-device (D2D) communication underlying cellular networks, allows direct transmission between two devices in each other's proximity that reuse the cellular resource blocks in an effort to increase the network capacity and spectrum efficiency. However, this imposes severe interference that degrades the system's performance. This problem may be circumvented by incorporating fractional frequency reuse (FFR) or soft frequency reuse (SFR) in OFDMA cellular networks. By carefully considering the downlink resource reuse of the D2D links, we propose beneficial frequency allocation schemes, when the macrocell has employed FFR or SFR as its frequency reuse technique. The performance of these schemes is quantified using both the analytical and simulation results for characterizing both the coverage probability and the capacity of D2D links under the proposed schemes that are benchmarked against the radical unity frequency reuse scheme. The impact of the D2D links on the coverage probability of macrocellular users (CUs) is also quantified, revealing that the CUs performance is only modestly affected under the proposed frequency allocation schemes. Finally, we provide insights concerning the power control design in order to strike a beneficial tradeoff between the energy consumption and the performance of D2D links.

We analytically characterize the data-aided error vector magnitude (EVM) performance of a single-input multiple-output (SIMO) communication system relying on maximal ratio combining (MRC) having either independent or correlated branches that are nonidentically distributed. In particular, exact closed form expressions are derived for the EVM in$\eta\text{-}\mu$fading and$\kappa W\mu$shadowed fading channels and these expressions arevalidatedby simulations. The derived expressions are expressed in terms of Lauricella’s function of the fourth kind$F_D^{(N)}(.)$, which can be easily computed. Furthermore, we have simplified the derived expressions for various special cases such as independent and identically distributed branches, Rayleigh fading, Nakagami-mfading, and$\kappa\text{-}\mu$fading. Additionally, a parametric study of the EVM performance of the wireless system is presented.

In soft frequency reuse (SFR) when the user is classified as a cell-center user based on signal-to-interference-plus-noise-ratio in a sub-band, the user retains its sub-band. On the other hand, if the user is classified as a cell-edge user, a new sub-band is allocated. We analyze the impact of correlation between the cell-center sub-band and the cell-edge sub-band for a user when the SFR technique is used in a cellular orthogonal frequency division multiple access (OFDMA) system. The coverage probability (CP) and the average rate are derived for the following two cases: 1) when the sub-bands are independent and 2) when the sub-bands are completely correlated. We show that correlation significantly decreases the edge CP and the average rate of the SFR technique, and as the power control factor increases, the impact of correlation decreases. Fractional frequency reuse (FFR) and SFR techniques are compared and it is shown that the impact of correlation on the FFR is significantly lower. Furthermore, it is also shown that the FFR provides better edge CP and average rate when compared with the SFR in single-input single-output (SISO) networks, thereby suggesting that the FFR should be preferred over SFR in cellular SISO OFDMA systems. However, for single-input multiple-output networks, the SFR provides a better average rate when compared with the FFR, especially when the sub-band correlation is not significant. Finally, the impact of log-normal shadowing has been carefully studied.

In current wireless systems, the base-station (eNodeB) tries to serve its user-equipment (TIE) at the highest possible rate that the TIE can reliably decode. The eNodeB obtains this rate information as a quantized feedback from the TIE at time n and uses this for rate selection until the next feedback is received at time n + δ. The feedback received at n can become outdated before n + δ, because of 1) Doppler fading, and 2) change in the set of active interferers for a TIE. Therefore, rate prediction becomes essential. Since the rates belong to a discrete set, we propose a discrete sequence prediction approach, wherein, frequency trees for the discrete sequences are built using source encoding algorithms like prediction by partial match (PPM). Finding the optimal depth of the frequency tree used for prediction is cast as a model order selection problem. The rate sequence complexity is analyzed to provide an upper bound on model order. Information-theoretic criteria are then used to solve the model order problem. Finally, two prediction algorithms are proposed, using the PPM with optimal model order and system level simulations demonstrate the improvement in packet loss and throughput due to these algorithms.

In this work, the authors derive the optimal signal‐to‐interference‐ratio (SIR) thresholds S t which maximise coverage probability for both fractional frequency reuse (FFR) and soft frequency reuse (SFR) networks with base station locations modelled using Poisson point process. It is analytically shown that for both FFR and SFR, the optimal SIR threshold is equal to the target SIR T , i.e, S t = T . The authors also show that at the optimal SIR threshold, FFR achieves a higher coverage than frequency reuse (1/Δ). Furthermore, for the cases when S t > T and S t < T , FFR achieves a higher coverage than reuse (1/Δ) and reuse 1, respectively. On the other hand, SFR coverage can be higher or lower than reuse (1/Δ) coverage, even when S t = T . However, when S t > T , SFR achieves a higher coverage than reuse 1, and when S t < T , the SFR coverage can be lower than reuse 1 coverage. The FFR and SFR coverages are also compared for a given Δ, and it is shown that FFR achieves a higher coverage than SFR at the optimal value of S t .

This work states and proves necessary and sufficient condition for a threshold based estimate of set of active regression coefficients to be high SNR consistent. It is further shown that popular thresholding schemes like universal threshold, Bonferroni correction etc fails to meet the necessary condition and hence are inconsistent at high SNR. The sufficient conditions provides a very rich class of threshold based estimators with varying rate of convergence to consistency. Simulation results demonstrates the superior performance of the proposed threshold based estimator over Lasso, Dantzig selector and Orthogonal Matching Pursuit.

Expressions are derived for the coverage probability and average rate of both multi-user multiple input multiple output (MU-MIMO) and single input multiple output (SIMO) systems in the context of a fractional frequency reuse (FFR) scheme. In particular, given a reuse region of 1/3 (FR3) and a reuse region of 1 (FR1) as well as a signal-to-interference-plus-noise-ratio (SINR) threshold Sth, which decides the user assignment to either the FR1 or FR3 regions, we theoretically show that: 1) the optimal choice of Sthwhich maximizes the coverage probability is Sth= T, where T is the target SINR required for ensuring adequate coverage, and 2) the optimal choice of Sthwhich maximizes the average rate is given by Sth= T', where T' is a function of the path loss exponent, the number of antennas and of the fading parameters. The impact of frequency domain correlation amongst the OFDM sub-bands allocated to the FR1 and FR3 cell-regions is analysed and it is shown that the presence of correlation reduces both the coverage probability and the average throughput of the FFR network. Furthermore, the performance of our FFR-aided MU-MIMO and SIMO systems is compared. Our analysis shows that the (2 × 2) MU-MIMO system achieves 22.5% higher rate than the (1 × 3) SIMO system and for lower target SINRs, the coverage probability of a (2 × 2) MU-MIMO system is comparable to a (1 × 3) SIMO system. Hence the former one may be preferred over the latter. Our simulation results closely match the analytical results.

The κ - μ and η - μ are general fading distributions, which model line-of-sight and non-line-of-sight propagation effects, respectively. In this work, expressions for the coverage probability and average rate when the user experiences κ - μ fading with arbitrary values of κ and μ, and interferers experience η - μ fading with arbitrary values of η and μ are derived for downlink of a cellular network. Both expressions can be expressed in terms of sum of Lauricella's function of the fourth kind. Further, using the properties of the special functions, the average rate expression is simplified for various special cases. Finally, simulation results are provided and these match our analytical results.

In cellular networks, all base stations (BSs) do not continuously transmit i.e., the BSs transmit only when their queues are non-empty. This implies that the system resources are only partially loaded, and the dynamics of such a network differs significantly from that of a fully-loaded system. The coverage probability in a fully- and partially-loaded cellular network is analysed. We consider a regular spatial arrangement of base stations, and obtain the coverage probability in the presence of interference. More specifically, expressions for coverage probability are obtained for square and hexagonal lattices with full and partial loading. The coverage probability is obtained using properties of lattice sums which were first used in physics to analyse potentials in crystal structures.

In orthogonal frequency division multiple access‐based systems where channel frequency response (CFR) estimation has to be carried out using only the user‐specific (localised) pilots within a small time frequency block, the accuracy of the estimates suffer because of the limited number of pilots and imperfect knowledge of the channel statistics. A biased estimator is proposed for the estimation of CFR over the time frequency block. Hypothesis tests are designed to ascertain the time and frequency selectivity of the CFR within the region of interest, and the outcome of these tests are used to determine a vector shrinkage target for the biased estimator. Simulation results indicate that the performance of the proposed estimator is comparable to that of the optimal minimum mean square error estimator, even though it does not have any knowledge of the channel statistics.

A closed form expression for the Cramer Rao lower bound (CRB) for parameter estimation in the presence of a two component Gaussian mixture noise model is derived. It is further shown that this closed form expression can be lower bounded by a simple two term expression. Closed form expressions are also derived for the variance of the maximum likelihood estimator (MLE) when the parameters of the Gaussian mixture model are misspecified. It is then shown that the MLE can handle a significant amount of misspecification of the parameters of the Gaussian mixture model and yet maintain a variance close to the CRB.

In this paper, we show that the asymptotic probability density function (pdf) of the maxima of n independent and identically distributed (i.i.d.) sums of independent non-identically (i.n.i.d.) distributed gamma random variables (RVs) is a Gumbel pdf using Extreme Value Theory (EVT). We will also show that the asymptotic pdf of the maxima of n i.i.d. sums of correlated gamma RVs is a Gumbel pdf. Some applications in wireless communication are discussed where the maxima of n i.i.d. sums of correlated gamma RVs and maxima of n i.i.d. sums of i.n.i.d. gamma RVs arise. We discuss the utility of our results in the context of these applications.

Analytical expressions for scheduling gain and spectral efficiency of the proportional fair and maximum rate scheduling algorithms for Orthogonal Frequency Division Multiple Access (OFDMA) based systems are derived for the following cases: a) multipath Rayleigh and multipath Nakagami fading, b) Composite channel models which model the combined effect of both small scale and large scale fading. It is shown using Extreme Value Theory (EVT) that the asymptotic distribution of the maxima of the received signal to noise power (SNR) across all the users converges to a Gumbel distribution for both cases. Therefore, we use the Gumbel distribution to derive expressions for both the spectral efficiency and scheduling gain. The scheduling gains obtained through numerical integration (whenever tractable) and simulations match with the analytical values obtained using the EVT based expressions. We also discuss how the moments and order statistics of the Gumbel distribution can be used to study other metrics of the scheduling algorithms.

In this work, we propose a cognitive interference management scheme for heterogeneous cellular wireless networks (LTE-A and WiMAX) with macrocells and femtocells (that operate in a closed-access mode). The scheme presented allocates resources (in time and frequency) and transmission opportunities to the macro/femtocells in the network by considering their potential to cause interference at each others' associated user equipments (UEs). We study the efficacy of the proposed scheme using a LTE-A system level simulator and compare with frequency reuse techniques and no interference management scenarios. We observe that our scheme significantly enhances average cell-edge UE throughput (5\%-tile throughput) with some degradation in overall sum throughput. Also we observe that the scheme decreases the probability of cell-edge users in the system experiencing degraded SINR.

Pilot assisted channel tracking (PACT) has been very popular for channel estimation in OFDM systems. However, as the mobility in the system increases and one has to maintain a high accuracy in channel estimation, the pilot overhead typically has to be increased. Emerging cellular OFDM standards are expected to use about 6 - 12% pilot overhead per stream, and any possible reduction in pilot overhead would be useful. Decision directed channel tracking (DDCT) can help reduce pilot overhead, but is known to suffer from error propagation at high fade rates. In emerging broadband wireless systems promising peak bit rates of 50 Mbps or more, saving on pilot overhead by using DDCT schemes would be highly attractive provided: (a) Such a DDCT approach does not suffer from error propagation and has an error rate performance comparable to (or better than) PACT schemes even at high fade rates; (b) The computational complexity of such a DDCT approach is not significantly more than that of the MMSE based PACT scheme. In this work, we propose a low complexity DDCT method which exploits the structure of the regression matrix in conjunction with robust statistics to mitigate the effect of error propagation. It has a much lower computational complexity and a better error rate performance than the decision directed EM-Kalman and other existing robust statistics based DDCT schemes. The proposed method also outperforms a 12.5% pilot overhead based PACT scheme with only a modest increase in computational complexity.

We look at the performance of turbo coded OFDM systems in the presence of narrowband interference (NBI) and co-channel interference (CCI). In systems employing standards such as the IEEE 802.16d/e, CCI behaves like NBI with the number of affected subcarriers ranging from 10% to 30%. Hence we treat symbol detection in such systems as detection in contaminated Gaussian (CG) noise and propose a robust log- likelihood ratio (LLR) computation for it. The proposed LLR computation method exploits the fact that NBI/CCI has a CG probability density function (pdf) but does not assume knowledge of the NBI power, NBI pdf and the fraction of subcarriers affected by NBI. Simulation results indicate that the proposed method performs very close to the optimal method which would have complete knowledge of the CG pdf parameters.

A robust cost function for log likelihood ratio (LLR) computation is proposed for turbo coded OFDM systems in the presence of narrowband interference (NBI) and co-channel interference (CCI). In systems employing standards such as the IEEE 802.16d/e, CCI behaves like NBI with the number of affected subcarriers ranging from 10% to 30%. The combined effect of NBI and thermal Gaussian noise leads to a contaminated Gaussian (CG) noise probability density function (pdf). Simulation results indicate that the proposed method performs very close to the optimal method where the optimal method computes the LLR using the CG pdf. While the optimal method requires knowledge of the NBI power, the fraction of subcarriers contaminated by NBI and the NBI pdf, the proposed method does not require knowledge of these parameters.

M estimators have been widely used for parameter estimation in the presence of outliers or impulsive noise. A number of papers use the iteratively reweighted least squares (IRLS) algorithm for M estimation. The IRLS method tries to iteratively converge to the non-linear M estimate using a weighted least squares algorithm. While the performance of the IRLS algorithm has been demonstrated through simulation, to our knowledge, the MSE of the IRLS based M estimation approach has not been theoretically derived in signal processing literature. In this paper, we derive the theoretical MSE of three M estimators, namely, the Huber's M (HM) estimator, the extreme value theory (EVT) based estimator and the Hampel's 3-part (HP) estimator when they are implemented using the IRLS algorithm. This theoretical MSE is a function of the M estimator cost function, the noise distribution, and the iteration number of the IRLS algorithm. Based on the theoretical analysis in this paper, we show that for both Cauchy and Gaussian impulsive noise, the MSE of the IRLS based M estimator converges to the MSE of the desired M estimator within 3 to 5 iterations.

Decision directed channel tracking (DDCT) at high fade rates in OFDM based systems is addressed in this paper. Existing DDCT algorithms like the expectation-maximization (EM) algorithm (Al-Naffouri et al., 2002) suffer from error propagation and exhibit poor performance when applied to large frames at high fade rates. We propose a robust EM algorithm which mitigates the effect of error propagation and is able to track the channel in the decision directed mode even over frame durations experiencing 2-3 fade cycles. This EM algorithm uses the Huber's cost function in the maximization step instead of the non-robust least squares or Kalman cost function. Further, the noise variance is estimated using the robust median absolute deviation estimator instead of the standard maximum likelihood estimator. The proposed robust EM based DDCT scheme has a better error rate and MSE performance when compared to Kalman filter based pilot assisted channel tracking scheme with a 6.25% pilot overhead, even at a normalized Doppler of 0.04.

A method for the mitigation of the effect of narrowband interference (NBI) on the turbo decoder in OFDM systems is proposed. The presence of NBI leads to a contaminated Gaussian (CG) noise probability density function (pdf) which induces an outlier effect in the data detection problem. The outlier effect leads to significant degradation in the performance of turbo coded OFDM systems which use Gaussian noise pdf based log likelihood ratios (LLRs), with the degradation increasing as a function of the power of NBI and the number of subcarriers affected by NBI. We propose to use outlier detection theory to detect subcarriers affected by NBI, and then downweigh the corresponding LLRs before passing them to the turbo decoder. Extreme value theory (EVT) is used to define the weight function in this weighted-LLR (W-LLR) method. The method is easy to implement, is of modest computational complexity, and shows a significant improvement in the simulated error rate performance when compared with the simple unweighted turbo decoder in the presence of NBI. Furthermore, frequency selectivity and diversity mapping in OFDM systems such as IEEE 802.16 d/e WMAN standard causes the co-channel interference (CCI) to look like NBI within the FEC block. Therefore, the W-LLR method can also be applied for CCI mitigation in these systems. Since reuse-one cellular systems have a CCI limited performance, the proposed method provides a significant improvement over the normal turbo decoder.

Decision feedback equalizers (DFEs) are designed to deal with AWGN noise, and hence, generally perform very poorly in the presence of impulsive noise. Extreme value theory (EVT) is used to modify the DFE structure to handle impulsive noise. The received measurements are modified using EVT based weights before passing it to the equalizer. A modified maximal ratio combining (MRC) scheme which also uses EVT is developed to further improve the error-rate performance in the presence of impulsive interference. The proposed method performs much better than the conventional DFE-MRC technique which uses the simple MRC in conjunction with the DFE at low signal-to-interference (SIR) ratios.

Channel estimation in the presence of multitone narrowband interference (MNBI) in OFDM systems is addressed in this paper. While pilot based OFDM channel estimation in the presence of only thermal noise at the receiver is a Gaussian regression problem, the presence of MNBI leads to an outlier contaminated Gaussian regression problem. Since Gaussian probability density function (pdf) based maximum likelihood (ML) estimators are highly sensitive to outliers, we define a M estimator based on the theory of robust regression for channel estimation in the presence of MNBI. The proposed iterative M estimator minimizes the Huber's cost function for p iterations and then minimizes a cost function defined by a redescending M estimator based on extreme value theory in the last few iterations. Simulation results indicate that the proposed estimator outperforms both the Gaussian pdf based ML estimator and a M estimator based only on Huber's cost function.

Decision directed channel tracking (DDCT) at high fade rates in OFDM based systems is addressed in this paper. Channel estimation in DDCT can be formulated as a linear errors-in-variables regression problem. While most of the errors in the regression matrix (equalization errors) are Gaussian in nature, few of the detected symbols can have high error due to the frequency and time selective fading. These poor symbol decisions behave like outliers in the regression matrix and give rise to contaminated Gaussian noise distributions. Classical estimators like total least squares (TLS) and the expectation-maximization (EM) based estimators exhibit poor performance in the presence of such outliers. We propose the Huber's M (HM) estimator and an extreme value theory (EVT) based M estimator for the DDCT problem. The proposed HM and EVT-HM estimators are robust to outliers and have an efficiency greater than 95% in purely Gaussian noise. The error rate performance of the proposed HM and EVT-HM estimators are compared with that of the TLS estimator, and the EM based estimator proposed in [4].

Decision directed channel tracking (DDCT) in OFDM systems can suffer from error propagation at high fade rates, due to the combined effect of rapid variation of the channel, long frame length and frequency selectivity of the channel. Conventional estimators like the 2D-minimum mean square error (MMSE) channel estimator and the expectation maximization (EM) based Kalman channel estimator [3] show poor performance when they are applied to DDCT over large frame lengths, due to the error propagation induced by wrong symbol decisions. The poor symbols decisions usually act like leverage points in the regression matrix, and can be identified using the hat matrix as a leverage diagnostic. We use extreme value theory (EVT) on the hat matrix to define a channel estimator, which, in addition to exploiting time and frequency correlation of the channel, downweighs leverage points before utilizing them in the estimator structure. The proposed EVT-leverage weighted (LW) estimator reduces error propagation in the frame since it downweighs possible wrong decisions before using them in the channel estimator structure. The proposed EVT-LW estimator has a significantly better error rate performance when compared to both the 2D-MMSE estimator [2] and the EM based Kalman estimator [3].