Designing digital filters with desired phase responses at selected frequencies is essential in several communication and control applications. While phase compensation is generally achieved using all-pass filters, the all-pass constraint limits the range of realizable stable, causal filters that match the desired phase characteristics. In this paper, we present a method for designing real, stable discrete-time filters that match phase constraints at selected frequencies. Our approach enables control over the phase response without affecting stability and with low complexity. Specifically, we construct an nth-order filter to match phase constraints at n distinct frequencies (for even n), achieving exact phase interpolation with a low filter order. The derived methodology cascades suitably designed second order sections, referred to as filter blocks, and uses a fixed-point iteration scheme to meet the phase specifications, with tunable design parameters that enable explicit control over the margin of stability. Simulations confirm the utility of our method for obtaining stable filters that satisfy phase specifications even where comparable methods, such as all-pass designs, fail.

Modulo-folding ADCs (MF-ADCs) offer a potential alternative to conventional ADCs by requiring fewer bits. However, the algorithms that follow an MF-ADC typically require an unfolding method, which demands significant oversampling. In this paper, we explore the problem of symbol detection in digital communication at a receiver using an MF-ADC. We demonstrate that, in certain noisy conditions, unfolding is not necessary for detection, allowing the MF-ADC to operate at a lower rate. Additionally, we show that any unfolding process may negate the benefits of fewer bits or reduced quantization error associated with MF-ADCs. We derive theoretical bounds and discuss optimal symbol design to achieve the best performance. The proposed approach, which eliminates the need for unfolding, can facilitate the development of low-rate MF-ADCs for various other applications.

With the increasing use of high frequency communication for high bandwidths, carrier synchronization becomes a significant bottleneck, since frequency drifts need to be tracked continuously. Even conventional systems including radar and satellite communication systems with high Dopplers require complex carrier tracking solutions. Thus, well performing frequency tracking is necessary, and typically implemented using multi-bit signal processors. Such systems require more computation and incur high energy costs. One approach to reduce the complexity is to employ one-bit quantized values for carrier synchronization at the receiver. While algorithms for tracking phase using one-bit samples are available, the theory and practice for tracking frequency deviation appears yet to be developed, and this is the main contribution of the current paper. Unlike past approaches in this domain, we employ Fourier Series sum based formulae to estimate phase and frequency from one-bit quantized samples, and propose efficient, low-complexity frequency discriminators. These Fourier-based discriminators convert the frequency estimation and tracking problems into a set of equations that can be solved efficiently and are shown to be performant as confirmed by appropriate simulations.

The time varying nature of the wireless propagation channel causes a mismatch between the true channel at the time of data transmission and its available estimate based on previously received pilot symbols, and is known to impair the performance of the massive multiple input multiple output (MIMO) systems. In this paper, we develop and evaluate adaptive data aided channel tracking and data detection algorithms to counter the effects of channel aging for uplink and downlink massive MIMO systems. We first present a recursive least squares (RLS) algorithm for tracking the matrix uplink channel at the base station (BS), and derive bounds on its MSE performance. We also derive a linear complexity stochastic gradient descent (SGD) algorithm for tracking the uplink channel, along with its performance bounds. Following this, we develop RLS and SGD based algorithms for tracking the scalar effective downlink channel at each UE, and derive their performance guarantees. Finally, via Monte Carlo simulations, we validate the efficacy of the algorithms in terms of their mean squared error performance, and demonstrate the gains achievable by channel tracking in the form of the improvement in the symbol error rates.

The transmitter in a cell-free massive multiple input multiple output (MIMO) system comprises several access points (APs) which can coordinate to serve multiple user equipments. In massive MIMO systems, precoders such as conjugate beam-forming (CB), zero forcing (ZF), minimum mean square error (MMSE) etc are used in conjunction with power optimization techniques at the transmitter, in order to efficiently exploit the available degrees of freedom. However, none of these precoding techniques achieve the sum capacity of the system for all signal to noise ratios (SNRs). We model a cell free massive MIMO system as a fading Gaussian broadcast channel (GBC) with a distributed transmitter (TX). We find optimal transmission policies, in single user as well as in multi-user case, that achieve the ergodic sum capacity, thus outperforming all other precoding schemes. In the process, we obtain a novel algorithm to determine the ergodic sum capacity of the GBC and multiple access channels (MAC) based on an alternating optimization technique.

Many signal processing applications involve designing an all-pass filter with a desired phase response. Earlier methods have largely focused on approximating the desired response using an optimisation based approach, or by using numerical computations of the group delay at specific frequencies with Blaschke interpolation. The former method does not offer any guarantee to match the estimated phase response at given points, whereas the latter one matches the phases at the input points, but is sensitive to the numerical precision of the specified group delays. In this work, we present a unimodular interpolation-based method to obtain all-pass filter coefficients that match the desired phase response at the given points without the need for group delays at the interpolating points. Through detailed simulations, we show that the proposed method is more suited for obtaining all-pass filters that match the target phases when compared to earlier approaches.

The use of massive multiple-input multiple-output (MIMO) technology has enabled increased efficiency and capacity of wireless communication systems. When the downlink channel to user terminals (UTs) is known at the base station (BS), the BS can precode transmission to simplify detection at the UTs. In frequency division duplexed (FDD) systems, obtaining CSI at the transmitter to fully exploit the advantages of massive MIMO is complicated, since the number of channel coefficients to be trained and fed back from the UT is very large. This is exacerbated in the case where the channel is time varying, where frequent retraining and feedback is required. However, if the channel coefficients are spatially correlated, the amount of feedback required can be reduced significantly. In this paper, we consider the case where the channel coefficients from the BS to the UTs are spatially correlated, and show that efficient allocation of training power based on eigenvalues of the channel correlation matrix significantly boosts achievable rates. Further, we show that using Kalman filters to track the evolving channel coefficients reduces the need to retrain channels, and the reduced training requirement translates to higher data rates. Simulations confirm that optimal training and tracking channel modes enhances rates significantly.

The use of channel state information (CSI) at the transmitter significantly enhances the performance of wireless communication systems. However, the requirement of CSI feedback places an undue burden on the reverse link, especially in links that employ multiple-input multiple-output (MIMO) and orthogonal frequency division multiplexing (OFDM), where CSI takes the form of a precoding matrix (precoder) for each subcarrier. Typical deployments use quantization and feedback of CSI at certain subcarriers, with interpolation to fill in missing CSI at the transmitter. Past work has used the orthogonal structure of precoders with Flag manifolds for quantization and interpolation of CSI, although interpolation is complicated due to the absence of analytic expressions for geodesics on Flag manifolds. Other approaches have involved the parameterization of the precoder into scalar parameters that are amenable to quantization and interpolation. In this paper, we present efficient methods to quantize and interpolate on Flag manifolds, using both optimal algorithms as well as simplified suboptimal algorithms. Further, we unify these with the parameterization based approaches and show that these translate directly to low-complexity quantization and interpolation on Flag manifolds. Simulations reveal that the proposed precoder quantization and interpolation effectively enhance achievable rates with limited complexity.

Obtaining a rational all-pass filter that matches a target phase response is a common problem in signal processing. Typical approaches have generally focused on optimizing filter coefficients while minimizing the deviation from the target phase response. However, these approaches typically do not offer a guarantee of exact match of the phase or any conditions on group delay. In this letter, we propose a Blaschke interpolation based all-pass filter design, wherein, if the phase response is known at n distinct frequencies, an all-pass filter that exactly satisfies the target values can be obtained. Moreover, the group delay at the interpolating points can be optimized or tuned to control the phase response for remaining frequencies. Simulations reveal that the design method is able to produce filters that closely match the target phase response accurately with much lower complexity than prior approaches.

Precoding transmissions in wireless MIMO systems is essential to enable optimal utilization of the spatial degrees of freedom. However, communicating the precoding matrices from the receiver is challenging, owing to large feedback requirements. Past work has shown that predictive quantization in time, as well as interpolation over frequency can be used to reconstruct the precoders over a wide band, although these techniques have not been used jointly. We propose both a predictive quantization as well as a joint time-frequency interpolation strategy for precoding matrices over the Stiefel manifold. The key insight that we use is that local tangent spaces in the manifold permit effective combination of both temporal and frequency domain information for more accurate precoder reconstruction. Simulations reveal that we obtain a significant improvement in achievable rate as well as BER reduction when compared to existing strategies.

Generalized Frequency Division Multiplexing (GFDM) offers the simultaneous benefits of flexibility, low latency and excellent spectral properties over conventional OFDM for modern wireless systems, making it a promising candidate for 5G and other wireless technologies. However, several implementation related issues remain, including estimation and equalization. We consider the problem of efficient estimation and channel tracking in GFDM systems. In particular, we discuss a scattered (and tessellated) pilot based channel estimation approach, and derive a Kalman filter based channel tracker to handle time varying channels. We extend this work to the GFDM-MIMO case. Simulations reveal that the proposed tracker minimizes estimation errors which significantly improves the BER performance of the system.

Smartphones are equipped with a range of highly responsive sensors. From gyroscopes to accelerometers, providing mobile applications a wide variety of ways to interact with the environment. Unfortunately, some applications may be able to use these sensors to monitor their surroundings in unintended ways. Acoustic emanations are the most commonly used side channel in attacking computer keyboards, ATMs, etc. However, if multiple uncorrelated sensors are used, then the attack can be much more effective. In this paper, we explore how data from various sensors can be fused to improve the accuracy in recovering characters typed in a nearby mechanical keyboard from a smartphone. Unlike conventional approaches wherein acoustic emanations or other sensor reading are used as side-channel vectors, we combine emanations recorded from multiple sensors available in a smartphone and fuse them to achieve higher accuracy than any single sensor. Experiments reveal that the use of fusion could achieve an accuracy of 80 percent which is an improvement of over 6 percent using only audio emanations.

The larger core diameter of multimode fibers (MMFs) allows several propagating modes. The differential group delays of these modes cause modal dispersion, thus limiting the data rate. Recent results, however, have shown the existence of a set of principal modes (PMs) that allow dispersion free communication, to the first order. Moreover, the orthogonal nature of these PMs allows for convenient multiplexing in MMFs with low mode-dependent losses. To effectively utilize these PMs at the transmitter, it is essential to estimate them and feed them back to the transmitter. In this paper, we propose two quantization schemes that enable efficient encapsulation of the PMs for feedback. For shorter length MMF links, we generate a vector quantization codebook based on the Linde-Buzo-Gray algorithm, while for long links with strong mode coupling, we show analytically that the PMs are Haar distributed, and use a Grassmannian line packing based quantization codebook. Simulations reveal that the quantization effectively limits dispersion and the performance of the quantized PMs is within 2 dB of the ideal principal modes with only 6 bits used for quantization. In addition, the quantized PMs allow for efficient multiplexing with just 3% cross-talk.

The larger core diameter of multimode fibers (MMFs) allows several propagating modes, but differential group delays and modal cross talk cause modal dispersion, thus limiting the data rate. Recent results have shown the existence of a set of principal modes (PMs) that allow dispersion free communication to the first order. Moreover, the linear independence of the PMs also permits multiplexing in MMFs. To effectively utilize these PMs at the transmitter, it is essential to estimate them and feed them back to the transmitter. In this paper, we propose quantization schemes that enable efficient encapsulation of the PMs for feedback for MMFs with a small number of modes. For shorter links, we use vector quantization codebooks based on the Linde-Buzo-Gray (LBG) algorithm, while for long links with low mode dependent losses (MDL), we show analytically that the PMs are Haar distributed, and use Grassmannian line packing based codebooks. Simulations reveal that the quantization limits dispersion and the performance of the quantized PMs is within 2 dB of the ideal principal modes with only 6 bits quantization, both with and without MDL. In addition, the quantized PMs permit efficient multiplexing with low crosstalk in both the lossless and MDL cases.

Optical fiber links have enabled the transmission of very high data rates over both short-range and long-range links. However, the recent growth in the bandwidth demand has created the need to enhance their data rate capacities. While modern modulation techniques and multiple-input multiple-output (MIMO) based mode-division multiplexing (MDM) techniques with multimode fibers (MMFs) have been demonstrated to be promising approaches to achieve higher data rates, the computational complexity required to perform data decoding at these high data rates makes these systems prohibitive. In this paper, we model the channel characteristics and mode-dependent losses of few-mode and many-mode MMFs and study the data rates obtained if only a few modes are chosen for decoding at the subset. Such an approach promises to reduce the decoding complexity while not sacrificing data rate significantly. Simulations reveal that a subset selection approach leads to large savings in computation while not compromising data rate significantly. In particular, the energy-per-bit requirement can be reduced by over 50% in few-mode fibers and upto 70% in large-core multimode fiber links, when compared to conventional MDM decoding.

Multimode fibers (MMF) are generally used in short and medium haul optical networks owing to the availability of low cost devices and inexpensive packaging solutions. However, the performance of conventional multimode fibers is limited primarily by the presence of high modal dispersion owing to large core diameters. While electronic dispersion compensation methods improve the bandwidth-distance product of MMFs, they do not utilize the fundamental diversity present in the different modes of the multimode fiber. In this paper, we draw from developments in wireless communication theory and signal processing to motivate the use of vector intensity modulation and signal processing to enable high-data rates over MMFs. Further, we discuss the implementation of a closed-loop system with limited channel state feedback to enable the use of precoding at the transmitter, and show that this technique enhances the performance in a 10 Gb/s MMF link, consisting of 3 km of conventional multimode fiber. Experimental results indicate that vector intensity modulation and direct detection with with two modulators and detectors, along with the use of limited feedback results in a 50% increase over the single laser and detector case.

Multimode fibers (MMFs) offer a cost-effective connection solution for small and medium length networks. However, data rates through multimode fibers are traditionally limited by modal dispersion. Signal processing and Multiple-Input Multiple-Output (MIMO) have been shown to be effective at combating these limitations, but device design for the specific purpose of MIMO in MMFs is still an open issue. This paper utilizes a statistical field propagation model for MMFs to aid the analysis and designs of MMF laser and detector arrays, and aims to improve data rates of the fiber. Simulations reveal that optimal device designs could possess 2-3 times the data carrying capacity of suboptimal ones.

A general method of coding over expansions is proposed, which allows one to reduce the highly non-trivial problem of coding over continuous channels to a much simpler discrete ones. More specifically, the focus is on the additive exponential noise (AEN) channel, for which the (binary) expansion of the (exponential) noise random variable is considered. It is shown that each of the random variables in the expansion corresponds to independent Bernoulli random variables. Thus, each of the expansion levels (of the underlying channel) corresponds to a binary symmetric channel (BSC), and the coding problem is reduced to coding over these parallel channels while satisfying the channel input constraint. This optimization formulation is stated as the achievable rate result, for which a specific choice of input distribution is shown to achieve a rate which is arbitrarily close to the channel capacity in the high SNR regime. Remarkably, the scheme allows for low-complexity capacity-achieving codes for AEN channels, using the codes that are originally designed for BSCs. Extensions to different channel models and applications to other coding problems are discussed.

This paper considers the problem of interference mitigation in multi-cell multi-antenna time division duplex (TDD) wireless systems for downlink transmission. An efficient way to obtain channel state information (CSI) at the base station is by using uplink pilots and reciprocity of the downlink channel. At the same time, it has been shown that pilots from different cells contaminate each other, resulting in corruption of precoding matrices used by base stations, and high inter-cell interference. This paper studies the effects of shifting the location of pilots in time frames used in neighboring cells, and its effectiveness in obtaining better channel estimates, and, thereby, inter-cell interference reduction.