Motivated by hyper-reliable low-latency communication in 6G, we consider error control coding for short block lengths in multi-antenna SIMO flat-fading channels. In general, the channel fading coefficients are unknown at both the transmitter and receiver, which is referred to as a non-coherent channel. Conventionally, pilot symbols are transmitted to facilitate channel estimation, causing power and bandwidth overhead. Our paper considers sparse regression codes (SPARCs) for non-coherent flat-fading channels without using pilots. We develop a novel greedy decoder for SPARC using maximum likelihood (ML) principles, referred to as maximum likelihood matching pursuit (MLMP). MLMP works based on successive combining principles as opposed to conventional greedy algorithms, which are based on successive cancellation. We also obtain the noiseless perfect recovery condition for our successive combining algorithm. We further introduce an enhanced version named parallel-MLMP (P-MLMP) to improve performance by mitigating error propagation in greedy methods. In addition, we develop an approximate message passing (AMP) SPARC decoder for the non-coherent SIMO flat-fading model. Using simulation studies, we show that the MLMP decoder for SPARC outperforms AMP and other greedy decoders. Also, SPARC with P-MLMP decoder outperforms polar codes employing pilot-based channel estimation and polar codes with non-coherent decoders.

Sparse Regression Code (SPARC) connects the sparse signal recovery framework with the error control coding techniques. In this paper, we focus on improving the block error performance of SPARC in short block length regime over the AWGN channel. Towards that, we introduce suitable candidates for dictionary matrices in real and complex fields using Gold sequences and mutually unbiased bases (MUB). We propose two generalizations of SPARC (GSPARC), develop a greedy decoder called Match and Decode (MAD) algorithm, and provide its analytical noiseless recovery guarantees. We propose a parallel greedy search technique called parallel MAD (PMAD) to improve performance. We describe the applicability of GSPARC with PMAD decoder for multi-user channels, providing a non-orthogonal multiple access scheme. We present numerical results comparing the block error rate (BLER) performance of the proposed algorithms for GSPARC in AWGN channels in the short block length regime. The PMAD decoder gives better BLER than the approximate message-passing decoder for SPARC. GSPARC with PMAD gives comparable and competitive BLER performance compared to other existing codes. In multi-user channels, GSPARC with PMAD decoder outperforms the sphere packing lower bounds of an orthogonal multiple access scheme with the same spectral efficiency.

In a multi-user millimeter (mm) wave communication system, we consider the problem of estimating the channel response between the base station (BS) and each of the user equipments (UEs). We propose three different pilot training schemes/strategies, namely: 1) estimating mm wave channels separately at the UE's; 2) joint estimation of mm wave channels of all the UE's simultaneously at the BS; and 3) two stage process involving estimation at both the UE's and the BS. We propose two random constructions for the pilot/training signals/beamforming weights and analytically characterize the mutual coherence parameter of the resulting sensing matrices for one of the constructions. By exploiting the structure in mm wave channels, we develop a generalized block orthogonal matching pursuit (G-BOMP) algorithm for channel estimation in all the three strategies. Furthermore, we establish sufficient conditions for exact support recovery by the proposed G-BOMP algorithm and derive an upper bound on the norm of the channel estimation error. We also study the performance of our G-BOMP algorithm in terms of the average beamforming gain and average spectral efficiency achieved via simulations. Our results show that the proposed G-BOMP algorithm outperforms the conventional OMP algorithm and other existing multiuser mm wave channel estimation techniques. G-BOMP also performs comparable to the computationally expensive compressive estimation using Newton 's refinement technique, for the first pilot training strategy in which the UE's estimate the channels separately.

We consider a change detection problem with an unknown post-change parameter. The optimal algorithm in minimizing worst case detection delay subject to a constraint on average run length, referred as parallel CUSUM, is computationally expensive. We propose a low complexity algorithm based on parameter estimation using Kiefer-Wolfowitz (KW) method with CUSUM based change detection. We also consider a variant of KW method where the tuning sequences of KW method are reset periodically. We study the performance under the Gaussian mean change model. Our results show that reset KW-CUSUM performs close to the parallel CUSUM in terms of worst case delay versus average run length. Non-reset KW-CUSUM algorithm has smaller probability of false alarm compared to the existing algorithms, when run over a finite duration.

Base stations (BS) in a cellular network send unique synchronization signals based on their physical layer cell-identity, in every frame. To synchronize with a BS, a mobile terminal (MT) needs to identify the following synchronization parameters-starting time of the frame, relative frequency offset and the cell-identity of the corresponding BS. In a heterogeneous cellular network, due to the increased density of low-powered base stations, the MT receives signals from multiple BS in its vicinity. We consider the downlink synchronization problem where the MT tries to recover the synchronization parameters of all the BS in its neighborhood, using which, MT can subsequently choose the suitable BS for its connection. In any given scenario, the number of BS in the neighborhood of MT is relatively small compared to the total number of BS in the entire network. Exploiting this sparseness, we present a two-stage synchronization approach where the first stage identifies the frame timing using an approximation to the maximum likelihood detector and the second stage recovers the cell identities and the corresponding frequency offsets of all the neighborhood BS using block sparse signal recovery framework of compressive sensing. We analytically and numerically study the recovery guarantees of our proposed techniques and establish their superior performance over existing successive interference cancellation and matched filtering approaches.

We consider the problem of recovering block sparse signals which share the same sparsity pattern given multiple measurements. We consider two different noisy measurement models. In the first model, the sensing matrix remains the same for all the measurements. In the second model, we employ different sensing matrices for different measurements. For both these models, we present greedy algorithms for block sparse signal recovery and theoretically establish the recovery guarantees of the proposed algorithms. Using numerical simulations, we study the performance of the proposed algorithms and some existing algorithms. Our results present insights on how the correlation between block sparse signals plays a role on the recovery performance.

We consider heterogeneous cellular networks (HetNet) where each base station (BS) sends unique training signal based on its physical layer cell identity. Received signal at mobile terminal (MT) is superposition of training signals from different BS. Neither BS identities nor their channel response is known apriori at MT. For this scenario, we consider the problem of finding constituent BS identities from superimposed components in received signal. Though number of BS with unique identities can be quite large in a HetNet, in any given scenario, actual number of BS interfering at MT is relatively few. By exploiting this sparseness, we show that our problem can be solved using block sparse signal reconstruction algorithms under compressive sensing framework where sensing matrix is block-matrix with circulant-blocks (BCB). We apply convex programming based \ell_2 / \ell_1 mixed norm minimization and greed based subspace matching pursuit approaches to recover interfering BS identities. We characterize block restricted isometry property, mutual subspace incoherence of BCB matrices with i.i.d. Rademacher distributed entries and establish certain recovery guarantees. Our proposed approaches give significant improvements over conventional successive interference cancellation approach over both randomly generated and 3GPP-LTE training signals.

We consider a heterogeneous cellular network where each base station sends a unique training signal based on its physical layer cell identity. The received signal at the mobile terminal (MT) is a superposition of training signals from different base stations (BS). Neither the identities of BS nor their channel response is known apriori at the MT. For this scenario, we consider the problem of finding the identities of constituent BS from the superimposed components in the received signal. Though the number of BS with unique identities can be quite large in a cellular network, in any given scenario, the actual number of BS interfering at a MT is relatively few. By exploiting this sparseness, we show that our problem can be solved using block sparse signal reconstruction algorithms under compressive sensing framework where the sensing matrix in our model is block matrix with circulant blocks (BCB). We apply convex programming based ℓ2/ℓ1mixed norm minimization approach and greedy based subspace matching pursuit approach to recover the identities of interfering BS. We characterize the block restricted isometry property and the mutual subspace incoherence of BCB matrices with i.i.d. Rademacher distributed entries and establish certain guarantees on the recovery. Our proposed approaches give significant improvements over conventional successive interference cancellation approach when used with both randomly generated training signals and 3GPP-LTE training signals. Our results offer new and promising avenues for signal processing problems in heterogeneous cellular networks.

This paper investigates the optimal sensing-order problem for the general case of multi-user and multi-channel cognitive radio networks in which channel sensing is performed by the individual cognitive users (CUs) in a decentralized manner. The aim is to determine a sensing-order for each CU so as to maximize the cognitive throughput, which is the expected sum-throughput of all CUs. We consider two broad multi-user scenarios - first, where the network uses a contention resolution strategy whenever two or more CUs try to access the same channel simultaneously, and second, where the CUs are organized into distinct preemptive priority levels. For each scenario, we present a procedure for computing the cognitive throughput in the network. In general, the optimal sensing-orders can then be determined via a computationally expensive brute-force search. We also propose a suboptimal low complexity search algorithm for each scenario and show their proximity to the optimal performance by means of simulations.

This paper investigates the optimal sensing-order problem in multi-user, multi-channel cognitive radio networks in which channel sensing and access decisions are made sequentially by a central coordinator according to a central sensing-order. Estimates of the primary-free probabilities of the different channels are assumed to be known. Cognitive throughput, which is the sum of expected throughputs of all cognitive users (CUs), is used as the reward function. When the CUs do not use rateadaptation, we show that the optimal central sensing-order is a simple ordering of the channels based on their primary-free probabilities. When the CUs use rate-adaptation, we describe the procedure for mathematically formulating the reward function. In general, a computationally expensive brute force search can be used to find the optimal central sensing-order. We also consider a couple of simple heuristic sensing-orders and compare their performance with that of the optimal sensing-order through simulations.

The problem of reliable communication over unknown frequency-selective block-fading channels with sparse impulse responses is considered. In particular, discrete-time impulse responses with block-fading interval N, length L; 0.1

This paper considers the problem of reliable communication over discrete-time channels whose impulse responses have lengthLand exactlyS≤Lnon-zero coefficients, and whose support and coefficients remain fixed over blocks ofN>;Lchannel uses but change independently from block to block. Here, it is assumed that the channel's support and coefficient realizations are both unknown, although their statistics are known. Assuming Gaussian non-zero-coefficients and noise, and focusing on the high-SNR regime, it is first shown that the ergodic noncoherent channel capacity has pre-log factor 1-(S)/(N) for any L. It is then shown that, to communicate with arbitrarily small error probability at rates in accordance with the capacity pre-log factor, it suffices to use pilot-aided orthogonal frequency-division multiplexing (OFDM) withSpilots per fading block, in conjunction with an appropriate noncoherent decoder. Since the achievability result is proven using a noncoherent decoder whose complexity grows exponentially in the number of fading blocksK, a simpler decoder, based onS+1 pilots, is also proposed. Its ε-achievable rate is shown to have pre-log factor equal to 1-(S+1)/(N) with the previously considered channel, while its achievable rate is shown to have pre-log factor 1-(S+1)/(N) when the support of the block-fading channel remains fixed over time.

In this paper, we consider noncoherent single-antenna communication over doubly selective block-fading channels with discrete block-fading intervalN. In our noncoherent setup, neither the transmitter nor the receiver know the channel fading coefficients, though both know the channel statistics. In particular, we consider discrete-time channels whose impulse-response trajectories obey a complex-exponential basis expansion model with uncorrelated coefficients, and we show that such a model holds in the limitN¿ ¿ for pulse-shaped transmission/reception over certain wide-sense stationary uncorrelated scattering channels. First, we show that, when the inputs are chosen from continuous distributions, the channel's multiplexing gain (i.e., capacity pre-log factor) equalsmax(0, 1 - NdelayNDopp/N) , for discrete delay spreadNdelayand discrete Doppler spreadNDopp. Next, for the case of strictly doubly selective fading (i.e.,NDopp> 1 andNdelay> 1), we establish that, for cyclic-prefixed affine pilot-aided transmission (PAT) schemes designed to minimize the mean-squared error (MSE) attained by pilot-aided minimum-MSE channel estimation, the pre-log factor of the achievable rate is less than the channel's multiplexing gain. We then provide guidelines for the design of PAT schemes whose achievable-rate pre-log factor equals the channel's multiplexing gain and construct an example.

We consider pilot-aided transmission (PAT) for a general class of systems encompassing linear modulation and a linear time-varying channel. For these systems, and given a pilot energy constraint, we derive a tight lower bound on the mean squared error (MSE) of pilot-aided channel estimates as well as necessary and sufficient conditions on PAT to attain this bound. We then apply these results to the design of single-antenna PAT for doubly selective channels and arrive at novel MSE-optimal PAT schemes. In this application, we assume a block-based cyclic-prefix PAT and a basis expansion model for the channel.