814 research outputs found
Minimum error probability MIMO-aided relaying: multihop, parallel, and cognitive designs
No full textA design methodology based on the minimum error probability (MEP) framework is proposed for a nonregenerative multiple-input multiple-output (MIMO) relayaided system. We consider the associated cognitive, the parallel and the multi-hop source-relay-destination (SRD) link design based on this MEP framework, including the transmit precoder, the amplify-and-forward (AF) relay matrix and the receiver equalizer matrix of our system. It has been shown in the literature that MEP based communication systems are capable of improving the error probability of other linear counterparts. Our simulation results demonstrate that the proposed scheme indeed achieves a significant BER reduction over the existing linear schemes
Bayesian Techniques for Joint Sparse Signal Recovery: Theory and Algorithms
No full textThis thesis contributes new theoretical results, solution concepts, and algorithms concerning the Bayesian
recovery of multiple joint sparse vectors from noisy and underdetermined linear measurements.
The thesis is written in two parts. The first part focuses on the recovery of nonzero support of multiple
joint sparse vectors from their linear compressive measurements, an important canonical problem in multisensor
signal processing. The support recovery performance of a well known Bayesian inference technique
called Multiple Sparse Bayesian Learning (MSBL) is analyzed using tools from large deviation theory.
New improved sufficient conditions are derived for perfect support recovery in MSBL with arbitrarily high
probability. We show that the support error probability in MSBL decays exponentially fast with the number
of joint sparse vectors and the rate of decay depends on the restricted eigenvalues and null space structure
of the self Khatri-Rao product of the sensing matrix used to generate the measurements. New insights into
MSBL’s objective are developed which enhance our understanding of MSBL’s ability to recover supports of
size greater than the number of measurements available per joint sparse vector. These new insights are
formalized into a novel covariance matching framework for sparsity pattern recovery.
Next, we characterize the restricted isometry property of a generic Khatri-Rao product matrix in terms of
its restricted isometry constants (RICs). Upper bounds for the RICs of Khatri-Rao product matrices are of
independent interest as they feature in the sample complexity analysis of several linear inverse problems
of fundamental importance, including the above support recovery problem. We derive deterministic and
probabilistic upper bounds for the RICs of Khatri-Rao product between two matrices. The newly obtained
RIC bounds are then used to derive performance bounds for MSBL based support recovery.
Building upon the new insights about MSBL, a novel covariance matching based support recovery
algorithm is conceived. It uses a R´enyi divergence objective which reverts to the MSBL’s objective in a special
case. We show that the R´enyi divergence objective can be expressed as a difference of two submodular set
functions, and hence it can be optimized via an iterative majorization-minimization procedure to generate
the support estimate. The resulting algorithm is empirically shown to be several times faster than existing
support recovery methods with comparable performance.
The second part of the thesis focuses on developing decentralized extensions of MSBL for in-network
estimation of multiple joint sparse vectors from linear compressive measurements using a network of nodes.
A common issue while implementing decentralized algorithms is the high cost associated with the exchange
of information between the network nodes. To mitigate this problem, we examine two different approaches
to reduce the amount of inter-node communication in the network. In the first decentralized extension of
MSBL, the network nodes exchange information only via a small set of predesignated bridge nodes. For
this bridge node based network topology, the MSBL optimization is then performed using decentralized
Alternating Directions Method of Multipliers (ADMM). The convergence of decentralized ADMM in a bridge
node based network topology for a generic consensus optimization is separately analyzed and a linear rate
of convergence is established. Our second decentralized extension of MSBL reduces the communication
complexity by adaptively censoring the information exchanged between the nodes of the network by
exploiting the inherent sparse nature of the exchanged information. The performance of the proposed
decentralized schemes is evaluated using both simulated as well as real-world data
Data Fusion Based Physical Layer Protocols for Cognitive Radio Applications
No full textThis thesis proposes and analyzes data fusion algorithms that operate on the physical layer of a wireless sensor network, in the context of three applications of cognitive radios: 1. Cooperative spectrum sensing via binary consensus; 2. Multiple transmitter localization and communication footprint identification; 3.Target self-localization using beacon nodes.
For the first application, a co-phasing based data combining scheme is studied under imperfect channel knowledge. The evolution of network consensus state is modeled as a Markov chain, and the average transition probability matrix is derived. Using this, the average hitting time and average consensus duration are obtained, which are used to determine and optimize the performance of the consensus procedure.
Second, using the fact that a typical communication footprint map admits a sparse representation, two novel compressed sensing based schemes are proposed to construct the map using 1-bit decisions from sensors deployed in a geographical area. The number of transmitters is determined using the K-means algorithm and a circular fitting technique, and a design procedure is proposed to determine the power thresholds for signal detection at sensors.
Third, an algorithm is proposed for self-localization of a target node using power measurements from beacon nodes transmitting from known locations. The geographical area is overlaid with a virtual grid, and the problem is treated as one of testing overlapping subsets of grid cells for the presence of the target node. The column matching algorithm from group testing literature is considered for devising the target localization algorithm. The average probability of localizing the target within a grid cell is derived using the tools from Poisson point processes and order statistics. This quantity is used to determine the minimum required node density to localize the target within a grid cell with high probability.
The performance of all the proposed algorithms is illustrated through Monte Carlo simulations
Finding A Subset Of Non-defective Items From A Large Population : Fundamental Limits And Efficient Algorithms
No full textConsider a large population containing a small number of defective items. A commonly
encountered goal is to identify the defective items, for example, to isolate them. In the classical non-adaptive group testing (NAGT) approach, one groups the items into subsets, or pools, and runs tests for the presence of a defective itemon each pool. Using the outcomes the tests, a fundamental goal of group testing is to reliably identify the complete set of defective items with as few tests as possible. In contrast, this thesis studies a non-defective subset identification problem, where the primary goal is to identify a “subset” of “non-defective” items given the test outcomes. The main contributions of this thesis are:
We derive upper and lower bounds on the number of nonadaptive group tests
required to identify a given number of non-defective items with arbitrarily small
probability of incorrect identification as the population size goes to infinity. We
show that an impressive reduction in the number of tests is achievable compared
to the approach of first identifying all the defective items and then picking the
required number of non-defective items from the complement set. For example, in the asymptotic regime with the population size N → ∞, to identify L nondefective items out of a population containing K defective items, when the tests are reliable, our results show that O _ K logK L N _ measurements are sufficient when L ≪ N − K and K is fixed. In contrast, the necessary number of tests using the conventional approach grows with N as O _ K logK log N K_ measurements. Our
results are derived using a general sparse signal model, by virtue of which, they
are also applicable to other important sparse signal based applications such as
compressive sensing.
We present a bouquet of computationally efficient and analytically tractable nondefective subset recovery algorithms. By analyzing the probability of error of the
algorithms, we obtain bounds on the number of tests required for non-defective subset recovery with arbitrarily small probability of error. By comparing with the information theoretic lower bounds, we show that the upper bounds bounds on the number of tests are order-wise tight up to a log(K) factor, where K is the number of defective items. Our analysis accounts for the impact of both the additive noise (false positives) and dilution noise (false negatives). We also provide extensive simulation results that compare the relative performance of the
different algorithms and provide further insights into their practical utility. The
proposed algorithms significantly outperform the straightforward approaches of testing items one-by-one, and of first identifying the defective set and then choosing the non-defective items from the complement set, in terms of the number of measurements required to ensure a given success rate.
We investigate the use of adaptive group testing in the application of finding a
spectrum hole of a specified bandwidth in a given wideband of interest. We propose
a group testing based spectrum hole search algorithm that exploits sparsity in the primary spectral occupancy by testing a group of adjacent sub-bands in a single test. This is enabled by a simple and easily implementable sub-Nyquist sampling scheme for signal acquisition by the cognitive radios. Energy-based hypothesis tests are used to provide an occupancy decision over the group of sub-bands, and this forms the basis of the proposed algorithm to find contiguous spectrum holes of a specified bandwidth. We extend this framework to a multistage sensing algorithm that can be employed in a variety of spectrum sensing scenarios, including non-contiguous spectrum hole search. Our analysis allows one to identify the sparsity and SNR regimes where group testing can lead to significantly lower detection delays compared to a conventional bin-by-bin energy detection scheme. We illustrate the performance of the proposed algorithms via Monte Carlo simulations
Sparse Bayesian Learning For Joint Channel Estimation Data Detection In OFDM Systems
No full textBayesian approaches for sparse signal recovery have enjoyed a long-standing history in signal processing and machine learning literature. Among the Bayesian techniques, the expectation maximization based Sparse Bayesian Learning(SBL) approach is an iterative procedure with global convergence guarantee to a local optimum, which uses a parameterized prior that encourages sparsity under an evidence maximization frame¬work. SBL has been successfully employed in a wide range of applications ranging from image processing to communications. In this thesis, we propose novel, efficient and low-complexity SBL-based algorithms that exploit structured sparsity in the presence of fully/partially known measurement matrices. We apply the proposed algorithms to the problem of channel estimation and data detection in Orthogonal Frequency Division Multiplexing(OFDM) systems. Further, we derive Cram´er Rao type lower Bounds(CRB) for the single and multiple measurement vector SBL problem of estimating compressible vectors and their prior distribution parameters. The main contributions of the thesis are as follows:
We derive Hybrid, Bayesian and Marginalized Cram´er Rao lower bounds for the problem of estimating compressible vectors drawn from a Student-t prior distribution. We derive CRBs that encompass the deterministic or random nature of the unknown parameters of the prior distribution and the regression noise variance. We use the derived bounds to uncover the relationship between the compressibility and Mean Square Error(MSE) in the estimates. Through simulations, we demonstrate the dependence of the MSE performance of SBL based estimators on the compressibility of the vector.
OFDM is a well-known multi-carrier modulation technique that provides high spectral efficiency and resilience to multi-path distortion of the wireless channel
It is well-known that the impulse response of a wideband wireless channel is approximately sparse, in the sense that it has a small number of significant components relative to the channel delay spread. In this thesis, we consider the estimation of the unknown channel coefficients and its support in SISO-OFDM systems using a SBL framework. We propose novel pilot-only and joint channel estimation and data detection algorithms in block-fading and time-varying scenarios. In the latter case, we use a first order auto-regressive model for the time-variations, and propose recursive, low-complexity Kalman filtering based algorithms for channel estimation. Monte Carlo simulations illustrate the efficacy of the proposed techniques in terms of the MSE and coded bit error rate performance.
• Multiple Input Multiple Output(MIMO) combined with OFDM harnesses the inherent advantages of OFDM along with the diversity and multiplexing advantages of a MIMO system. The impulse response of wireless channels between the Nt transmit and Nr receive antennas of a MIMO-OFDM system are group approximately sparse(ga-sparse),i.e. ,the Nt Nr channels have a small number of significant paths relative to the channel delay spread, and the time-lags of the significant paths between transmit and receive antenna pairs coincide. Often, wire¬less channels are also group approximately-cluster sparse(ga-csparse),i.e.,every ga-sparse channel consists of clusters, where a few clusters have all strong components while most clusters have all weak components. In this thesis, we cast the problem of estimating the ga-sparse and ga-csparse block-fading and time-varying channels using a multiple measurement SBL framework. We propose a bouquet of novel algorithms for MIMO-OFDM systems that generalize the algorithms proposed in the context of SISO-OFDM systems. The efficacy of the proposed techniques are demonstrated in terms of MSE and coded bit error rate performance
Design of Communication Systems with Energy Harvesting Transmitters and Receivers
No full textAn energy harvesting node (EHN) operates using the energy harvested from the environment, e.g., solar, piezoelectric and radio frequency, which presents the tantalizing possibility of perpetually operating of sensor nodes. However, the operation of an EHN is governed by the energy neutrality constraint (ENC), which makes it mandatory that, at any point in time, the total cumulative energy consumed by a node must not exceed the total cumulative energy harvested by it. Due to the random and sporadic nature of the harvested energy, energy management becomes the central issue in the optimization of energy harvesting (EH) communication systems. The design of energy management policies for the systems where only the transmitter is an EHN has been considered extensively in the literature. On the other hand, designing the policies for the networks where both the transmitter and receiver use harvested energy to operate is significantly more challenging, as aspects of coordination of the transmission attempts as well as nonzero decoding cost come into play. In this thesis, we present the design of energy management policies for a variety of scenarios where all nodes in a network are energy harvesting. The main contributions of this thesis are as follows:
• In the initial part of the thesis (Chapters 2-5), we present the design of packet drop probability (PDP)-optimal power control policies for retransmission-based multi-hop EH links where all the nodes are EHNs and the cost of decoding the data at the receiver is nonzero. In order to design the policies, we first derive closed-form PDP expressions for multi-hop EH links employing retransmission index based policies (RIPs) that are unaware of the state-of-charge (SoC) of the batteries at the nodes. Since the transmit power prescribed by an SoC-unaware RIP is independent of the current battery state, the RIPs obviate the need to measure the SoC of the battery. In practice, it is difficult to accurately measure the SoC of the battery,
and therefore this is an added benefit of the proposed policy.
• Using the derived PDP expressions, we formulate and solve a PDP optimization problem to obtain near-optimal RIPs. To design the SoC-unaware RIPs we use the notion of energy unconstrained regime (EUR), in which, the average energy con-sumed is less than the average energy harvested. We show that policies designed to operate in the EUR are near-optimal, even with finite sized energy buffers. This, in turn, allows us to replace the ENC in the PDP optimization problem with a single EUR constraint. This significantly simplifies the complexity of designing the optimal policies. We show that the RIPs obtained under EUR constraints are near-optimal and achieve the lower bound on the PDP. Moreover, these policies can be implemented in a distributed fashion.
• In the later part of the thesis (Chapter 6), we investigate impact of lack of coordination between the transmitter and receiver, i.e., when the transmitter (receiver) does not have the information about the SoC of the battery at the receiver (transmitter). The lack of coordination leads to the wastage of energy when, in a slot, only the transmitter (or receiver) is on. The goal here is to maximize the through-put between a transmitter and receiver without any explicit coordination, and only using the statistical information about the energy arrivals at both the nodes. We derive a genie-aided upper bound on the throughput achievable, by analyzing a system that has non-causal knowledge of energy arrivals. Next, we present an online, distributed energy management policy which achieves the through-put within a gap of one bit from the upper bound and requires an occasional one bit feedback. The above policy is modified to obtain a time-dilated policy which achieves the upper bound asymptotically, with the battery size at both the nodes. We also propose a near-optimal, deterministic, fully uncoordinated policy which requires no feedback from the receiver. Our simulation results confirm the theoretical findings and illustrate the trade-offs between system parameters. The policies presented here not only achieve the upper bound but are also simple to implement. Our policies allow the nodes to operate in a truly uncoordinated fashion which, in turn, completely removes the overhead in the feedback
Design and Analysis of Random Access Protocols for Massive Machine-Type Communications
No full textMassive machine-type communications (mMTC) is a 5G and beyond use case, where the network is expected to serve millions of devices per square kilometre. Typical mMTC devices include smart energy meters, pressure sensors, temperature indicators, smart factory equipment, etc. These devices sporadically transmit short packets, i.e., they transmit a short burst of data once in a while and then largely remain inactive. In order to serve mMTC scenarios, we need to use grant-free random access (GFRA) protocols since they have the advantage of a low control and signalling overhead as well as non-orthogonal use of the channel. GFRA for mMTC is a relatively new research topic and has received immense interest in the recent past. In this thesis, we analyze several practical aspects of irregular repetition slotted aloha (IRSA), which is a GFRA protocol for mMTC.
IRSA is a distributed GFRA protocol where users transmit multiple replicas of their packets in randomly selected resource blocks within a frame to a base station (BS). The BS recovers the packets using successive interference cancellation (SIC). Existing studies have analyzed IRSA with idealized assumptions, i.e., neglecting fading, path-loss, channel estimation errors, pilot contamination, multi-cell interference, etc. These non-idealities can greatly reduce the performance of the system and must be accounted for in the design and analysis of any mMTC system.
In this thesis, we first analyze channel estimation in IRSA, exploiting the sparsity structure of IRSA transmissions, when non-orthogonal pilots are employed across users to facilitate channel estimation at the BS. Allowing for the use of non-orthogonal pilots is important, as the length of orthogonal pilots scales linearly with the total number of devices, leading to prohibitive overhead as the number of devices increases. Next, we present a novel analysis of the throughput of IRSA under practical channel estimation errors, and with the use of multiple antennas at the BS. Finally, we theoretically characterize the asymptotic throughput of IRSA using a density evolution based analysis. Simulation results underline the importance of accounting for channel estimation errors in analyzing IRSA, which can even lead to 70% loss in performance in severely interference-limited regimes. We also provide novel insights on the effect of parameters such as pilot length, SNR, number of antennas at the BS, etc, on the system throughput.
Next, we develop a novel Bayesian user activity detection (UAD) algorithm for IRSA, which exploits both the sparsity in user activity as well as the underlying structure of IRSA transmissions. We then derive the Cramer-Rao bound (CRB) on the mean squared error in channel estimation. We empirically show that the channel estimates obtained as a by-product of the proposed UAD algorithm achieves the CRB. Then, we analyze the signal to interference plus noise ratio achieved by the users, accounting for UAD, channel estimation errors, and pilot contamination. Finally, we illustrate the impact of these non-idealities on the throughput of IRSA via Monte Carlo simulations. For example, in a system with 1500 users and 10% of the users being active per frame, a pilot length of as low as 20 symbols is sufficient for accurate user activity detection. In contrast, using classical compressed sensing approaches for UAD would require a pilot length of about 346 symbols. Our results reveal crucial insights into dependence of UAD errors and throughput on parameters such as the length of the pilot sequence, the number of antennas at the BS, the number of users, and the SNR.
Then, we develop an enhanced version of IRSA that can be operated at the peak performance even at high system loads. IRSA can be used to serve a large number of users in mMTC while achieving a near-zero packet loss rate (PLR). However, in overloaded mMTC scenarios, the system is interference-limited, and the PLR is close to one. We develop a variant of IRSA in the interference limited-regime, namely Censored-IRSA (C-IRSA), in which users with poor channel states self-censor, i.e., they refrain from transmitting their packets. This censoring depends on a censor threshold that can be varied depending on the number of users in the system. Firstly, we empirically and theoretically analyze the performance of C-IRSA. Next, we derive the optimal choice of the censor threshold via a semi-analytic approach and a PLR-optimal algorithmic approach. This choice of the threshold maximizes the throughput while achieving zero PLR among uncensored users. Through extensive numerical simulations, we show that C-IRSA operates at full system throughput at high system loads compared to vanilla IRSA which has near-zero throughput.
After this, we analyze IRSA in the multi-cell (MC) and cell-free (CF) setups, accounting for pilot contamination, channel estimation errors, and multi-user interference. Via extensive simulations, we illustrate that, in practical settings, MC IRSA can have a drastic loss of throughput, up to 70%, compared to SC IRSA. Further, MC IRSA requires a significantly higher training length, in order to support the same user density and achieve the same throughput: for example, MC IRSA may need about 4−5x compared to SC IRSA. We provide insights into the effect of system parameters such as number of antennas, pilot length, and SNR on the throughput of MC IRSA and CF IRSA. With the proposed CF architectures, we show that we can achieve more than 14x improvement in the throughput of CF IRSA compared to a massive MIMO SC setup. We also study the densification trends in MC IRSA, where we observe an inverse behaviour in the throughput compared to CF IRSA.
Finally, we optimize the repetition distributions in IRSA with the throughput and the energy efficiency objectives. Via extensive numerical simulations, we study the effect of various system parameters such as the maximum repetition factor, the average repetition factor, the number of antennas, and the pilot length, on the repetition distributions, the inflection load, and the peak energy efficiency. Compared to the best existing distributions, we show that our optimized distributions can achieve up to 58% increase in the inflection load and up to 49% increase in the peak energy efficiency.
Overall, this thesis analyzes and designs the IRSA protocol under several practical non-idealities. The developed algorithms vastly outperform state-of-the-art and can efficiently serve mMTC applications
Spectrum Sensing Techniques For Cognitive Radio Applications
No full textCognitive Radio (CR) has received tremendous research attention over the past decade, both in the academia and industry, as it is envisioned as a promising solution to the problem of spectrum scarcity. ACR is a device that senses the spectrum for occupancy by licensed users(also called as primary users), and transmits its data only when the spectrum is sensed to be available. For the efficient utilization of the spectrum while also guaranteeing adequate protection to the licensed user from harmful interference, the CR should be able to sense the spectrum for primary occupancy quickly as well as accurately. This makes Spectrum Sensing(SS) one of the where the goal is to test whether the primary user is inactive(the null or noise-only hypothesis), or not (the alternate or signal-present hypothesis). Computational simplicity, robustness to uncertainties in the knowledge of various noise, signal, and fading parameters, and ability to handle interference or other source of non-Gaussian noise are some of the desirable features of a SS unit in a CR.
In many practical applications, CR devices can exploit known structure in the primary signal. IntheIEEE802.22CR standard, the primary signal is a wideband signal, but with a strong narrowband pilot component. In other applications, such as military communications, and blue tooth, the primary signal uses a Frequency Hopping (FH)transmission. These applications can significantly benefit from detection schemes that are tailored for detecting the corresponding primary signals. This thesis develops novel detection schemes and rigorous performance analysis of these primary signals in the presence of fading. For example, in the case of wideband primary signals with a strong narrowband pilot, this thesis answers the further question of whether to use the entire wideband for signal detection, or whether to filter out the pilot signal and use narrowband signal detection. The question is interesting because the fading characteristics of wideband and narrowband signals are fundamentally different. Due to this, it is not obvious which detection scheme will perform better in practical fading environments.
At another end of the gamut of SS algorithms, when the CR has no knowledge of the structure or statistics of the primary signal, and when the noise variance is known, Energy Detection (ED) is known to be optimal for SS. However, the performance of the ED is not robust to uncertainties in the noise statistics or under different possible primary signal models. In this case, a natural way to pose the SS problem is as a Goodness-of-Fit Test (GoFT), where the idea is to either accept or reject the noise-only hypothesis. This thesis designs and studies the performance of GoFTs when the noise statistics can even be non-Gaussian, and with heavy tails. Also, the techniques are extended to the cooperative SS scenario where multiple CR nodes record observations using multiple antennas and perform decentralized detection.
In this thesis, we study all the issues listed above by considering both single and multiple CR nodes, and evaluating their performance in terms of(a)probability of detection error,(b) sensing-throughput trade off, and(c)probability of rejecting the null-hypothesis. We propose various SS strategies, compare their performance against existing techniques, and discuss their relative advantages and performance tradeoffs. The main contributions of this thesis are as follows:
The question of whether to use pilot-based narrowband sensing or wideband sensing is answered using a novel, analytically tractable metric proposed in this thesis called the error exponent with a confidence level.
Under a Bayesian framework, obtaining closed form expressions for the optimal detection threshold is difficult. Near-optimal detection thresholds are obtained for most of the commonly encountered fading models.
Foran FH primary, using the Fast Fourier Transform (FFT) Averaging Ratio(FAR) algorithm, the sensing-through put trade off are derived in closed form.
A GoFT technique based on the statistics of the number of zero-crossings in the observations is proposed, which is robust to uncertainties in the noise statistics, and outperforms existing GoFT-based SS techniques.
A multi-dimensional GoFT based on stochastic distances is studied, which pro¬vides better performance compared to some of the existing techniques. A special case, i.e., a test based on the Kullback-Leibler distance is shown to be robust to some uncertainties in the noise process.
All of the theoretical results are validated using Monte Carlo simulations. In the case of FH-SS, an implementation of SS using the FAR algorithm on a commercially off-the ¬shelf platform is presented, and the performance recorded using the hardware is shown to corroborate well with the theoretical and simulation-based results. The results in this thesis thus provide a bouquet of SS algorithms that could be useful under different CRSS scenarios
Structured Sparse Signal Recovery for mmWave Channel Estimation: Intra-vector Correlation and Modulo Compressed Sensing
No full textThis thesis contributes new theoretical results and recovery algorithms for the area of sparse signal recovery motivated by applications to the problem of channel estimation in mmWave communication systems.
The presentation is in two parts. The first part focuses on the recovery of sparse vectors with correlated non-zero entries from their noisy low dimensional projections. Such structured sparse signals can be recovered using the technique of covariance matching. Here, we first estimate the covariance of the signal from the compressed measurements, and then use the obtained covariance matrix estimate as a plug-in to the linear minimum mean squared estimator to obtain an estimate of the sparse vector. We present a novel parametric Gaussian prior model, inspired by sparse Bayesian learning (SBL), which captures the underlying correlation in addition to the sparsity. Based on this prior, we develop a novel Bayesian learning algorithm called Corr-SBL, using the expectation-maximization procedure. This algorithm learns the parameters of the prior and updates the posterior estimates in an iterative fashion, thereby yielding a sparse vector estimate upon convergence. We present a closed form solution for the hyperparameter update based on fixed-point iterations. In case of imperfect correlation information, we present a pragmatic approach to learn the parameters of the correlation matrix in a data-driven fashion.
Next, we apply Corr-SBL to the channel estimation problem in mmWave multiple-input multiple-output systems employing a hybrid analog-digital architecture. We use noisy low dimensional projections of the channel obtained in the pilot transmission phase to estimate the channel across multiple coherence blocks. We show the efficacy of the Corr-SBL prior by analyzing the error in the channel estimates. Our results show that, compared to a genie-aided estimator and other existing sparse recovery algorithms, exploiting both sparsity and correlation results in significant performance gains, even under imperfect covariance estimates obtained using a limited number of samples.
In the second part of the presentation, we consider the sparse signal recovery problem when low-resolution ADCs with finite resolution are used in the measurement acquisition process. To counter the effect of signal clipping in these systems, we use modulo arithmetic to fold the measurements crossing the range back into the dynamic range of the system. For this setup, termed as modulo-CS, we answer the fundamental question of signal identifiability, by deriving conditions on the measurement matrix and the minimal number of measurements required for unique recovery of sparse vectors. We also show that recovery using the minimum required number of measurements is possible when the entries of the measurement matrix are drawn independently from any continuous distribution. Finally, we present an algorithm based on convex relaxation, and formulate a mixed integer linear program (MILP) for recovery of sparse vectors under modulo-CS. Our empirical results show that the minimum number of measurements required for the MILP is close to the theoretical result, for signals with low variance
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