arXiv subjects

Saeid Haghighatshoar

Publications and source records attributed to Saeid Haghighatshoar.

At least 19 recordsLinked to original sources

arXiv2024

Low-power SNN-based audio source localisation using a Hilbert Transform spike encoding scheme

Sound source localisation is used in many consumer devices, to isolate audio from individual speakers and reject noise. Localization is frequently accomplished by ``beamforming'', which combines phase-shifted audio streams to increase power from chosen source directions, under a known microphone array geometry. Dense band-pass filters are often needed to obtain narrowband signal components from wideband audio. These approaches achieve high accuracy, but narrowband beamforming is computationally demanding, and not ideal for low-power IoT devices. We demonstrate a novel method for sound source localisation on arbitrary microphone arrays, designed for efficient implementation in ultra-low-power spiking neural networks (SNNs). We use a Hilbert transform to avoid dense band-pass filters, and introduce a new event-based encoding method that captures the phase of the complex analytic signal. Our approach achieves state-of-the-art accuracy for SNN methods, comparable with traditional non-SNN super-resolution beamforming. We deploy our method to low-power SNN inference hardware, with much lower power consumption than super-resolution methods. We demonstrate that signal processing approaches co-designed with spiking neural network implementations can achieve much improved power efficiency. Our new Hilbert-transform-based method for beamforming can also improve the efficiency of traditional DSP-based signal processing.

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arXiv2023

Exact Gradient Computation for Spiking Neural Networks Through Forward Propagation

Spiking neural networks (SNN) have recently emerged as alternatives to traditional neural networks, owing to energy efficiency benefits and capacity to better capture biological neuronal mechanisms. However, the classic backpropagation algorithm for training traditional networks has been notoriously difficult to apply to SNN due to the hard-thresholding and discontinuities at spike times. Therefore, a large majority of prior work believes exact gradients for SNN w.r.t. their weights do not exist and has focused on approximation methods to produce surrogate gradients. In this paper, (1) by applying the implicit function theorem to SNN at the discrete spike times, we prove that, albeit being non-differentiable in time, SNNs have well-defined gradients w.r.t. their weights, and (2) we propose a novel training algorithm, called \emph{forward propagation} (FP), that computes exact gradients for SNN. FP exploits the causality structure between the spikes and allows us to parallelize computation forward in time. It can be used with other algorithms that simulate the forward pass, and it also provides insights on why other related algorithms such as Hebbian learning and also recently-proposed surrogate gradient methods may perform well.

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arXiv2022

Structured Channel Covariance Estimation from Limited Samples for Large Antenna Arrays

In massive multiple-input multiple-output (MIMO) systems, the knowledge of the users' channel covariance matrix is crucial for minimum mean square error (MMSE) channel estimation in the uplink as well as it plays an important role in several multiuser beamforming schemes in the downlink. Due to the large number of base station antennas in massive MIMO, accurate covariance estimation is challenging especially in the case where the number of samples is limited and thus comparable to the channel vector dimension. As a result, the standard sample covariance estimator may yield a too large estimation error which in turn may yield significant system performance degradation with respect to the ideal channel covariance knowledge case. To address such problem, we propose a method based on a parametric representation of the channel angular scattering function. The proposed parametric representation includes a discrete specular component which is addressed using the well-known MUltiple SIgnal Classification (MUSIC) method, and a diffuse scattering component, which is modeled as the superposition of suitable dictionary functions. To obtain the representation parameters we propose two methods, where the first solves a non-negative least-squares problem and the second maximizes the likelihood function using expectation-maximization. Our simulation results show that the proposed methods outperform the state of the art with respect to various estimation quality metrics and different sample sizes.

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arXiv2022

EXODUS: Stable and Efficient Training of Spiking Neural Networks

Spiking Neural Networks (SNNs) are gaining significant traction in machine learning tasks where energy-efficiency is of utmost importance. Training such networks using the state-of-the-art back-propagation through time (BPTT) is, however, very time-consuming. Previous work by Shrestha and Orchard [2018] employs an efficient GPU-accelerated back-propagation algorithm called SLAYER, which speeds up training considerably. SLAYER, however, does not take into account the neuron reset mechanism while computing the gradients, which we argue to be the source of numerical instability. To counteract this, SLAYER introduces a gradient scale hyperparameter across layers, which needs manual tuning. In this paper, (i) we modify SLAYER and design an algorithm called EXODUS, that accounts for the neuron reset mechanism and applies the Implicit Function Theorem (IFT) to calculate the correct gradients (equivalent to those computed by BPTT), (ii) we eliminate the need for ad-hoc scaling of gradients, thus, reducing the training complexity tremendously, (iii) we demonstrate, via computer simulations, that EXODUS is numerically stable and achieves a comparable or better performance than SLAYER especially in various tasks with SNNs that rely on temporal features. Our code is available at https://github.com/synsense/sinabs-exodus.

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arXiv2021

Non-Bayesian Activity Detection, Large-Scale Fading Coefficient Estimation, and Unsourced Random Access with a Massive MIMO Receiver

In this paper, we study the problem of user activity detection and large-scale fading coefficient estimation in a random access wireless uplink with a massive MIMO base station with a large number $M$ of antennas and a large number of wireless single-antenna devices (users). We consider a block fading channel model where the $M$-dimensional channel vector of each user remains constant over a coherence block containing $L$ signal dimensions in time-frequency. In the considered setting, the number of potential users $K_\text{tot}$ is much larger than $L$ but at each time slot only $K_a<<K_\text{tot}$ of them are active. Previous results, based on compressed sensing, require that $K_a\leq L$, which is a bottleneck in massive deployment scenarios such as Internet-of-Things and unsourced random access. In this work we show that such limitation can be overcome when the number of base station antennas $M$ is sufficiently large. We also provide two algorithms. One is based on Non-Negative Least-Squares, for which the above scaling result can be rigorously proved. The other consists of a low-complexity iterative componentwise minimization of the likelihood function of the underlying problem. Finally, we use the discussed approximated ML algorithm as the decoder for the inner code in a concatenated coding scheme for unsourced random access, a grant-free uncoordinated multiple access scheme where all users make use of the same codebook, and the massive MIMO base station must come up with the list of transmitted messages irrespectively of the identity of the transmitters. We show that reliable communication is possible at any $E_b/N_0$ provided that a sufficiently large number of base station antennas is used, and that a sum spectral efficiency in the order of $\mathcal{O}(L\log(L))$ is achievable.

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arXiv2020

Dual-Polarized FDD Massive MIMO: A Comprehensive Framework

We propose a comprehensive scheme for realizing a massive multiple-input multiple-output (MIMO) system with dual-polarized antennas in frequency division duplexing (FDD) mode. Employing dual-polarized elements in a massive MIMO array has been common practice recently and can, in principle, double the number of spatial degrees of freedom with a less-than-proportional increase in array size. However, processing a dual-polarized channel is demanding due to the high channel dimension and the lack of Uplink-Downlink (UL-DL) channel reciprocity in FDD mode. In particular, the difficulty arises in channel covariance acquisition for both UL and DL transmissions and in common training of DL channels in a multi-user setup. To overcome these challenges, we develop a unified framework consisting of three steps: (1) a covariance estimation method to efficiently estimate the UL covariance from noisy, orthogonal UL pilots; (2) a UL-DL covariance transformation method that obtains the DL covariance from the estimated UL covariance in the previous step; (3) a multi-user common DL channel training with limited DL pilot dimension method, which enables the BS to estimate effective user DL channels and use them for interference-free DL beamforming and data transmission. We provide extensive empirical results to prove the applicability and merits of our scheme.

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arXiv2020

Joint Approximate Covariance Diagonalization with Applications in MIMO Virtual Beam Design

We study the problem of maximum-likelihood (ML) estimation of an approximate common eigenstructure, i.e. an approximate common eigenvectors set (CES), for an ensemble of covariance matrices given a collection of their associated i.i.d vector realizations. This problem has a direct application in multi-user MIMO communications, where the base station (BS) has access to instantaneous user channel vectors through pilot transmission and attempts to perform joint multi-user Downlink (DL) precoding. It is widely accepted that an efficient implementation of this task hinges upon an appropriate design of a set of common "virtual beams", that captures the common eigenstructure among the user channel covariances. In this paper, we propose a novel method for obtaining this common eigenstructure by casting it as an ML estimation problem. We prove that in the special case where the covariances are jointly diagonalizable, the global optimal solution of the proposed ML problem coincides with the common eigenstructure. Then we propose a projected gradient descent (PGD) method to solve the ML optimization problem over the manifold of unitary matrices and prove its convergence to a stationary point. Through exhaustive simulations, we illustrate that in the case of jointly diagonalizable covariances, our proposed method converges to the exact CES. Also, in the general case where the covariances are not jointly diagonalizable, it yields a solution that approximately diagonalizes all covariances. Besides, the empirical results show that our proposed method outperforms the well-known joint approximate diagonalization of eigenmatrices (JADE) method in the literature.

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arXiv2019

Uplink-Downlink Channel Covariance Transformations and Precoding Design for FDD Massive MIMO

A large majority of cellular networks deployed today make use of Frequency Division Duplexing (FDD) where, in contrast with Time Division Duplexing (TDD), the channel reciprocity does not hold and explicit downlink (DL) probing and uplink (UL) feedback are needed in order to achieve spatial multiplexing gain. To support massive MIMO, the overhead incurred by conventional DL probing and UL feedback schemes scales linearly with the number of BS antennas and, therefore, may be very large. In this paper, we present a new approach to achieve a very competitive trade-off between spatial multiplexing gain and probing-feedback overhead in such systems. Our approach is based on two novel methods: (i) an efficient regularization technique based on Deep Neural Networks (DNN) that learns the Angular Spread Function (ASF) of users channels and permits to estimate the DL covariance matrix from the noisy i.i.d. channel observations obtained freely via UL pilots (UL-DL covariance transformation), (ii) a novel "sparsifying precoding" technique that uses the estimated DL covariance matrix from (i) and imposes a controlled sparsity on the DL channel such that given any assigned DL pilot dimension, it is able to find an optimal sparsity level and a corresponding sparsifying precoder for which the "effective" channel vectors after sparsification can be estimated at the BS with a low mean-square error. We compare our proposed DNN-based method in (i) with other methods in the literature via numerical simulations and show that it yields a very competitive performance. We also compare our sparsifying precoder in (ii) with the state-of-the-art statistical beamforming methods under the assumption that those methods also have access to the covariance knowledge in the DL and show that our method yields higher spectral efficiency since it uses in addition the instantaneous channel information after sparsification.

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arXiv2019

Grant-Free Massive Random Access With a Massive MIMO Receiver

We consider the problem of unsourced random access (U-RA), a grant-free uncoordinated form of random access, in a wireless channel with a massive MIMO base station equipped with a large number $M$ of antennas and a large number of wireless single-antenna devices (users). We consider a block fading channel model where the $M$-dimensional channel vector of each user remains constant over a coherence block containing $L$ signal dimensions in time-frequency. In the considered setting, the number of potential users $K_\text{tot}$ is much larger than $L$ but at each time slot only $K_a \ll K_\text{tot}$ of them are active. Previous results, based on compressed sensing, require that $K_a < L$, which is a bottleneck in massive deployment scenarios such as Internet-of-Things and U-RA. In the context of activity detection it is known that such a limitation can be overcome when the number of base station antennas $M$ is sufficiently large and a covariance based recovery algorithm is employed at the receiver. We show that, in the context of U-RA, the same concept allows to achieve high spectral efficiencies in the order of $\mathcal{O}(L \log L)$, although at an exponentially growing complexity. We show also that a concatenated coding scheme can be used to reduce the complexity to an acceptable level while still achieving total spectral efficiencies in the order of $\mathcal{O}(L/\log L)$.

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arXiv2019

Structured Channel Covariance Estimation from Limited Samples in Massive MIMO

Obtaining channel covariance knowledge is of great importance in various Multiple-Input Multiple-Output MIMO communication applications, including channel estimation and covariance-based user grouping. In a massive MIMO system, covariance estimation proves to be challenging due to the large number of antennas ($M\gg 1$) employed in the base station and hence, a high signal dimension. In this case, the number of pilot transmissions $N$ becomes comparable to the number of antennas and standard estimators, such as the sample covariance, yield a poor estimate of the true covariance and are undesirable. In this paper, we propose a Maximum-Likelihood (ML) massive MIMO covariance estimator, based on a parametric representation of the channel angular spread function (ASF). The parametric representation emerges from super-resolving discrete ASF components via the well-known MUltiple SIgnal Classification (MUSIC) method plus approximating its continuous component using suitable limited-support density function. We maximize the likelihood function using a concave-convex procedure, which is initialized via a non-negative least-squares optimization problem. Our simulation results show that the proposed method outperforms the state of the art in various estimation quality metrics and for different sample size to signal dimension ($N/M$) ratios.

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arXiv2019

Machine Learning for Geometrically-Consistent Angular Spread Function Estimation in Massive MIMO

In the spatial channel models used in multi-antenna wireless communications, the propagation from a single-antenna transmitter (e.g., a user) to an M-antenna receiver (e.g., a Base Station) occurs through scattering clusters located in the far field of the receiving antenna array. The Angular Spread Function (ASF) of the corresponding M-dim channel vector describes the angular density of the received signal power at the array. The modern literature on massive MIMO has recognized that the knowledge of covariance matrix of user channel vectors is very useful for various applications such as hybrid digital analog beamforming, pilot decontamination, etc. Therefore, most literature has focused on the estimation of such channel covariance matrices. However, in some applications such as uplink-downlink covariance transformation (for FDD massive MIMO precoding) and channel sounding some form of ASF estimation is required either implicitly or explicitly. It turns out that while covariance estimation is well-known and well-conditioned, the ASF estimation is a much harder problem and is in general ill-posed. In this paper, we show that under additional geometrically-consistent group-sparsity structure on the ASF, which is prevalent in almost all wireless propagation scenarios, one is able to estimate ASF properly. We propose sparse dictionary-based algorithms that promote this group-sparsity structure via suitable regularizations. Since generally it is difficult to capture the notion of group-sparsity through proper regularization, we propose another algorithm based on Deep Neural Networks (DNNs) that learns this structure. We provide numerical simulations to assess the performance of our proposed algorithms. We also compare the results with that of other methods in the literature, where we re-frame those methods in the context of ASF estimation in massive MIMO.

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arXiv2019

Multiple Measurement Vectors Problem: A Decoupling Property and its Applications

We study a Compressed Sensing (CS) problem known as Multiple Measurement Vectors (MMV) problem, which arises in joint estimation of multiple signal realizations when the signal samples have a common (joint) sparse support over a fixed known dictionary. Although there is a vast literature on the analysis of MMV, it is not yet fully known how the number of signal samples and their statistical correlations affects the performance of the joint estimation in MMV. Moreover, in many instances of MMV the underlying sparsifying dictionary may not be precisely known, and it is still an open problem to quantify how the dictionary mismatch may affect the estimation performance. In this paper, we focus on $\ell_{2,1}$-norm regularized least squares ($\ell_{2,1}$-LS) as a well-known and widely-used MMV algorithm in the literature. We prove an interesting decoupling property for $\ell_{2,1}$-LS, where we show that it can be decomposed into two phases: i) use all the signal samples to estimate the signal covariance matrix (coupled phase), ii) plug in the resulting covariance estimate as the true covariance matrix into the Minimum Mean Squared Error (MMSE) estimator to reconstruct each signal sample individually (decoupled phase). As a consequence of this decomposition, we are able to provide further insights on the performance of $\ell_{2,1}$-LS for MMV. In particular, we address how the signal correlations and dictionary mismatch affects its performance. Moreover, we show that by using the decoupling property one can obtain a variety of MMV algorithms with performances even better than that of $\ell_{2,1}$-LS. We also provide numerical simulations to validate our theoretical results.

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arXiv2019

Massive MIMO Unsourced Random Access

We consider an extension of the massive unsourced random access originally proposed by Polyanskiy to the case where the receiver has a very large number of antennas (a massive MIMO base station) and no channel state information is given to the receiver (fully non-coherent detection). Our coding approach borrows the concatenated coding idea from Amalladinne et. al., combined with a novel non-Bayesian `activity detection' algorithm for massive MIMO random access channels, that outperforms currently proposed Bayesian vector AMP (VAMP) schemes currently proposed for activity detection, and does not suffer from the numerical instabilities and requirement for accurate a priori statistics as VAMP. We show that the required transmit $E_b/N_0$ for reliable communication can be made arbitrarily small as the number of receiver antennas M grows sufficiently large.

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arXiv2018

FDD Massive MIMO via UL/DL Channel Covariance Extrapolation and Active Channel Sparsification

We propose a novel method for massive Multiple-Input Multiple-Output (massive MIMO) in Frequency Division Duplexing (FDD) systems. Due to the large frequency separation between Uplink (UL) and Downlink (DL), in FDD systems channel reciprocity does not hold. Hence, in order to provide DL channel state information to the Base Station (BS), closed-loop DL channel probing and Channel State Information (CSI) feedback is needed. In massive MIMO this incurs typically a large training overhead. For example, in a typical configuration with M = 200 BS antennas and fading coherence block of T = 200 symbols, the resulting rate penalty factor due to the DL training overhead, given by max{0, 1 - M/T}, is close to 0. To reduce this overhead, we build upon the well-known fact that the Angular Scattering Function (ASF) of the user channels is invariant over frequency intervals whose size is small with respect to the carrier frequency (as in current FDD cellular standards). This allows to estimate the users' DL channel covariance matrix from UL pilots without additional overhead. Based on this covariance information, we propose a novel sparsifying precoder in order to maximize the rank of the effective sparsified channel matrix subject to the condition that each effective user channel has sparsity not larger than some desired DL pilot dimension T_{dl}, resulting in the DL training overhead factor max{0, 1 - T_{dl} / T} and CSI feedback cost of T_{dl} pilot measurements. The optimization of the sparsifying precoder is formulated as a Mixed Integer Linear Program, that can be efficiently solved. Extensive simulation results demonstrate the superiority of the proposed approach with respect to concurrent state-of-the-art schemes based on compressed sensing or UL/DL dictionary learning.

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arXiv2018

Low-Complexity Statistically Robust Precoder/Detector Computation for Massive MIMO Systems

Massive MIMO is a variant of multiuser MIMO in which the number of antennas at the base station (BS) $M$ is very large and typically much larger than the number of served users (data streams) $K$. Recent research has illustrated the system-level advantages of such a system and in particular the beneficial effect of increasing the number of antennas $M$. These benefits, however, come at the cost of dramatic increase in hardware and computational complexity. This is partly due to the fact that the BS needs to compute suitable beamforming vectors in order to coherently transmit/receive data to/from each user, where the resulting complexity grows proportionally to the number of antennas $M$ and the number of served users $K$. Recently, different algorithms based on tools from random matrix theory in the asymptotic regime of $M,K \to \infty$ with $\frac{K}{M} \to ρ\in (0,1)$ have been proposed to reduce such complexity. The underlying assumption in all these techniques, however, is that the exact statistics (covariance matrix) of the channel vectors of the users is a priori known. This is far from being realistic, especially that in the high-dim regime of $M\to \infty$, estimation of the underlying covariance matrices is well known to be a very challenging problem. In this paper, we propose a novel technique for designing beamforming vectors in a massive MIMO system. Our method is based on the randomized Kaczmarz algorithm and does not require knowledge of the statistics of the users channel vectors. We analyze the performance of our proposed algorithm theoretically and compare its performance with that of other competitive techniques via numerical simulations. Our results indicate that our proposed technique has a comparable performance while it does not require the knowledge of the statistics of the users channel vectors.

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arXiv2018

A New Scaling Law for Activity Detection in Massive MIMO Systems

In this paper, we study the problem of \textit{activity detection} (AD) in a massive MIMO setup, where the Base Station (BS) has $M \gg 1$ antennas. We consider a block fading channel model where the $M$-dim channel vector of each user remains almost constant over a \textit{coherence block} (CB) containing $D_c$ signal dimensions. We study a setting in which the number of potential users $K_c$ assigned to a specific CB is much larger than the dimension of the CB $D_c$ ($K_c \gg D_c$) but at each time slot only $A_c \ll K_c$ of them are active. Most of the previous results, based on compressed sensing, require that $A_c\le D_c$, which is a bottleneck in massive deployment scenarios such as Internet-of-Things (IoT) and Device-to-Device (D2D) communication. In this paper, we show that one can overcome this fundamental limitation when the number of BS antennas $M$ is sufficiently large. More specifically, we derive a \textit{scaling law} on the parameters $(M, D_c, K_c, A_c)$ and also \textit{Signal-to-Noise Ratio} (SNR) under which our proposed AD scheme succeeds. Our analysis indicates that with a CB of dimension $D_c$, and a sufficient number of BS antennas $M$ with $A_c/M=o(1)$, one can identify the activity of $A_c=O(D_c^2/\log^2(\frac{K_c}{A_c}))$ active users, which is much larger than the previous bound $A_c=O(D_c)$ obtained via traditional compressed sensing techniques. In particular, in our proposed scheme one needs to pay only a poly-logarithmic penalty $O(\log^2(\frac{K_c}{A_c}))$ for increasing the number of potential users $K_c$, which makes it ideally suited for AD in IoT setups. We propose low-complexity algorithms for AD and provide numerical simulations to illustrate our results. We also compare the performance of our proposed AD algorithms with that of other competitive algorithms in the literature.

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arXiv2018

Efficient Beam Alignment for mmWave Single-Carrier Systems with Hybrid MIMO Transceivers

Communication at millimeter wave (mmWave) bands is expected to become a key ingredient of next generation (5G) wireless networks. Effective mmWave communications require fast and reliable methods for beamforming at both the User Equipment (UE) and the Base Station (BS) sides, in order to achieve a sufficiently large Signal-to-Noise Ratio (SNR) after beamforming. We refer to the problem of finding a pair of strongly coupled narrow beams at the transmitter and receiver as the Beam Alignment (BA) problem. In this paper, we propose an efficient BA scheme for single-carrier mmWave communications. In the proposed scheme, the BS periodically probes the channel in the downlink via a pre-specified pseudo-random beamforming codebook and pseudo-random spreading codes, letting each UE estimate the Angle-of-Arrival / Angle-of-Departure (AoA-AoD) pair of the multipath channel for which the energy transfer is maximum. We leverage the sparse nature of mmWave channels in the AoA-AoD domain to formulate the BA problem as the estimation of a sparse non-negative vector. Based on the recently developed Non-Negative Least Squares (NNLS) technique, we efficiently find the strongest AoA-AoD pair connecting each UE to the BS. We evaluate the performance of the proposed scheme under a realistic channel model, where the propagation channel consists of a few multipath scattering components each having different delays, AoAs-AoDs, and Doppler shifts.The channel model parameters are consistent with experimental channel measurements. Simulation results indicate that the proposed method is highly robust to fast channel variations caused by the large Doppler spread between the multipath components. Furthermore, we also show that after achieving BA the beamformed channel is essentially frequency-flat, such that single-carrier communication needs no equalization in the time domain.

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arXiv2018

Theoretical Bounds on MAP Estimation in Distributed Sensing Networks

The typical approach for recovery of spatially correlated signals is regularized least squares with a coupled regularization term. In the Bayesian framework, this algorithm is seen as a maximum-a-posterior estimator whose postulated prior is proportional to the regularization term. In this paper, we study distributed sensing networks in which a set of spatially correlated signals are measured individually at separate terminals, but recovered jointly via a generic maximum-a-posterior estimator. Using the replica method, it is shown that the setting exhibits the decoupling property. For the case with jointly sparse signals, we invoke Bayesian inference and propose the "multi-dimensional soft thresholding" algorithm which is posed as a linear programming. Our investigations depict that the proposed algorithm outperforms the conventional $\ell_{2,1}$-norm regularized least squares scheme while enjoying a feasible computational complexity.

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