arXiv subjects

Kareem M. Attiah

Publications and source records attributed to Kareem M. Attiah.

9 recordsLinked to original sources

arXiv2026

Connections Between Quadratic Transform for Fractional Programming and Schur Complement

This paper shows that there are intimate connections between the quadratic transform technique for solving fractional programming (FP) problems and the Schur-complement technique in matrix analysis. We demonstrate that the quadratic transform technique is related to two aspects of the Schur complement: (i) the linear matrix inequality (LMI) condition for positive semidefiniteness and (ii) the matrix determinant formula. Specifically, we establish that the quadratic transform and the Schur-complement LMI condition imply each other. This connection allows us to provide new interpretations of the auxiliary variable in the quadratic transform, and it allows us to rederive the Schur-complement determinant formula. Furthermore, this connection leads to generalizations of the quadratic transform in FP and the Schur-complement LMI that can accommodate generalized matrix inverse. As an application in information theory, we apply the generalized FP framework to the least-favorable-noise minimax formulation of the Gaussian vector broadcast channel sum capacity problem. When the least-favorable noise covariance is singular, matrix-inverse-based Karush-Kuhn-Tucker (KKT) analysis would require a careful analysis of the input and output spaces of the channel. We show using generalized FP that an auxiliary-variable representation of the singular matrix fraction directly yields the reciprocal multiple-access channel and recovers the uplink-downlink duality relation for sum capacity.

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arXiv2026

How Many Simultaneous Beamformers are Needed for Integrated Sensing and Communications?

Consider a downlink integrated sensing and communications (ISAC) system in which a base station employs linear beamforming to communicate to $K$ users, while simultaneously uses sensing beams to perform a sensing task of estimating $L$ real parameters. How many beamformers are needed to achieve the best performance for both sensing and communications? This paper establishes bounds on the minimum number of downlink beamformers, in which sensing performance is measured in terms of the Cramér-Rao bound for parameter estimation and communications performance is measured in terms of the signal-to-interference-and-noise ratios. We show that an ISAC system requires at most $K + \sqrt{\frac{L(L+1)}{2}}$ beamformers if the remote users have the ability to cancel the interference caused by the sensing beams. If cancelling interference due to the sensing beams is not possible, the bound becomes $\sqrt{K^2 + \frac{L(L+1)}{2}}$. Interestingly, in the latter case, the bound on the number of beamformers is less than the sum of the bounds for each task individually. These results can be extended to sensing tasks for which the performance is measured as a function of $d$ quadratic terms in the beamformers. In this case, the bound becomes $K + \sqrt{d}$ and $\sqrt{K^2 + d}$, respectively. Specifically, for estimating complex path losses and angles-of-arrival of $N_\text{tr}$ targets while communicating to $K$ users, the bound on the minimum number of beamformers scales linearly in $K$ and in $N_\text{tr}$, assuming interference from sensing can be cancelled. When interference cancellation is not possible, the following exact characterization for the case of $N_\text{tr} = 1$ can be obtained: when $K=0$ or $1$, two beamformers should be used; when $K \ge 2$, exactly $K$ beamformers should be used, i.e., communication beamformers alone are already sufficient.

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arXiv2026

Uplink-Downlink Duality for Beamforming in Integrated Sensing and Communications

This paper considers the beamforming and power optimization problem for a class of integrated sensing and communications (ISAC) problems that utilize the communication signals simultaneously for sensing. We formulate the problem of minimizing the Bayesian Cramér-Rao bound (BCRB) on the mean-squared error of estimating a vector of parameters, while satisfying downlink signal-to-interference-and-noise-ratio constraints for a set of communication users at the same time. The proposed optimization framework comprises two key new ingredients. First, we show that the BCRB minimization problem corresponds to maximizing beamforming power along certain sensing directions of interest. Second, the classical uplink-downlink duality for multiple-input multiple-output communications can be extended to the ISAC setting, but unlike the classical communication problem, the dual uplink problem for ISAC may entail negative noise power and needs to include an extra condition on the uplink beamformers. This new duality theory opens doors for efficient iterative algorithm for optimizing power and beamformers for ISAC.

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arXiv2026

Active MIMO Sensing With Exploration-Exploitation Tradeoff

This paper develops an active sensing framework for designing the transmit and receive beamformers of a multiple-input multiple-output (MIMO) radar system. In the proposed technique, the beamformers are adaptively designed in each sensing stage based on the measurements made in the previous sensing stages. The beamformers are determined by minimizing the Bayesian Cram{é}r-Rao bound (BCRB) for the estimation of the unknown sensing parameters at each stage via Lagrangian dual optimization. To address the exploration-exploitation tradeoff that is inherent to such an adaptive design, this paper proposes two variants of the BCRB optimization problem: an exploration-centric variant, that ensures that multiple orthogonal beamforming directions are probed in each sensing stage, and an exploitation-centric variant, that does not restrict the number of optimal beamformers. Each variant of the optimization problem is solved via an alternating optimization algorithm that alternates between solving for the transmit beamformers and solving for the receive beamformers. The algorithm is shown to converge to a stationary point provided that each optimization problem is solved to global optimality. Moreover, this paper studies each of the two BCRB optimization sub-problems in the Lagrangian dual domain and shows that despite the non-convexity, global optimality is guaranteed provided that certain sufficient conditions hold. The conditions pertain to the multiplicity of the eigenvalues of a specific direction matrix that can be analytically written in terms of the optimal dual variables. These conditions further imply the tightness of the semidefinite relaxation of the optimization problems. Simulation results demonstrate the benefits of the proposed BCRB-based design compared to state-of-the-art adaptive beamforming strategies.

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arXiv2025

RIS-Assisted Joint Sensing and Communications via Fractionally Constrained Fractional Programming

This paper studies an uplink dual-functional sensing and communication system aided by a reconfigurable intelligent surface (RIS), whose reflection pattern is configured to trade-off sensing and communication functionalities. Specifically, the Bayesian Cramér-Rao lower bound (BCRLB) for estimating the azimuth angle of a sensing user is minimized while ensuring the signal-to-interference-plus-noise ratio constraints for communication users. We show that this problem can be formulated as a novel fractionally constrained fractional programming (FCFP) problem. To deal with this nontrivial optimization problem, we extend a quadratic transform technique, originally proposed to handle optimization problems containing fractional structures only in objectives, to the scenario where the constraints also include ratios. First, we consider the case where the fading coefficient is known. Using the quadratic transform, the FCFP problem can be turned into a sequence of subproblems that are convex except for the constant-modulus constraints which can be tackled using a penalty-based approach. To further reduce the computational complexity, we leverage the constant-modulus conditions and propose a novel linear transform. This new transform enables the FCFP problem to be turned into a sequence of linear programming (LP) subproblems, which can be solved efficiently. Then, we consider the case where the fading coefficient is unknown. A modified BCRLB is used to make the problem more tractable, and the proposed quadratic transform based algorithm is used to solve the problem. Numerical results unveil nontrivial and effective reflection patterns that can be synthesized by the RIS to facilitate both communication and sensing functionalities.

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arXiv2025

Coded Downlink Massive Random Access and a Finite de Finetti Theorem

This paper considers a massive connectivity setting in which a base-station (BS) aims to communicate sources $(X_1,\cdots,X_k)$ to a randomly activated subset of $k$ users, among a large pool of $n$ users, via a common message in the downlink. Although the identities of the $k$ active users are assumed to be known at the BS, each active user only knows whether itself is active and does not know the identities of the other active users. A naive coding strategy is to transmit the sources alongside the identities of the users for which the source information is intended. This requires $H(X_1,\cdots,X_k) + k\log(n)$ bits, because the cost of specifying the identity of one out of $n$ users is $\log(n)$ bits. For large $n$, this overhead can be significant. This paper shows that it is possible to develop coding techniques that eliminate the dependency of the overhead on $n$, if the source distribution follows certain symmetry. Specifically, if the source distribution is independently and identically distributed (i.i.d.) then the overhead can be reduced to at most $O(\log(k))$ bits, and in case of uniform i.i.d. sources, the overhead can be further reduced to $O(1)$ bits. For sources that follow a more general exchangeable distribution, the overhead is at most $O(k)$ bits, and in case of finite-alphabet exchangeable sources, the overhead can be further reduced to $O(\log(k))$ bits. The downlink massive random access problem is closely connected to the study of finite exchangeable sequences. The proposed coding strategy allows bounds on the Kullback-Leibler (KL) divergence between finite exchangeable distributions and i.i.d. mixture distributions to be developed and gives a new KL divergence version of the finite de Finetti theorem, which is scaling optimal.

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arXiv2024

Beamforming Design for Integrated Sensing and Communications Using Uplink-Downlink Duality

This paper presents a novel optimization framework for beamforming design in integrated sensing and communication systems where a base station seeks to minimize the Bayesian Cramér-Rao bound of a sensing problem while satisfying quality of service constraints for the communication users. Prior approaches formulate the design problem as a semidefinite program for which acquiring a beamforming solution is computationally expensive. In this work, we show that the computational burden can be considerably alleviated. To achieve this, we transform the design problem to a tractable form that not only provides a new understanding of Cramér-Rao bound optimization, but also allows for an uplink-downlink duality relation to be developed. Such a duality result gives rise to an efficient algorithm that enables the beamforming design problem to be solved at a much lower complexity as compared to the-state-of-the-art methods.

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arXiv2022

Deep Learning for Channel Sensing and Hybrid Precoding in TDD Massive MIMO OFDM Systems

This paper proposes a deep learning approach to channel sensing and downlink hybrid beamforming for massive multiple-input multiple-output systems operating in the time division duplex mode and employing either single-carrier or multicarrier transmission. The conventional precoding design involves a two-step process of first estimating the high-dimensional channel, then designing the precoders based on such estimate. This two-step process is, however, not necessarily optimal. This paper shows that by using a learning approach to design the analog sensing and the hybrid downlink precoders directly from the received pilots without the intermediate high-dimensional channel estimation, the overall system performance can be significantly improved. Training a neural network to design the analog and digital precoders simultaneously is, however, difficult. Further, such an approach is not generalizable to systems with different number of users. In this paper, we develop a simplified and generalizable approach that learns the uplink sensing matrix and downlink analog precoder using a deep neural network that decomposes on a per-user basis, then designs the digital precoder based on the estimated low-dimensional equivalent channel. Numerical comparisons show that the proposed methodology results in significantly less training overhead and leads to an architecture that generalizes to various system settings.

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arXiv2021

Deep Learning for Distributed Channel Feedback and Multiuser Precoding in FDD Massive MIMO

This paper shows that deep neural network (DNN) can be used for efficient and distributed channel estimation, quantization, feedback, and downlink multiuser precoding for a frequency-division duplex massive multiple-input multiple-output system in which a base station (BS) serves multiple mobile users, but with rate-limited feedback from the users to the BS. A key observation is that the multiuser channel estimation and feedback problem can be thought of as a distributed source coding problem. In contrast to the traditional approach where the channel state information (CSI) is estimated and quantized at each user independently, this paper shows that a joint design of pilots and a new DNN architecture, which maps the received pilots directly into feedback bits at the user side then maps the feedback bits from all the users directly into the precoding matrix at the BS, can significantly improve the overall performance. This paper further proposes robust design strategies with respect to channel parameters and also a generalizable DNN architecture for varying number of users and number of feedback bits. Numerical results show that the DNN-based approach with short pilot sequences and very limited feedback overhead can already approach the performance of conventional linear precoding schemes with full CSI.

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