Integrated sensing and communication (ISAC) has emerged as a key technology for future communication systems. In this paper, we provide a general framework to reveal the fundamental trade-off between sensing and communication in OFDM systems, where a unified ISAC signal is exploited to perform both tasks. To evaluate the sensing performance, we introduce two representative performance metrics: The Cramér-Rao Bound (CRB) and the Barakin Bound (BRB). For the asymptotic case when the number of subcarriers is large, we show that the asymptotically optimal input distribution that achieves the Pareto boundary point of the Capacity-CRB\BRB region is Gaussian and the entire Pareto boundary can be obtained by solving a power allocation problem. We prove that the power allocation problem for obtaining the Capacity-CRB region can be calculated by solving a convex optimization problem. However, the Capacity-BRB region is more difficult to be characterized due to the non-convexity of the optimization problem. Therefore, we propose an iterative algorithm to obtain an inner bound of the Capacity-BRB region. Moreover, we derive the sufficient conditions under which the Gaussian distribution remains asymptotically optimal when the number of subcarriers approaches infinity and the delay gap between two targets approaches zero simultaneously. For the non-asymptotic case, an optimization problem is formulated for sensing-optimal input distribution and the capacity-achieving distribution is derived under the sensing-optimal constraints. Finally, numerical simulations are conducted to verify the theoretical analysis and provide useful insights.

In fifth generation (5G) new radio (NR) time-division duplex (TDD) systems, the base station (BS) can estimate downlink channels based on the received uplink pilots due to the channel reciprocity. As the number of users increases, determining how to accommodate more users in the uplink channel estimation stage with limited pilot resources has emerged as a challenging problem. This paper proposes a non-orthogonal pilot reuse scheme based on Zadoff-Chu (ZC) pilot sequence partitioning, where a single ZC sequence is partitioned into two subsequences to support two users, thus doubling the number of users in the uplink channel estimation stage. Additionally, an efficient sequence partitioning optimization algorithm is first employed to suppress the energy leakage caused by the non-orthogonal pilot reuse, and then a successive interference cancellation (SIC)-based multi-user Turbo channel estimation algorithm is proposed to mitigate the residual interference. Through the optimization of sequence partitioning and the utilization of the SIC-based multi-user Turbo channel estimation, more users can be accommodated with minimal channel estimation performance loss, as verified by the simulation results.

Pilot pattern optimization in orthogonal frequency division multiplexing (OFDM) systems has been widely investigated due to its positive impact on channel estimation. In this paper, we consider the problem of multi-user pilot pattern optimization in OFDM systems. In particular, the goal is to enhance channel extrapolation performance for 5G NR systems by optimizing multi-user pilot patterns in frequency-domain. We formulate a novel pilot pattern optimization problem with the objective of minimizing the maximum integrated side-lobe level (ISL) among all users, subject to a statistical resolution limit (SRL) constraint. Unlike existing literature that only utilizes ISL for controlling side-lobe levels of the ambiguity function, we also leverage ISL to mitigate multi-user interference in code-domain. Additionally, the introduced SRL constraint ensures sufficient delay resolution of the system to resolve multipath, thereby improving channel extrapolation performance. Then, we employ the estimation of distribution algorithm (EDA) to solve the formulated problem in an offline manner. Simulation results demonstrate that the optimized pilot pattern yields significant performance gains in channel extrapolation over the conventional pilot patterns.

Pilot pattern optimization in orthogonal frequency division multiplexing (OFDM) systems has been widely investigated due to its positive impact on channel estimation. In this paper, we consider the problem of multi-user pilot pattern optimization for OFDM systems. In particular, the goal is to enhance channel extrapolation performance for 5G NR systems by optimizing multi-user pilot patterns in frequency-domain. We formulate a novel pilot pattern optimization problem with the objective of minimizing the maximum integrated side-lobe level (ISL) among all users, subject to a statistical resolution limit (SRL) constraint. Unlike existing literature that only utilizes ISL for controlling side-lobe levels of the ambiguity function, we also leverage ISL to mitigate multi-user interference in code-domain multiplexing. Additionally, the introduced SRL constraint ensures sufficient delay resolution of the system to resolve multipath, thereby improving channel extrapolation performance. Then, we employ the estimation of distribution algorithm (EDA) to solve the formulated problem in an offline manner. Finally, we extend the formulated multi-user pilot pattern optimization problem to a multiband scenario, in which multiband gains can be exploited to improve channel extrapolation performance. Simulation results demonstrate that the optimized pilot pattern yields significant performance gains in channel extrapolation over the conventional pilot patterns.

Future wireless systems are supposed to provide high-resolution sensing services via communication signals. Under this background, multiband sensing has recently become a promising technology due to that it can improve the sensing performance by jointly utilizing multiple non-contiguous frequency bands at a low cost. However, few studies have investigated the fundamental limits of multiband sensing, especially in the presence of phase distortion factors. In this paper, we investigate the fundamental limits of multiband sensing in terms of time delay. We derive a closed-form expression of the Cramér-Ran bound (CRB) for the delay separation to reveal useful insights. Additionally, a metric called the statistical resolution limit (SRL) is employed to investigate the fundamental limits of delay resolution. The fundamental limits of delay estimation error are also investigated based on the CRB and Ziv-Zakai bound (ZZB). Based on the above derived fundamental limits, numerical results are presented to provide key insights on the performance limits of the multiband sensing.

Multiband fusion enhances delay estimation by jointly utilizing signals from multiple noncontiguous frequency bands. However, in the multiband signal model, there are many local optimums in the associated likelihood function due to the existence of high-frequency component and phase distortion factors, posing challenges for high-accuracy parameter estimation. To address this, we propose a two-stage scheme equipped with different signal models derived from the original model, where the first-stage coarse estimation is performed using a weighted root MUSIC algorithm to narrow down the search range for the subsequent stage, and the second-stage refined estimation utilizes a Bayesian approach to avoid convergence to bad suboptimal solutions. Specifically, we apply the block stochastic successive convex approximation (SSCA) approach to derive a novel stochastic particle-based variational Bayesian inference (SPVBI) algorithm in the refined stage. Unlike conventional particle-based VBI (PVBI) that optimizes only particle probability and incurs exponential per-iteration complexity with particle count, our more flexible SPVBI algorithm optimizes both the position and probability of each particle. Additionally, it utilizes block SSCA to significantly improve sampling efficiency by averaging over iterations, making it suitable for high-dimensional problems. Extensive simulations demonstrate the superiority of our proposed algorithm over various baseline methods.

Multiband technology has recently received incremental attention for its ability to jointly utilize multiple noncontiguous frequency bands to achieve high-resolution delay estimation. In multiband scenarios, numerous signal processing algorithms for delay estimation have been proposed, while research on the fundamental limits remains under explored. In this article, we focus on the analysis of fundamental limits and the optimization of multiband delay estimation in orthogonal frequency division multiplexing (OFDM) systems. We derive a closed-form expression of the Cramer-Rao bound (CRB) for the delay separation to reveal useful insights. Additionally, a metric called statistical resolution limit (SRL) that provides a resolution performance bound is employed to research the fundamental limits of delay resolution. The fundamental limits of the delay estimation error are also investigated using the performance bounds CRB and Ziv-Zakai bound (ZZB). Based on these derived performance bounds, numerical results have been presented to analyse the effect of frequency band apertures and phase distortions on the fundamental limits of the multiband delay estimation error. Inspired by the analysis of fundamental limits, we formulate an optimization problem to find the optimal system configuration in multiband systems with the objective of minimizing the delay SRL. To solve this nonconvex constrained problem, we propose an efficient alternating optimization (AO)-based algorithm that iteratively optimizes the variables using the successive convex approximation (SCA) and 1-D search. Simulation results demonstrate the effectiveness of the proposed algorithm and give useful insights for the multiband system design.

Recently, channel extrapolation has been widely investigated in frequency-division duplex (FDD) massive multiple-input multiple-output (MIMO) systems. However, in time-division duplex (TDD) fifth generation (5G) new radio (NR) systems, the channel extrapolation problem also arises due to the hopping uplink pilot pattern, which has not been fully researched yet. This paper addresses this gap by formulating a channel extrapolation problem in TDD massive MIMO-OFDM systems for 5G NR, incorporating imperfection factors. A novel two-stage two-dimensional (2D) channel extrapolation scheme in frequency-time domain is proposed, designed to mitigate the effects of imperfection factors and ensure high-accuracy channel estimation. Specifically, in the channel estimation stage, we propose a novel multi-band multi-timeslot based high-resolution parameter estimation algorithm to achieve 2D channel extrapolation in the presence of imperfection factors. Then, to avoid repeated multi-timeslot channel estimation, a channel tracking stage is designed during the subsequent time instants, where a sparse Markov channel model is formulated to capture the dynamic sparsity of massive MIMO-OFDM channels under the influence of imperfection factors. Next, an expectation-maximization (EM) based compressive channel tracking algorithm is designed to estimate unknown imperfection and channel parameters by exploiting the high-resolution prior information of the delay/angle parameters from previous timeslots. Simulation results underscore the superior performance of our proposed channel extrapolation scheme over baselines.

Recently, massive multiple input multiple output (MIMO) channel tracking in the fifth generation (5G) new radio (NR) systems has attracted intensive interest. By exploiting the dynamic sparsity of massive MIMO channels, it is possible to design a high-accuracy channel tracking scheme. However, the existing channel estimation/tracking algorithms often ignore the practical imperfections in real systems, such as the channel aging effect due to the hopping Sounding Reference Signal (SRS) pattern, the time offset, phase noise, and multi-user SRS interference. In this paper, we propose a robust multi-user uplink channel tracking scheme, which is compatible with 5G NR systems and robust against various system imperfections. Specifically, we propose a sparse Markov channel model to capture the dynamic sparsity of massive MIMO-OFDM channels under the consideration of imperfect factors. Then, we propose a robust multi-user channel tracking scheme, which iterates between two components until convergence. Particularly, in thechannel estimation component, we employ the Turbo-CS method to exploit the channel dynamic sparsity to perform efficient multi-user channel estimation under non-orthogonal SRSs, where a multi-stage successive interference cancellation (MSIC) scheme is proposed to mitigate the multi-user SRS interference. Then, in theimperfection parameter estimation component, we further estimate the unknown imperfection parameters based on the updated Bayesian channel estimates from thechannel estimation component. Simulation results verify the superior channel tracking performance of our proposed scheme over the baselines.

In integrated sensing and communication (ISAC) systems, communication signals are exploited to achieve high-accuracy sensing. Multiband Wi-Fi sensing, which jointly utilizes Wi-Fi signals from multiple non-contiguous frequency bands to improve the sensing performance, has recently emerged as a promising technology for ISAC. However, the multi-dimensional non-convex likelihood function associated with the multiband WiFi sensing contains many local optimums due to the existence of high frequency components and phase distortion factors in the signal model, making it difficult to exploit the multiband gain for high-accuracy parameter estimation. To address this, we divide the target parameter estimation into two stages equipped with different signal models derived from the original model, where the first-stage coarse estimation is used to narrow down the search range for the next stage, and the second-stage refined estimation is based on the Bayesian approach to avoid the convergence to a bad local optimum of the likelihood function. Specifically, we apply the block stochastic successive convex approximation (SSCA) approach to derive a novel stochastic particle-based variational Bayesian inference (SPVBI) algorithm in the refined stage. Unlike the conventional particle-based VBI (PVBI) in which only particle probability is optimized and the per-iteration computational complexity increases exponentially with particle count, the proposed SPVBI optimizes both the position and probability of each particle, and it adopts the block SSCA to significantly improve the sampling efficiency by averaging over iterations. As such, the proposed SPVBI can achieve a better performance than the conventional PVBI with a much lower complexity. Finally, simulations verify the advantage of the proposed algorithm over various baseline algorithms.

The time of arrival (TOA)-based localization techniques, which need to estimate the delay of the line-of-sight (LoS) path, have been widely employed in location-aware networks. To achieve a high-accuracy delay estimation, a number of multiband-based algorithms have been proposed recently, which exploit the channel state information (CSI) measurements over multiple non-contiguous frequency bands. However, to the best of our knowledge, there still lacks an efficient scheme that fully exploits the multiband gains when the phase distortion factors caused by hardware imperfections are considered, due to that the associated multi-parameter estimation problem contains many local optimums and the existing algorithms can easily get stuck in a “bad” local optimum. To address these issues, we propose a novel two-stage global estimation (TSGE) scheme for multiband delay estimation. In the coarse stage, we exploit the group sparsity structure of the multiband channel and propose a Turbo Bayesian inference (Turbo-BI) algorithm to achieve a good initial delay estimation based on a coarse signal model, which is transformed from the original multiband signal model by absorbing the carrier frequency terms. The estimation problem derived from the coarse signal model contains fewer local optimums and thus a more stable estimation can be achieved than directly using the original signal model. Then in the refined stage, with the help of coarse estimation results to narrow down the search range, we perform a global delay estimation using a particle swarm optimization-least square (PSO-LS) algorithm based on a refined multiband signal model to exploit the multiband gains to further improve the estimation accuracy. Simulation results show that the proposed TSGE significantly outperforms the benchmarks with comparative computational complexity.

In location-aware networks, the time of arrival (TOA)-based localization techniques have been widely employed. To achieve high-accuracy delay estimation, a number of multiband-based algorithms have been proposed recently, which exploit the channel state information (CSI) measurements over multiple non-contiguous frequency bands. However, to our best knowledge, there still lacks an efficient scheme that fully exploits the multiband gains when phase distortion factors are considered, due to that the associated multi-parameter estimation problem contains many local optimums and the existing algorithms can easily get stuck in a “bad” local optimum. To address these issues, we propose a novel two-stage global estimation (TSGE) scheme for multiband delay estimation. In the coarse stage, we propose a weighted multiple signal classification (MUSIC) algorithm to achieve an initial delay estimation based on a coarse signal model. The estimation problem derived from the coarse signal model contains less local optimums and thus a more stable estimation can be achieved than directly using the original signal model. Then in the refined stage, with the help of coarse estimation results to narrow down the search range, we perform a global delay estimation using a particle swarm optimization (PSO) algorithm based on a refined multiband signal model to exploit the multiband gains to further improve the estimation accuracy. Simulation results show that the proposed TSGE significantly outperforms the benchmarks.

Intelligent reflecting surface (IRS) is an emerging technology that is able to reconfigure the wireless channel via tunable passive signal reflection and thereby enhance the spectral/energy efficiency of wireless networks cost-effectively. In this paper, we study an IRS-aided multiuser multiple-input single-output (MISO) wireless system and adopt the two-timescale (TTS) transmission to reduce the signal processing complexity and channel training overhead as compared to the existing schemes based on the instantaneous channel state information (I-CSI), and at the same time, exploit the multiuser channel diversity in transmission scheduling. Specifically, the long-term passive beamforming (i.e., IRS phase shifts) is designed based on the statistical CSI (S-CSI) of all links, while the short-term active beamforming (i.e., transmit precoding vectors at the access point (AP)) is designed to cater to the I-CSI of all users' reconfigured channels with optimized IRS phase shifts. We aim to minimize the average transmit power at the AP, subject to the users' individual quality of service (QoS) constraints on the achievable long-term average rate. The formulated stochastic optimization problem is non-convex and difficult to solve since the long-term and short-term design variables are complicatedly coupled in the QoS constraints. To tackle this problem, we propose an efficient algorithm, called the primal-dual decomposition based TTS joint active and passive beamforming (PDD-TJAPB), where the original problem is decomposed into a long-term passive beamforming problem and a family of short-term active beamforming problems, and the deep unfolding technique is employed to extract gradient information from the short-term problems to construct a convex surrogate problem for the long-term problem. We show that both the long-term and short-term problems can be efficiently solved and the proposed algorithm is proved to converge to a stationary solution of the original problem almost surely. Simulation results are presented which demonstrate the advantages and effectiveness of the proposed algorithm as compared to benchmark schemes.