This paper provides a thorough mathematical analysis of continuous movable antenna (MA) arrays. Focusing on the multiple antenna case, we consider a linear antenna array with multiple fixed antenna elements that moves along a line. We assume a full, spatially coherent correlation model and continuous positioning of the array. We provide asymptotically exact approximations to the upper tail of the cumulative distribution function (cdf) of the signal-to-noise ratio (SNR), considering both correlated and uncorrelated antenna elements in the array. We also obtain a novel closed-form expression for the level crossing rate (LCR) of the SNR under correlated array elements, where a non-separable two-dimensional correlation is present. The analysis is validated through simulations, confirming both the accuracy of the LCR expressions and the tightness of the cdf bounds in the upper tail. Numerical results show that the proposed MA array outperforms single fluid antenna and fixed array systems, with reduced inter-element spacing providing further performance gains.

Reconfigurable intelligent surfaces (RISs) offer a novel paradigm for wireless communication by effectively manipulating the propagation environment. This paper proposes a layered design for a multi-RIS-assisted system, where a structured principle establishes line-of-sight (LOS) links between successive RISs, enabling cascaded signal reflections. The channels between the base station and RIS, as well as between RIS and user equipment, are modeled as correlated fading, while inter- RIS links are pure LOS. To evaluate system performance, the probability density function (PDF) and cumulative distribution function (CDF) of the signal-to-noise ratio (SNR) are derived. In particular, exact expressions are obtained for Rayleigh fading under the fully correlated case. For general and uncorrelated scenarios (including both Rician and Rayleigh fading), the sums of the channel amplitudes are approximated as Gammadistributed random variables, which enables tractable analysis of the cascaded channel product. To address numerical instability in direct PDF evaluation, a stable numerical formulation is also developed. Extensive simulations validate the theoretical models and show the impact of spatial correlation under different fading conditions. Furthermore, the impact of imperfect channel state information is investigated. Results show that angular mismatch leads to a rate loss that increases with the number of RIS elements due to beam narrowing, whereas CSI uncertainty introduces a nearly constant loss determined by its variance.Increasing the number of cascaded RIS hops introduces additional path loss, but remains important for bypassing severe blockages.

This paper develops a physically-consistent channel model for analyzing super wideband (SW) multiple-input-multiple-output (MIMO) communication systems that experience strong mutual coupling (MC). Starting from circuit theory, we derive a generalized MIMO model incorporating MC and physical noise sources, allowing a direct mapping to standard communication models. We develop a correlated Rician channel model with frequency-dependent spatial correlation, frequency correlation, and Rician K-factor, specifically tailored for SW MIMO systems. The performance of single and multiuser SW MIMO systems is analyzed using the developed channel model. Specifically, beamforming performance is evaluated under various receiver architectures, highlighting the impact of distorted steering vectors in beamforming due to high MC. Our studies show that strong MC inherently reduces the effective spatial correlations in SW MIMO arrays, assisting faster channel hardening and enhancing favorable propagation. We also investigate uplink multi-user systems through both orthogonal scheduling and linear combining techniques for these SW MIMO systems.

This paper considers a frequency- and phase-keying (FPK) waveform for integrated sensing and communications (ISAC). Compared to FSK-based ISAC waveforms in the literature, the proposed waveform shows superior performance both in terms of data rates and radar global accuracy, while maintaining a constant modulus that is attractive in both communications and sensing. Also, while the proposed waveform has lower data rates than the state-of-the-art OFDM waveform, it shows similar radar performance while achieving low and constant PAPR. The ambiguity function (AF) is used as a tool to evaluate the radar performance of the FPK waveform. We show that incorporating phase modulation into the FSK waveform to produce the FPK waveform generally reduces the values of sidelobe levels (SLs) in the AF. To achieve this, we first derive an expression for the AF SLs of the FPK waveform. Since the AF SLs vary depending on the data embedded into the waveform, we analyze the distribution of the AF SLs. Furthermore, we provide two approximations of the distribution of the AF SL based on a random walk model and a Rayleigh model. While the Rayleigh approximation is easier to compute, numerical results show that the random walk approximation is more accurate, especially for waveforms with fewer subpulses and higher FSK modulation orders. Numerical examples illustrate the accuracy of our approximations and show the performance improvements of the FPK waveform compared to traditional FSK waveforms.

Phase selection design for reconfigurable intelligent surfaces (RISs) is a significant research challenge, as a closed-form optimal solution for a multi-user (MU) system is believed to be intractable. While existing methods achieve strong near-optimal performance, they typically entail high computational complexity. In this work, we take a different approach and propose a practical method that achieves competitive performance while substantially reducing computational complexity. To do so, we consider a RIS divided into subsurfaces. Each subsurface is designed specifically for one user, who is served on their own frequency band. The other subsurfaces (those not designed for this user) provide additional uncontrolled scattering. We derive the exact closed-form expression for the mean signal-to-noise ratio (SNR) for the proposed subsurface design (SD) when all channels experience correlated Ricean fading. We simplify this to find the mean SNR for line-of-sight (LoS) channels and channels experiencing correlated Rayleigh fading. An iterative SD (ISD) process is proposed, where subsurfaces are designed sequentially, and the phases that are already set are used to enhance the design of the remaining subsurfaces. This is extended to a converged ISD (CISD), where the ISD process is repeated multiple times until the SNR increases by less than a specified tolerance. The ISD and CISD both provide a performance improvement over the SD, which increases as the number of RIS elements increases. The SD is significantly simpler than the lowest complexity MU method we know of, and despite each user having less bandwidth, the SD outperforms the existing method in some key scenarios. The SD is more robust to strongly LoS channels and clustered users, as it does not rely on spatial multiplexing like other MU methods. Combined with the complexity reduction, this makes the SD an attractive phase selection method.

A key challenge facing reconfigurable intelligent surfaces (RISs) is channel state information acquisition. Passive RISs cannot generate pilot signals or process data, making rapid temporal changes in the channel problematic. Additionally, the impact of spatial changes in RIS channels has not been thoroughly investigated. Therefore, in this work, we use second order statistics to investigate the spatio-temporal behaviour of a single-user (SU) RIS system. Assuming a line-of-sight (LoS) RIS to base station (BS) link, we derive an exact expression for the level crossing rate (LCR) of the RIS link (user equipment (UE)-RIS-BS path) and propose a numerically stable approximation for the LCR of the global UE-BS channel. Each LCR expression attained is then utilised to find the corresponding average fade duration (AFD). The temporal signal-to-noise ratio (SNR) correlation is also derived assuming an LoS RIS-BS link. Assuming a Ricean RIS-BS link, expressions for the spatial correlation matrix of the global channel and the mean SNR loss due to channel ageing are derived. All of the analyses are verified by simulation, and the impact of key system parameters is investigated. We show that the use of an RIS does not significantly amplify changes in the channel.

Motivated by the constant modulus property of frequency shift keying (FSK) based waveforms and the stabilisation of its radar performance with an increase in the number of subpulses, in this paper an FSK-based dynamic subpulse number joint communications and radar waveform design is proposed. From a communications point of view, the system operates based on traditional FSK modulation. From a sensing point of view, although the subpulses are continuously generated and transmitted, radar waveforms are dynamically formed by monitoring the flatness of the spectrum which in turn guarantees the accuracy of the delay estimation. Other constraints on the waveform length are used to ensure satisfactory values of the root mean square time duration, ambiguity function sidelobe levels and prevent overly long waveforms. To provide an estimation of the probability of generating extremely long waveforms, the distribution of the number of subpulses is approximated using a Brownian motion process and an existing result on its one-sided exit density. Numerical examples are provided to evaluate the accuracy of the approximate distribution, as well as the ambiguity function sidelobe levels and the delay and Doppler shift estimation performance of the transmitted waveforms.

Integrated sensing and communications (ISAC) is considered a key enabler to support application scenarios such as the Internet-of-Things (IoT) in which both communications and sensing play significant roles. Multi-carrier waveforms, such as orthogonal frequency division multiplexing (OFDM), have been considered as good candidates for ISAC due to their high communications data rate and good time bandwidth property for sensing. Nevertheless, their high peak-to-average-power-ratio (PAPR) values lead to either performance degradation or an increase in system complexity. This can make OFDM unsuitable for IoT applications with insufficient resources in terms of power, system complexity, hardware size or cost. This article provides IoT-centric constant modulus signalling scheme designs that leverage the advantage of unit PAPR and thus are more suitable in resource-limited scenarios. More specifically, several single-carrier frequency and/or phase signalling schemes are considered. A comprehensive discussion on their radar sensing and communications performance is conducted based on performance metrics including the radar ambiguity function, the bandwidth property, the data rate, and the communications receiver complexity. Results demonstrate that under the constraint of unit PAPR, the sensing-communications tardeoff can be achieved by selecting among the discussed signalling schemes. Recommendations for linking particular low-rate IoT scenarios with those signalling schemes are also provided based on the their performance.

Continuous aperture arrays (CAPAs) provide a theoretical upper bound on the performance of densely packed antenna arrays, but their analysis is limited by the lack of closed-form signal-to-noise ratio (SNR) distributions under realistic fading conditions. This paper derives accurate analytical expressions for the matched-filter SNR distribution of one-dimensional CAPAs in correlated Rayleigh environments under both the sinc and Jakes correlation models using the Karhunen-Loeve expansion. By applying a truncated hypoexponential model, we obtain accurate approximations for the probability density function and cumulative distribution function of the SNR that closely match simulations, including the outage probability region where precise characterization is critical. Compared to a standard gamma approximation, our approach provides significantly improved accuracy in this regime. Additionally, the CAPA system considered is shown to outperform discrete antenna arrays. The derived expressions enable tractable and accurate evaluation of CAPAs under practical channel models.

This paper considers a hybrid frequency- and phase-shift keying (FPK) waveform for integrated sensing and communications (ISAC). Compared to FSK-based ISAC waveforms in the literature, the proposed waveform shows similar local radar estimation accuracy and superior performance both in terms of data rates and radar global accuracy. The ambiguity function (AF) is used as a tool to evaluate the radar performance of the FPK waveform. We show that incorporating phase modulation into the FSK waveform generally has an insignificant effect on the sharpness of the AF main lobe while reducing the values of the peak sidelobe levels (SLs) in the AF. We also derive the Cramer-Rao lower bounds of the delay and Doppler shift estimates for the FPK waveform. Additionally, since the AF SLs vary depending on the data embedded in the waveform, we analyze and provide approximations for the distribution of the AF SLs. Finally, we analyze the error performance of both the optimal and suboptimal communication receivers, and derive the nearest-neighbors approximation for the symbol error probability using the optimal receiver. Numerical examples illustrate the accuracy of our approximations and show the performance improvements of the FPK waveform compared to FSK.

This paper analyses frequency shift keying (FSK)-based waveforms for joint communications and radar (JCR) in terms of radar estimation local accuracy. More specifically, the Cramer-Rao lower bounds for delay and Doppler shift estimation are characterised using the root mean square (RMS) time duration and RMS bandwidth of the waveform. We show that the Doppler shift estimation performance of the proposed waveform is invariant to the frequency sequence, under the analysis-friendly assumption that the width of the pulse shaping function does not exceed the pulse repetition interval. Under a similar assumption in the frequency domain, we derive an accurate approximation of the RMS bandwidth and its distribution, which allows the delay estimation accuracy to be quantified. The frequency permutation-based waveform is highlighted as a special case. Importantly, we show that FSK achieves an acceptable delay local accuracy by deriving the probability that its RMS bandwidth is greater than a given fraction of the permutation-based value. Finally, the observations are generalised by relaxing the previous assumptions. Numerical results illustrate the accuracy of the derived approximations and the performance of the proposed scheme. Comparisons between FSK and benchmarks indicate that it is a suitable candidate for resource-limited JCR scenarios.

Continuous fluid antenna systems (CFASs) represent an upper bound on the spatial diversity performance of fluid antenna systems (FASs), achieved when antennas may be positioned anywhere within a defined spatial region. This article examines the fundamental relationships governing CFAS performance. The focus is on the probability that the signal-to-noise ratio (SNR) exceeds a prescribed high threshold, termed the high SNR probability (HSP). This is among the few FAS performance metrics that admit the derivation of closed-form expressions. Following a survey of recent analytical advances in FAS performance limits, a dimensional scaling law derived for the HSP of a single-user, single-antenna CFAS is examined. This law is then applied to the per-user high signal-to-interference-plus-noise ratio (SINR) probability of a two-antenna, two-user CFAS employing minimum mean-squared error (MMSE) combining. For both scenarios, performance gains are shown to increase consistently with both dimensionality and region size. Remarkably, the scaling law remains accurate in the two-user case, showing that, in both scenarios, the influence of additional dimensions is dominated by the CFAS size and considered threshold. Moreover, the per-user high SINR probability of the two-user system exceeds the single-user HSP, despite the addition of inter-user interference.

This paper focuses on the port selection problem of a discrete fluid antenna system (FAS). We consider the uplink of a multi-user setup where an FAS is employed at the receiver. The objective is to maximize the overall sum rate based on a linear minimum mean squared error (LMMSE) combiner. Identifying the complexity of optimal selection, we propose a maximum distance-based sub-optimal low-complexity port selection algorithm, where ports are selected such that the minimum Euclidean distance between selected ports is maximized. We also propose two other sub-optimal algorithms, namely sequential selection, where ports are selected sequentially, and orthogonal selection, where ports that maximize the orthogonal user power are selected. Comparing with several benchmark methods, we demonstrate that the proposed sub-optimal low-complexity algorithms effectively reduce computational cost while maintaining performance close to optimal selection. In particular, simulation results demonstrate that the proposed maximum distance-based method enables a flexible performance–complexity trade-off through appropriate selection of its design parameter.

In this paper, we consider the connectivity of a random network of N mobile devices in three dimensions (3D), where the location of each device or node has a Gaussian distribution in each dimension. For each pair of nodes, the probability of connectivity is related to the nodes' separation by a Gaussian connectivity function. The fundamental analytical tool for studying such systems is the probability of a given network state, derived and expressed in terms of its graph Laplacian. Leveraging this result, we obtain results for the connectivity of small networks, the probability of a complete network (where all nodes are connected to all other nodes), and the probability of an isolated node, which gives an approximation to the connectivity probability of larger networks. The general results are then simplified for special cases and limiting scenarios.

When precast pavement slabs were first introduced for rapidly replacing and repairing concrete pavement in the early 2000’s, it was commonly believed by roadway engineers and precasters that flat, single-plane slabs could be used in most roadway locations. It has now become apparent that, while flat single-plane panels works in locations where the original roadway is straight and even slightly curved, contoured roadways require similarly-contoured (warped) precast replacement panels. This paper focuses on how highway geometrical features, such as horizontal and vertical curves, super-elevation transitions, vertical and horizontal departures of existing pavement from as-built locations and vertical and horizontal geometry of intersecting roadways, may significantly affect the geometric design, fabrication and installation of mildly-reinforced and precast prestressed pavement slabs. Particular reference will be made to the importance of including parameters for designing and installing nonplanar precast pavements in contract plans and specifications.

We consider a single-user (SU) continuous fluid antenna system (CFAS) employing matched filtering (MF) operating over a Ricean fading channel. Focusing on the upper tail of the received signal-to-noise ratio (SNR) distribution (the high SNR probability (HSP)), we derive accurate approximations for the HSP in 1, 2, and 3 dimensions using the expected Euler characteristic (EEC), presenting the first analytical results for a CFAS in a Ricean environment. In the process, we provide the first closed-form expression for the Euler characteristic density of a non-central chi-squared random field. We then examine the impact of the Ricean K-factor on the CFAS performance, emphasizing the critical role of channel variations in achieving a strong HSP.

Antenna arrays with discrete antenna elements have been conventionally used in multiple-input multiple-output (MIMO) communications. Improved spectral efficiency resulting from more antenna elements has motivated the idea of packing very large numbers of elements in an array, yielding continuous-like antennas. This letter conducts a performance analysis of continuous antennas, employing matched filtering. We derive a gamma approximation for the instantaneous received signal-to-noise ratio (SNR) under a Rician channel with a spatially-correlated non-line-of-sight (NLoS) component. We also derive the mean and an upper bound for achievable rate. Numerical results demonstrate the accuracy of our approximations across a range of parameters.

Beyond-5G wireless systems increasingly rely on distributed massive multiple-input multiple-output (MIMO) architectures to achieve high spectral efficiency, low latency, and wide coverage. A key challenge in such networks is that cooperating base stations (BSs) often possess different levels of channel state information (CSI) due to fronthaul constraints, user mobility, or hardware limitation. In this paper, we propose two novel detectors that enable cooperation between BSs with differing CSI availability. In this setup, some BSs have access to instantaneous CSI, while others only have long-term channel information. The proposed detectors—termed the coherent/non-coherent (CNC) detector and the differential CNC detector—integrate coherent and non-coherent approaches to signal detection. This framework allows BSs with only long-term information to actively contribute to the detection process, while leveraging instantaneous CSI where available. This approach enables the system to integrate the advantages of non-coherent detection with the precision of coherent processing, improving overall performance without requiring full CSI at all cooperating BSs. We formulate the detectors based on the maximum likelihood (ML) criterion and derive analytical expressions for their pairwise block error probabilities under Rayleigh fading channels. Leveraging the pairwise block error probability expression for the CNC detector, we derive a tight upper bound on the average block error probability. Numerical results show that the CNC and differential CNC detectors outperform their respective single-BS baseline-coherent ML and non-coherent differential detection. Moreover, both detectors demonstrate strong resilience to mid-to-high range correlation at the BS antennas.

Recent developments in Multiple-Input-Multiple-Output (MIMO) technology include packing a large number of antenna elements in a compact array to access the bandwidth benefits provided by higher mutual coupling (MC). The resulting super-wideband (SW) systems require a circuit-theoretic framework to handle the MC and channel models which span extremely large bands. Hence, in this paper, we make two key contributions. First, we develop a physically-consistent Rician channel model for use with SW systems. Secondly, we express the circuit-theoretic models in terms of a standard MIMO model, so that insights into the effects of antenna layouts, MC, and bandwidth can be made using standard communication theory. For example, we show the bandwidth widening resulting from the new channel model. In addition, we show that MC distorts line-of-sight paths which has beamforming implications. We also highlight the interaction between spatial correlation and MC and show that tight coupling reduces spatial correlations at low frequencies.