This paper models the line-of-sight (LOS) channel between two continuous circular antennas (CCAs) as a bounded linear normal operator whose kernel is defined by a deployment parameter: the product of the antenna radii divided by the product of the wavelength and transmission distance. Eigendecomposition reveals that orbital angular momentum (OAM) serves as the eigenmodes, with eigenvalues given by Bessel functions of the first kind, evaluated at the deployment parameter. By linking discrete circular arrays to CCAs through spatial sampling, we derive analytical expressions for the singular values of the LOS multiple-input multiple-output (MIMO) channel. The analysis considers two configurations: one where receive antennas form a single uniform circular array (UCA) with a rotational angular offset, and one with multiple sub-UCAs having different angular offsets, in both cases with the number of receive antennas being an integer multiple of the transmit antennas. For each setup, discrete Fourier transform (DFT)-based transceiver structures are proposed to achieve channel capacity. Numerical evaluations reveal: (i) The number of effective spatial degrees of freedom generally increases with the deployment parameter, but not monotonically (for fixed angular offsets); (ii) Channel capacity does not necessarily increase with the deployment parameter when the number of antennas is fixed; (iii) Angular offset significantly impacts performance when the number of antennas is small relative to the parameter; (iv) With a large number of antennas, the singular values of both configurations approach the CCA singular values, and the impact of angular offsets diminishes; (v) The non-uniform configuration studied in this paper yield small or no gains compared to the uniform configuration when angular offsets are optimized.

The Shannon capacity for the line-of-sight (LOS) multiple-input multiple-output (MIMO) channel between two perfectly aligned uniform circular arrays (UCAs) is derived from first principles in a tutorial fashion. It is well known that harmonically related complex exponentials (also known in the literature as orbital angular momentum (OAM) modes) are eigenmodes for the spatially continuous channel. We show that the corresponding eigenvalues can be expressed as Bessel functions of the first kind. We also show that the spatially discrete channel between two UCAs with the same finite number of Hertzian dipole antennas on both sides has eigenmodes that are spatially sampled continuous OAM modes, and discrete eigenvalues that are aliased versions of the continuous eigenvalues. Through numerical solution of Maxwell's equations, we verify that the discrete eigenvalues for UCAs with realistic dipole antennas are the same as with the Hertzian dipoles for the studied geometries (1 km hop distance, UCA radius 1 and 2 m, carrier frequency 70 GHz) as long as antenna spacing is not very dense.

We present an upper bound on the error probability achievable using variable-length stop feedback (VLSF) codes, for a fixed size of the information payload and a given constraint on the maximum latency and the average service time. Differently from the bound proposed in Polyanskiy et al. (2011), which pertains to the scenario in which the stop signal is sent over a noiseless feedback channel, our bound applies to the practically relevant setup in which the feedback link is noisy. Numerical evaluation of our bound suggests that, for fixed latency and reliability constraints, noise in the feedback link may increase the minimum average service time for the VLSF scheme considered in this paper, to the extent that fixed-length codes without feedback may be preferable in some scenarios.

We investigate the probability that the peak age of information in a point-to-point communication system operating over a multiantenna wireless fading channel exceeds a predetermined value. The packets are scheduled according to a last-come first-serve policy with preemption in service, and are transmitted over the channel using a simple automatic repetition request protocol. We consider quadrature phase shift keying modulation, pilot-assisted transmission, maximum-likelihood channel estimation, and mismatched scaled nearest-neighbor decoding. Our analysis, which exploits nonasymptotic tools in information theory, allows one to determine, for a given information packet size, the physical layer parameters such as the SNR, the number of transmit and receive antennas, the amount of frequency diversity to exploit, and the number of pilot symbols, to ensure that the system operates below a target peak-age violation probability.

We present an upper bound on the error probability achievable using variable-length stop-feedback codes, for a fixed size of the information payload and a given constraint on both the average and the maximum latency. Differently from the bound proposed in Polyanskiy et at. (2011), which pertains to the scenario in which the stop signal is sent over a noiseless feedback channel, our bound applies to the practically relevant scenario in which the feedback link is noisy. Through numerical results, we illustrate that, in scenarios in which the desired average latency is small, noise in the feedback link can deteriorate the performance of variable-length stop-feedback codes to the extent that it becomes inferior to that of fixed-length codes without feedback.

This work investigates the probability that the delay and the peak-age of information exceed a desired threshold in a point-to-point communication system with short information packets. The packets are generated according to a stationary memoryless Bernoulli process, placed in a single-server queue and then transmitted over a wireless channel. A variable-length stop-feedback coding scheme---a general strategy that encompasses simple automatic repetition request (ARQ) and more sophisticated hybrid ARQ techniques as special cases---is used by the transmitter to convey the information packets to the receiver. By leveraging finite-blocklength results, the delay violation and the peak-age violation probabilities are characterized without resorting to approximations based on large-deviation theory as in previous literature. Numerical results illuminate the dependence of delay and peak-age violation probability on system parameters such as the frame size and the undetected error probability, and on the chosen packet-management policy. The guidelines provided by our analysis are particularly useful for the design of low-latency ultra-reliable communication systems.

This paper investigates the distribution of delay and peak age of information in a communication system where packets, generated according to an independent and identically distributed Bernoulli process, are placed in a single-server queue with first-come first-served discipline and transmitted over an additive white Gaussian noise (AWGN) channel. When a packet is correctly decoded, the sender receives an instantaneous error-free positive acknowledgment, upon which it removes the packet from the buffer. In the case of negative acknowledgment, the packet is retransmitted. By leveraging finite-blocklength results for the AWGN channel, we characterize the delay violation and the peak-age violation probability without resorting to approximations based on large deviation theory as in previous literature. Our analysis reveals that there exists an optimum blocklength that minimizes the delay violation and the peak-age violation probabilities. We also show that one can find two blocklength values that result in very similar average delay but significantly different delay violation probabilities. This highlights the importance of focusing on violation probabilities rather than on averages.

We study short-packet communications, subject to latency and reliability constraints, under the premises of limited frequency diversity and no time diversity. The question addressed is whether, and when, hybrid automatic repeat request (HARQ) outperforms fixed-blocklength schemes with no feedback (FBL-NF) in such a setting. We derive an achievability bound for HARQ, under the assumption of a limited number of transmissions. The bound relies on pilot-assisted transmission to estimate the fading channel and scaled nearest-neighbor decoding at the receiver. We compare our achievability bound for HARQ to state-of-the-art achievability bounds for FBL-NF communications and show that for a given latency, reliability, number of information bits, and number of diversity branches, HARQ may significantly outperform FBL-NF. For example, for an average latency of 1 ms, a target error probability of 10 -3 , 30 information bits, and 3 diversity branches, the gain in energy per bit is about 4 dB.

We present nonasymptotic achievability and converse bounds on the maximum coding rate (for a fixed average error probability and a fixed average blocklength) of variable-length full-feedback (VLF) and variable-length stop-feedback (VLSF) codes operating over a binary erasure channel (BEC). For the VLF setup, the achievability bound relies on a scheme that maps each message onto a variable-length Huffman codeword and then repeats each bit of the codeword until it is received correctly. The converse bound is inspired by the meta-converse framework by Polyanskiy, Poor, and Verdú (2010) and relies on binary sequential hypothesis testing. For the case of zero error probability, our achievability and converse bounds match. For the VLSF case, we provide achievability bounds that exploit the following feature of BEC: the decoder can assess the correctness of its estimate by verifying whether the chosen codeword is the only one that is compatible with the erasure pattern. One of these bounds is obtained by analyzing the performance of a variable-length extension of random linear fountain codes. The gap between the VLSF achievability and the VLF converse bound, when number of messages is small, is significant: 23% for 8 messages on a BEC with erasure probability 0.5. The absence of a tight VLSF converse bound does not allow us to assess whether this gap is fundamental.

A centralized coordinated multipoint downlink joint transmission in a frequency division duplex system requires channel state information (CSI) to be fed back from the cell-edge users to their serving BS, and aggregated at the central coordination node for precoding, so that interference can be mitigated. The control signals comprising of CSI and the precoding weights can easily overwhelm the backhaul resources. Relative thresholding has been proposed to alleviate the burden; however, this is at the cost of reduction in throughput. In this paper, we propose utilizing the long term channel statistics comprising of pathloss and shadow fading in the precoder design to model the statistical interference for the unknown CSI. In this regard, a successive second order cone programming (SSOCP) based precoder for maximizing the weighted sum rate is proposed. The accuracy of the solution obtained is bounded with the branch and bound technique. An alternative optimization framework via weighted mean square error minimization is also derived. Both these approaches provide an efficient solution close to the optimal, and also achieve efficient backhauling, in a sense that the precoding weights are generated only for the active links. For comparison, a stochastic approach based on particle swarm optimization is also considered.

We provide nonasymptotic upper and lower bounds on the sum-rate capacity of Rayleigh block-fading multiple-access channels for the set up where a priori channel state information is not available. The upper bound relies on a dual formula for channel capacity and on the assumption that the users can cooperate perfectly. The lower bound is derived assuming a noncooperative scenario where each user employs unitary space-time modulation (independently from the other users). Numerical results show that the gap between the upper and the lower bound is small already at moderate SNR values. This suggests that the sum-rate capacity gains obtainable through user cooperation are minimal for the scenarios considered in the paper.

We present bounds and a closed-form high-SNR expression for the capacity of multiple-antenna systems affected by Wiener phase noise. Our results are developed for the scenario where a single oscillator drives all the radio-frequency circuitries at each transceiver (common oscillator setup), the input signal is subject to a peak-power constraint, and the channel matrix is deterministic. This scenario is relevant for line-of-sight multiple-antenna microwave backhaul links with sufficiently small antenna spacing at the transceivers. For the 2×2 multiple-antenna case, for a Wiener phase-noise process with standard deviation equal to 6°, and at the medium/high SNR values at which microwave backhaul links operate, the upper bound reported in the paper exhibits a 3dB gap from a lower bound obtained using 64-QAM. Furthermore, in this SNR regime the closed-form high-SNR expression is shown to be accurate.

We present a finite-blocklength analysis of the throughput and the average delay achievable in a wireless system where i) several uncoordinated users transmit short coded packets, ii) interference is treated as noise, and iii) 1-bit feedback from the intended receivers enables the use of a simple automatic repeat request (ARQ) protocol. Our analysis exploits the recent results on the characterization of the maximum coding rate at finite blocklength and finite block-error probability by Polyanskiy, Poor, and Verdú (2010), and by Yang et al. (2013). For a given number of information bits, we determine the coded-packet size that maximize the per-user throughput and minimize the average delay. Our numerical results indicate that, when optimal codes are used, very short coded packets (of length between 50 to 100 channel uses) yield significantly lower average delay at an almost negligible throughput loss, compared to longer coded packets.