This paper presents the characterization of near-field propagation regions for phased array antennas, with a particular focus on the propagation boundaries defined by Fraunhofer and Fresnel distances. These distances, which serve as critical boundaries for understanding signal propagation behavior, have been extensively studied and characterized in the literature for single-element antennas. However, the direct application of these results to phased arrays, a common practice in the field, is argued to be invalid and non-exact. This work calls for a deeper understanding of near-field propagation to accurately characterize such boundaries around phased array antennas. More specifically, for a single-element antenna, the Fraunhofer distance is $d^{\mathrm{F}}=2D^2 \sin^2(\theta)/\lambda$ where $D$ represents the largest dimension of the antenna, $\lambda$ is the wavelength and $\theta$ denotes the observation angle. We show that for phased arrays, $d^{\mathrm{F}}$ experiences a fourfold increase (i.e., $d^{\mathrm{F}}=8D^2 \sin^2(\theta)/\lambda$) provided that $|\theta-\frac{\pi}{2}|>\theta^F$ (which holds for most practical scenarios), where $\theta^F$ is a small angle whose value depends on the number of array elements, and for the case $|\theta-\frac{\pi}{2}|\leq\theta^F$, we have $d^{\mathrm{F}}\in[2D^2/\lambda,8D^2\cos^2(\theta^F)/\lambda]$, where the precise value is obtained according to some square polynomial function $\widetilde{F}(\theta)$. Besides, we also prove that the Fresnel distance for phased array antennas is given by $d^{\mathrm{N}}=1.75 \sqrt{{D^3}/{\lambda}}$ which is $\sqrt{8}$ times greater than the corresponding distance for a conventional single-element antenna with the same dimension.
We consider the cross-layer utility maximization problem for wireless networks. It is well known that the optimal network control policy can be decomposed in three separate subproblems: 1) flow control at the network layer, 2) routing and scheduling at the network layer, and 3) resource allocation (RA) at the medium access control and physical layers. The main contribution of this paper is a power and rate control algorithm for the RA subproblem. In the case of single-hop networks, the proposed algorithm provides a locally optimal solution for the RA subproblem. Even though the global optimality of the solution cannot be guaranteed due to the nonconvexity of the problem, the numerical results show that the algorithm can provide significant gains at the network layer in terms of end-to-end rates and network congestion as compared to the optimal time division multiple access (TDMA) based RA. For solving the RA subproblem in the case of multi-hop networks, the proposed algorithm must be used in conjunction with an exhaustive search for the optimal set of transmitter nodes. However, the numerical results show that even with a random selection of the set of transmitter nodes, the proposed algorithm can provide significant improvement at the network layer in terms of end-to-end rates and network congestion as compared the optimal TDMA based RA.
Belief propagation (BP) is an iterative decoding algorithm for polar codes which can be parallelized effectively to achieve higher throughput. However, because of the presence of error floor due to cycles and stopping sets in the factor graph, the performance of the BP decoder is far from the performance of state of the art cyclic redundancy check (CRC) aided successive cancellation list (CA-SCL) decoders. It has been shown that successive BP decoding on multiple permuted factor graphs, which is called the multi-trellis BP decoder, can improve the error performance. However, when permuting the entire factor graph, since the decoder dismisses the information from the previous permutation, the number of iterations required is significantly larger than that of the standard BP decoder. In this work, we propose a new variant of the multi-trellis BP decoder which permutes only a subgraph of the original factor graph. This enables the decoder to retain information of variable nodes in the subgraphs, which are not permuted, reducing the required number of iterations needed in-between the permutations. As a result, the proposed decoder can perform permutations more frequently, hence being more effective in mitigating the effect of cycles which cause oscillation errors. Experimental results show that for a polar code with block length 1024 and rate 0.5 the error performance gain of the proposed decoder at the frame error rate of 10^(-6) is 0.25 dB compared to multi-trellis decoder based on full permutations. This performance gain is achieved along with reduced latency in terms of the number of iterations.
A new system model is introduced for spectrum sharing in a multi-operator environment. The infrastructure based cognitive radio network operates in underlay/overlay (hybrid) transmission mode sharing the spectrum of licensed users. Primary user networks (PUNs) are benefitted by the relaying capability of the cognitive radio base station so that their service degraded users due to low coverage, can enhance the performance. The cognitive radio network (CRN) also helps itself by transmitting its own data along with the primary data on the same band, while agreeing to maintain the signal to interference plus noise ratios of primary users' at a predetermined level. CRN operates in an underlay mode with an imposed interference threshold. In addition, maximizing the secondary user capacity by strategically changing the available frequencies from time slot to time slot is discussed with the introduction of two primary data relaying schemes (asynchronous / synchronous). The objective of the secondary user capacity maximization is reformulated into a linear programming problem with interference cancellation techniques. Power allocation for all the active users and the capacity of the secondary user is analyzed in both of the schemes.
The IEEE 802.11 contention-based distributed coordination function has been used in ad hoc networks, and so far, a comprehensive mathematical analysis of such multihop systems has not been reported in the literature due to complicating factors such as hidden terminals and the unreachability problem. In this paper, we propose a new analytical model based on the parallel space-time Markov chain for IEEE 802.11 medium access control (MAC) in multihop ad hoc networks. The proposed scheme is able to model the hidden-terminal and unreachability phenomena. Extensive evaluation is conducted to demonstrate the accuracy of the proposed framework.
The linear combination of Student's $t$ random variables (RVs) appears in many statistical applications. Unfortunately, the Student's $t$ distribution is not closed under convolution, thus, deriving an exact and general distribution for the linear combination of $K$ Student's $t$ RVs is infeasible, which motivates a fitting/approximation approach. Here, we focus on the scenario where the only constraint is that the number of degrees of freedom of each $t-$RV is greater than two. Notice that since the odd moments/cumulants of the Student's $t$ distribution are zero, and the even moments/cumulants do not exist when their order is greater than the number of degrees of freedom, it becomes impossible to use conventional approaches based on moments/cumulants of order one or higher than two. To circumvent this issue, herein we propose fitting such a distribution to that of a scaled Student's $t$ RV by exploiting the second moment together with either the first absolute moment or the characteristic function (CF). For the fitting based on the absolute moment, we depart from the case of the linear combination of $K= 2$ Student's $t$ RVs and then generalize to $K\ge 2$ through a simple iterative procedure. Meanwhile, the CF-based fitting is direct, but its accuracy (measured in terms of the Bhattacharyya distance metric) depends on the CF parameter configuration, for which we propose a simple but accurate approach. We numerically show that the CF-based fitting usually outperforms the absolute moment -based fitting and that both the scale and number of degrees of freedom of the fitting distribution increase almost linearly with $K$.
Antenna correlation is usually viewed as a detrimental effect in a multiple input multiple output (MIMO) system. This paper investigates how this affects the performance of an amplify-and-forward (AF) relay network. We consider multiple antennas at all nodes with a general correlation matrix structure having an arbitrary eigenvalue distribution. We derive exact closed form expression for the ergodic capacity and simplify to special case of distinct eigenvalues. Further, we investigate the system in high signal-to-noise ratio (SNR) and derive a simple asymptotic expression. Our results provide a comprehensive analysis and useful insight about the ergodic capacity of the system.
