arXiv subjects
Publications and source records attributed to Elsayed Ahmed.
We construct a 4-state 2-letter bireversible automaton generating the lamplighter group $(\mathbb Z_2^2)\wr\mathbb Z$ of rank two. The action of the generators on the boundary of the tree can be induced by the affine transformations on the ring $\mathbb Z_2[[t]]$ of formal power series over $\mathbb Z_2$.
We show that every polynomial in $\mathbb Z[x]$ defines an endomorphism of the $d$-ary rooted tree induced by its action on the ring $\mathbb Z_d$ of $d$-adic integers. The sections of this endomorphism also turn out to be induced by polynomials in $\mathbb Z[x]$ of the same degree. In the case of permutational polynomials acting on $\mathbb Z_d$ by bijections the induced endomorphisms are automorphisms of the tree. In the case of $\mathbb Z_2$ such polynomials were completely characterized by Rivest. As our main application we utilize the result of Rivest to derive the condition on the coefficients of a permutational polynomial $f(x)\in\mathbb Z[x]$ that is necessary and sufficient for $f$ to induce a level transitive automorphism of the binary tree, which is equivalent to the ergodicity of the action of $f(x)$ on $\mathbb Z_2$ with respect to the normalized Haar measure.
Full-duplex systems are expected to double the spectral efficiency compared to conventional half-duplex systems if the self-interference signal can be significantly mitigated. Digital cancellation is one of the lowest complexity self-interference cancellation techniques in full-duplex systems. However, its mitigation capability is very limited, mainly due to transmitter and receiver circuit's impairments. In this paper, we propose a novel digital self-interference cancellation technique for full-duplex systems. The proposed technique is shown to significantly mitigate the self-interference signal as well as the associated transmitter and receiver impairments. In the proposed technique, an auxiliary receiver chain is used to obtain a digital-domain copy of the transmitted Radio Frequency (RF) self-interference signal. The self-interference copy is then used in the digital-domain to cancel out both the self-interference signal and the associated impairments. Furthermore, to alleviate the receiver phase noise effect, a common oscillator is shared between the auxiliary and ordinary receiver chains. A thorough analytical and numerical analysis for the effect of the transmitter and receiver impairments on the cancellation capability of the proposed technique is presented. Finally, the overall performance is numerically investigated showing that using the proposed technique, the self-interference signal could be mitigated to ~3dB higher than the receiver noise floor, which results in up to 76% rate improvement compared to conventional half-duplex systems at 20dBm transmit power values.
Full-duplex systems are expected to achieve 100% rate improvement over half-duplex systems if the self-interference signal can be significantly mitigated. In this paper, we propose the first full-duplex system utilizing Multi-Reconfigurable Antenna (MRA) with ?90% rate improvement compared to half-duplex systems. MRA is a dynamically reconfigurable antenna structure, that is capable of changing its properties according to certain input configurations. A comprehensive experimental analysis is conducted to characterize the system performance in typical indoor environments. The experiments are performed using a fabricated MRA that has 4096 configurable radiation patterns. The achieved MRA-based passive self-interference suppression is investigated, with detailed analysis for the MRA training overhead. In addition, a heuristic-based approach is proposed to reduce the MRA training overhead. The results show that at 1% training overhead, a total of 95dB self-interference cancellation is achieved in typical indoor environments. The 95dB self-interference cancellation is experimentally shown to be sufficient for 90% full-duplex rate improvement compared to half-duplex systems.
Oscillator phase noise has been shown to be one of the main performance limiting factors in full-duplex systems. In this paper, we consider the problem of self-interference cancellation with phase noise suppression in full-duplex systems. The feasibility of performing phase noise suppression in full-duplex systems in terms of both complexity and achieved gain is analytically and experimentally investigated. First, the effect of phase noise on full-duplex systems and the possibility of performing phase noise suppression are studied. Two different phase noise suppression techniques with a detailed complexity analysis are then proposed. For each suppression technique, both free-running and phase locked loop based oscillators are considered. Due to the fact that full-duplex system performance highly depends on hardware impairments, experimental analysis is essential for reliable results. In this paper, the performance of the proposed techniques is experimentally investigated in a typical indoor environment. The experimental results are shown to confirm the results obtained from numerical simulations on two different experimental research platforms. At the end, the tradeoff between the required complexity and the gain achieved using phase noise suppression is discussed.
One of the main bottlenecks in practical full-duplex systems is the oscillator phase noise, which bounds the possible cancellable self-interference power. In this paper, a digitaldomain self-interference cancellation scheme for full-duplex orthogonal frequency division multiplexing systems is proposed. The proposed scheme increases the amount of cancellable selfinterference power by suppressing the effect of both transmitter and receiver oscillator phase noise. The proposed scheme consists of two main phases, an estimation phase and a cancellation phase. In the estimation phase, the minimum mean square error estimator is used to jointly estimate the transmitter and receiver phase noise associated with the incoming self-interference signal. In the cancellation phase, the estimated phase noise is used to suppress the intercarrier interference caused by the phase noise associated with the incoming self-interference signal. The performance of the proposed scheme is numerically investigated under different operating conditions. It is demonstrated that the proposed scheme could achieve up to 9dB more self-interference cancellation than the existing digital-domain cancellation schemes that ignore the intercarrier interference suppression.
In full-duplex systems, due to the strong self-interference signal, system nonlinearities become a significant limiting factor that bounds the possible cancellable self-interference power. In this paper, a self-interference cancellation scheme for full-duplex orthogonal frequency division multiplexing systems is proposed. The proposed scheme increases the amount of cancellable self-interference power by suppressing the distortion caused by the transmitter and receiver nonlinearities. An iterative technique is used to jointly estimate the self-interference channel and the nonlinearity coefficients required to suppress the distortion signal. The performance is numerically investigated showing that the proposed scheme achieves a performance that is less than 0.5dB off the performance of a linear full-duplex system.
In this paper, we analytically study the regime in which practical full-duplex systems can achieve larger rates than an equivalent half-duplex systems. The key challenge in practical full-duplex systems is uncancelled self-interference signal, which is caused by a combination of hardware and implementation imperfections. Thus, we first present a signal model which captures the effect of significant impairments such as oscillator phase noise, low-noise amplifier noise figure, mixer noise, and analog-to-digital converter quantization noise. Using the detailed signal model, we study the rate gain region, which is defined as the region of received signal-of-interest strength where full-duplex systems outperform half-duplex systems in terms of achievable rate. The rate gain region is derived as a piece-wise linear approximation in log-domain, and numerical results show that the approximation closely matches the exact region. Our analysis shows that when phase noise dominates mixer and quantization noise, full-duplex systems can use either active analog cancellation or base-band digital cancellation to achieve near-identical rate gain regions. Finally, as a design example, we numerically investigate the full-duplex system performance and rate gain region in typical indoor environments for practical wireless applications.
Complex systems (CS) are ubiquitous in nature. It is argued that fractional order (FO) calculus is more suitable to describe fractal systems. Motivated by the fractal space time theory some fractional generalizations of Scrodinger and Klein-Gordon equations are given. In many CS systems statistics is described by heavy tailed distributions e.g. fractal and Levy-Weibull ones. Here a generalized Weibull (GW) distribution is proposed to interpolate between them.