Amplify-and-Forward in Wireless Relay Networks

A general class of wireless relay networks with a single source-destination pair is considered. Intermediate nodes in the network employ an amplify-and-forward scheme to relay their input signals. In this case the overall input-output channel from the source via the relays to the destination effectively behaves as an intersymbol interference channel with colored noise. Unlike previous work we formulate the problem of the maximum achievable rate in this setting as an optimization problem with no assumption on the network size, topology, and received signal-to-noise ratio. Previous work considered only scenarios wherein relays use all their power to amplify their received signals. We demonstrate that this may not always maximize the maximal achievable rate in amplify-and-forward relay networks. The proposed formulation allows us to not only recover known results on the performance of the amplify-and-forward schemes for some simple relay networks but also characterize the performance of more complex amplify-and-forward relay networks which cannot be addressed in a straightforward manner using existing approaches. Using cut-set arguments, we derive simple upper bounds on the capacity of general wireless relay networks. Through various examples, we show that a large class of amplify-and-forward relay networks can achieve rates within a constant factor of these upper bounds asymptotically in network parameters.Comment: Minor revision: fixed a typo in eqn. reference, changed the formatting. 30 pages, 8 figure

Influence of bandwidth restriction on the signal-to-noise performance of a modulated PCM/NRZ signal, part 2

Analyzing effects of bandlimiting on performance of digital transmission corrupted by additive white Gaussian noise by averaging and series expansio

A Coordinate System for Gaussian Networks

This paper studies network information theory problems where the external noise is Gaussian distributed. In particular, the Gaussian broadcast channel with coherent fading and the Gaussian interference channel are investigated. It is shown that in these problems, non-Gaussian code ensembles can achieve higher rates than the Gaussian ones. It is also shown that the strong Shamai-Laroia conjecture on the Gaussian ISI channel does not hold. In order to analyze non-Gaussian code ensembles over Gaussian networks, a geometrical tool using the Hermite polynomials is proposed. This tool provides a coordinate system to analyze a class of non-Gaussian input distributions that are invariant over Gaussian networks

Kalman filter equalization for QPSK communications

The discrete complex Kalman filter is considered as an equalizer for quadrature phase shift keyed (QPSK) systems in the presence of additive noise and intersymbol interference (ISI). For a known linear time-invariant channel with finite duration impulse response, the finite n-dimension complex Kalman filter equalizer is able to reduce the degradation caused by ISI. When the channel is unknown, an adaptive Kalman equalizer is used in which the channel complex tap gains are estimated by decision feedback. A two component multipath channel QPSK system is used as an example. Using the Chernoff upper bound to calculate the error probabilities, the computer simulation shows that both the Kalman filter equalizer and adaptive equalizer have a better performance than the integrate-and-dump correlator with no equalizer --Abstract, page ii

Frequency-Domain Modeling of OFDM Transmission with Insufficient Cyclic Prefix using Toeplitz Matrices

A novel mathematical framework is proposed to model Intersymbol Interference (ISI) phenomenon in wireless communication systems based on Orthogonal Frequency Division Multiplexing (OFDM) with or without cyclic prefix. The framework is based on a new formula to calculate the Fast Fourier Transform (FFT) of a triangular Toeplitz matrix, which is derived and proven in this paper. It is shown that distortion inducted by the ISI from a given subcarrier is the most significant for the closest subcarriers and the contribution decays as the distance between subcarriers grows. According to numerical experiments, knowledge of ISI coefficients concentrated around the diagonal of Channel Frequency Response (CFR) matrix improves the receiver's error floor significantly. The potential use of the framework for real-time frequency domain channel simulation was also investigated and demonstrated to be more efficient than conventional time domain Tapped Delay Line (TDL) model when a number of simulated users is high.Comment: Conference: IEEE VTC-Fall 2018, 5 pages, 3 figure

Numerical Values of Bernoulli Convolution

Intersymbol interference is reported as a random power series with Bernoulli variables as coefficients. When theargument is the p-th root of 1/2, an explicit function is given. Here, numerical calculations of the distribution functionfor several values of p are presented.Intersymbol interference is reported as a random power series with Bernoulli variables as coefficients. When theargument is the p-th root of 1/2, an explicit function is given. Here, numerical calculations of the distribution functionfor several values of p are presented