Abstract
Cognitive radio applications require flexible waveforms to overcome several challenges such as opportunistic spectrum allocation and white spaces utilization. In this context, multicarrier modulations generalizing traditional cyclic-prefix orthogonal frequency-division multiplexing are particularly justified to fit time-frequency characteristics of the channel while improving spectral efficiency.In our theoretical framework, a multicarrier signal is described as a Gabor family the coefficients of which are the symbols to be transmitted and the generators are the time-frequency shifted pulse shapes to be used. In this article, we consider the case where non-rectangular pulse shapes are used with a signaling density increased such that inter-pulse interference is unavoidable. Such an interference is minimized when the Gabor family used is a tight frame. We show that, in this case, interference can be approximated as an additive Gaussian noise. This allows us to compute theoretical and simulated bit-error-probability for a non-coded system using a quadrature phase-shift keying constellation. Such a characterization is then used in order to predict the convergence of a coded system using low-density parity check codes. We also study the robustness of such a system to errors on the received bits in an interference cancellation context.
Highlights
In most of current communication systems, the linear part allows for perfect symbol reconstruction: the synthesis and analysis families used in the transmitter and the receiver form biorthogonal frames
We focus on the closed-form expression of the bit-error-probability of our linear system provided that tight frames are used, as prescribed in [10] in order to maximize the signal to interference plus noise ratio (SINR)
An increase of the spectral efficiency beyond-orthogonal systems yields interference between pulse-shapes
Summary
In most of current communication systems, the linear part allows for perfect symbol reconstruction: the synthesis and analysis families used in the transmitter and the receiver form biorthogonal frames ( known as Riesz bases). FTN transmission techniques can be extended to multicarrier modulations [4] In this case, denoting F0 the inter-carrier spacing and T0 the multicarrier symbol duration, it can be shown that if the density ρ = 1/(F0T0) of the system is strictly greater than one, the synthesis and analysis families, respectively used for transmission and reception, can no longer be biorthogonal but can still form overcomplete frames [5]. This leads to IPI both in time and/or frequency.
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