On the frame error rate of transmission schemes on quasi-static fading channels

Abstract

Abstract-It is known that the frame error rate of turbo codes on quasi-static fading channels can be accurately approximated using the convergence threshold of the corresponding iterative decoder. This paper considers quasi-static fading channels and demonstrates that non-iterative schemes can also be characterized by a similar threshold based on which their frame error rate can be readily estimated. In particular, we show that this threshold is a function of the probability of successful frame detection in additive white Gaussian noise, normalized by the squared instantaneous signal-to-noise ratio. We apply our approach to uncoded binary phase shift keying, convolutional coding and turbo coding and demonstrate that the approximated frame error rate is within 0.4 dB of the simulation results. Finally, we introduce performance evaluation plots to explore the impact of the frame size on the performance of the schemes under investigation.

Approximations of the packet error rate under quasi-static fading in direct and relayed links

“…A similar argument may be extended to the criterion of [14]; if (21) is not verified, then both integrals in (19) and (20) are effectively unbounded. Equation (21) thus provides a necessary condition for minimizing either the absolute or relative error over the SNR range, but a priori not a sufficient one.…”

“…We then express that a unit step approximation can be derived for the packet error rate of block fading channels that closely matches the numerical computation of the packet error rate in a tractable closed-form expression. Such an approximation has been studied in the context of long block codes [13,14] as well as [15]. We survey these results and show in fact that both approximations depend on the same parameters, thereby allowing to easily compute one given the other.…”

“…This approach has been shown to be particularly efficient in turbo-coded schemes that are iteratively decoded [13,14], when the threshold is set to the waterfall threshold of the decoding scheme -the SNR beyond which the decoding algorithm provably converges. In the uncoded case, we can arbitrarily set this threshold to the solution of:…”

“…Using the relation between the Q function and the incomplete gamma function ( [17], Eq.7.11.2), we can express (14) and thus an upper bound on the coding gain G (block,th) c of theoretical PSK modulations in block fading channels using the following proposition, with N the block size and a, t from Table 2.…”

“…The quality of the approximation is heavily dependent on the choice of γ 0 . Following the work of [13], the authors of [14] proposed to use an absolute error criterion to compute γ 0 . In mathematical form, the chosen threshold verifies:…”