Distance distribution for turbo-equalized systems over static frequency selective channels

Abstract

In this paper we investigate the Euclidean distance distribution in turbo-equalized systems over static frequency-selective (ISI) channels 1 . We propose a novel approach in evaluating the squared Euclidean distance between transmitted sequences at the output of the ISI channel based on the correlogram of error sequences. By inspecting autocorrelation properties of error sequences, we derive the main statistics of the output Euclidean distance. The proposed method provides a more comprehensive tool to predict system behavior with finite or infinite packet length. We exploit obtained results to evaluate the frame error rate (FER) performance of the system under maximum-likelihood sequence estimation.

Bound estimation for coded faster‐than‐Nyquist system

“…Therefore, it is computational prohibitive to directly calculate needed in (3) using the extended state diagram proposed in [9]. An alternative method with low complexity to estimate the EDD over ISI channel is given in [10] by using the autocorrelation properties of error sequences. Adopting this idea, the EDD evaluation of FTN will also be solved similarly.…”

“…Let denote the error sequence between the transmitted modulated code sequence and the estimated sequence , whose Hamming weight is defined as the number of non‐zero elements in . Then, the squared Euclidean distance between these two sequence is depicted as [10] where and are the autocorrelation function of e and tap coefficients vector g defined in (2), respectively. That's to say, is only related to the autocorrelation function of error sequence.…”

“…However, the EDD of FTN signalling is hard to obtain through the extended state diagram because of its very long memory length. In [10], a method to evaluate the squared Euclidean distance between transmitted sequences at the output of the intersymbol interference (ISI) channel is given based on the correlation of error sequence. Inspired by this, we first analyse the statistical property of EDD for FTN signalling in this Letter and then the frame error rate bound for coded FTN system is derived.…”

“…tT . As the OBM model is employed, w n is the white Gaussian noise variable [10]. L in (2) is theoretically infinite but practically finite on account that g m is very small and can be ignored when m is large enough.…”

“…As illustrated in (4), d 2 E is a weighted sum of R e m ( ), meaning that it's also a random variable. The mean and variance of d 2 E derived from (4) and (6) under the condition that d H e ( ) = d and interleaver length N is [10]…”