Equalization of the Non-Linear Satellite Communication Channel with an Echo State Network

Abstract

Abstract-Because of the small energy available aboard a satellite, the power amplifier must achieve a very high power efficiency which suggest to work close to the saturation point. This would be power efficient, but unfortunately would add non-linear distortions to the communication channel. Several equalization algorithms have been proposed to compensate for this non-linear behaviour. The Echo State Network (ESN), an algorithm coming from the field of artificial neural networks, has also been proposed for this task but has never been compared to state-of-the-art equalizers for non-linear channel. The aim of this paper is to adapt the ESN to the satellite communication channel and to compare it to the baseband Volterra equalizer. We show that the ESN is able to reach the same performances as the Volterra equalizer, evaluated in terms of bit error rate, and has similar complexity. In addition, we propose a new training strategy for the ESN and the Volterra equalizer to improve their performance.

Non-linear satellite channel equalization based on a low complexity Echo State Network

“…It has the advantage to reduce number of operations by reducing the number of connections. The matrix has also been used in [13] to equalize the DVB-S2 communication channel. It has been shown in [13] that the performances of the ESN can be improved, if it is trained to recover a constellation defined by the new centroids instead of the transmitted ones.…”

“…The matrix has also been used in [13] to equalize the DVB-S2 communication channel. It has been shown in [13] that the performances of the ESN can be improved, if it is trained to recover a constellation defined by the new centroids instead of the transmitted ones. In the case of a 16-QAM constellation, we have 16 centroids in the transmitted constellation defined by (X i ) 16 i=1 .…”

“…We will start with the ESN proposed in [13]. In this paper, we proposed to use the following activation function instead of the hyperbolic tangent used in most of the papers [11] [12] [14]:…”

“…where the values c 1 = 0.716 and c 3 = −0.0478 have been considered in [13]. If we also use the interconnection matrix (6), the evolution of the ESN becomes:…”

“…The comparison was however only made with a linear filter [11], or assuming a theoretical unrealistic channel model [12]. In [13], we applied the ESN to the satellite communication channel and compared its performance with the baseband Volterra equalizer. We demonstrated that the ESN is capable of performing equally well while incurring a similar computational complexity.…”