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

Abstract

Abstract-Satellite communications systems designers are continuously struggling to improve the link capacity. A critical challenge comes from the limited power available aboard the satellite. To ensure a sufficient signal-to-noise power ratio (SNR) at the terrestrial receiving side, the amplifier aboard the satellite is usually operated close to the amplifier saturation point which adds non-linear distortions to the communication channel. Several algorithms have been proposed to equalize the non-linear satellite channel. The Echo State Network (ESN) algorithm, coming from the field of artificial neural networks, has been shown to perform well in this task: it can achieve a similar bit error rate (BER) as the state-of-the-art Volterra equalizer. In the present paper we show that with an appropriate design, the complexity of the ESN can be significantly lower than that of the Volterra equalizer, while conserving the low BER.

High performance bio-inspired analog equalizer for DVB-S2 non-linear communication channel

“…Namely, the Volerra equalizer widely used in the state-of-the-art and the ESN described in section 3. The latter is similar to the digital solutions proposed in [8] [9].…”

“…We will see that this can easily be implemented with optoelectronic components. We also show that, as with the activation function used in [8] and [9], we achieve similar performances to the Volterra equalizer.…”

“…They have proven useful for tasks such as speech recognition or time-series prediction [7]. We showed in [8] that digital ESNs can reach similar performances as the Volterra equalizer with a similar or even lower algorithm complexity when the ESN parameters are optimized [9].…”

Reservoir-Computing Based Equalization With Optical Pre-Processing for Short-Reach Optical Transmission

“…Additionally, multiplications by constants can be practically implemented by using shifters and adders, resulting in a lower complexity implementation, e.g. as shown in [33]. The reservoir is described by the M ×M square matrix W res .…”

“…Concerning f act , the properties of ESN, including its universal approximation property, are strictly defined for sigmoid functions [26], [34], [35], [36]. However, in a number of demonstrations [13], [33], using alternative functions, even linear functions, to replace a sigmoid has been shown to be computationally effective. Linear activation functions have also been shown to provide a better memory capacity, then nonlinear functions [28], [37].…”