Estimation of required hardware resources for symbol-spaced equalizers for use in troposcatter communication systems

It is known that the signals in tropospheric digital communication systems is subject to the negative impact of inter-symbol interference caused by multipath propagation. That is why, adaptive equalizers are often used to remove the inter-symbol interference. Depending the architecture and the used adaptive algorithms, the equalizers have the different computational complexity. Since high computational complexity requires high hardware costs in the implementation of equalizers, it is desirable in the design to strive to reduce it. Therefore, there is a need to estimate the required hardware cost of different equalizer architectures. It is established that for the examined in this paper tropospheric scattering radio channel. So, it is sufficient to use Symbol Spaced Feed Backward equalizers, accordingly, it is required to estimate their computational complexity. The purpose of this paper is to estimate the required hardware cost of implementing Symbol Spaced Feed Backward equalizers for modems of tropospheric scattering communication systems. Estimates of the computational complexity of adaptive symbol rate feedback equalizers for an optimal number of weights equal to 50 are obtained. The results show that for the equalizer based on Least Mean Squares (LMS) algorithm it is required 402 real multipliers. At the same time for the equalizer based on the Recursive Least Squares (RLS) algorithm, constructed as a stabilized version of the fast (computationally efficient) RLS algorithm, requires 3346 such multiplications. Estimates of hardware costs for equalizers based on LMS algorithm and stabilized version of fast RLS algorithm at different number of weight coefficients obtained as a result of synthesis allow to estimate in the process of designing the expediency of application of those or other equalizers.