Most reverse conversions in Residue Number Systems (RNS) are based on the Chinese Remainder Theorem (CRT) and the Mixed Radix Conversion (MRC). The complexity of the circuitry of the CRT is high due to the large modulo-M operation. The MRC has a simple circuitry but it's a sequential process in nature. The purpose of this research is to obtain an efficient reverse conversion method to reduce the computational overhead found in the conventional reverse conversion algorithms. In this paper, new algorithms for reverse conversion in RNS for four-moduli set and five-moduli set have been proposed and their correctness evaluated. Numerical evaluations to ascertain the correctness and simplicity of the algorithm have been presented. These algorithms have fewer multiplicative index operations than those in the conventional CRT and MRC. The large modulo-M operation has been eliminated which reduces the computational overhead.

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Good signal reception depends on a reliable communication link. However, as the signal travels through the communication medium, several factors affect the quality of the signal at the receiver. In Ku band digital satellite transmission, rain is the major cause of link impairment. Global rain rate and rain attenuation prediction models have been developed to predict rain rate and rain attenuation at various locations. These models have not been applied and tested with measured data to determine their prediction accuracy in the Ghanaian tropical region. In this paper, the Moupfouma and International Telecommunication Union Recommendation (ITU-R) rain rate models were applied and compared with measured local 1-minute data for Kumasi. The result was used to select an appropriate prediction model to be applied to all 22 synoptic stations across Ghana. The ITU-R rain attenuation model was then used to predict the rain attenuation for Ghana. The values obtained were used to develop a rain rate and rain attenuation geographical map for Ghana using the inverse-distance weighting method and Arc GIS software. As Ghana migrates from analogue to digital satellite television broadcasting, it is imperative to investigate the effect of rain on the signal. This will serve as a tool for system designers to determine the appropriate effective isotropic radiated power (EIRP) and receiver characteristics for Ghana.

Rain fade is the loss of signal power at the receiver of a telecommunication system mainly due to absorption and scattering caused by rain in the transmission medium, especially at frequencies above 10 GHz. In order to combat the loss of the signal power at the receiver, there is the need to employ rain fade mitigation techniques. Consequently, researchers have been studying how rain affects the signal in different geographical locations as well as proposing some mitigation techniques. Power control is one of the mitigation techniques that have been proposed. But this technique has some associated challenges. Increasing the power will lead to an increase in cost of transmission which will eventually be passed on to the consumer thereby making satellite services expensive. It requires high power in uplink and downlink which increases the burden either on user terminal or satellite payload. Also, because of health concerns there is a limit to the amount of power that can be radiated to the ground and this is governed by international agreements. Another power management drawback in using this technique is that, uplink power control is not efficient in directing the added power to only the ground station experiencing path attenuation, because the additional power is distributed to all locations within the satellite antenna coverage area. In this paper, we address the power control challenges, by leveraging on the inherent properties of Residue Number System (RNS) and Redundant Residue Number System (RRNS) to propose an RNS architecture using the moduli set {2 2n+1 -1, 2 2n -1, 2 2n , 2 4n+1 -1, 2 2n +1} that can mitigate rain fade in the satellite link as well as detect and correct multiple errors. In digital communication systems, the bit energy, e b , is the most important parameter in determining the communications link performance. Numerical analysis shows that the proposed scheme performs better than the traditional method as indicated in the high energy per bit value obtained in the proposed system in comparison with the traditional method, all other things being equal.