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In a power constrained relay network environment, the§performance can be improved by using various§forwarding techniques and position dependent optimal§power allocation strategy. We use our three terminal§model to optimize the power allocation under total§transmit power constraint, to maximize the§instantaneous signal-to-noise ratio (SNR) at§destination, and thus achieve improved throughput and§BER performance, while using AF and DF protocols. We§evaluate the performance of our system for both§coherent and non-coherent modulation in a Rayleigh§block fading channel. QPSK is used in the coherent§case and 4-FSK is used in the non-coherent case. We§derive expressions for instantaneous SNR using our§model and optimize the power allocation based on §that, thus achieving improved uncoded BER. We §compare the performance of the AF and DF protocols §based on their positional BER and throughput at §different received SNR and notice that our power §optimized schemes outperform existing power control §schemes at certain areas. Finally we also identify §the shape and area of the regions where relaying §would provide performance gains for both the§protocols at different received SNRs.