An Accurate Approximation of the Exponential Integral Function Using a Sum of Exponentials

This paper proposes a novel approximation for the exponential integral function, E₁[x], using a sum of exponential functions. This approximation facilitates studying the error probability of a number of communication techniques in the presence of Co-Channel Interference (CCI). These include Hybrid Automatic Repeat Request (HARQ) with soft combining, selection relaying, incremental relaying, and opportunistic incremental relaying, just to name a few. To illustrate the usefulness and accuracy of the proposed approximation, we study the error probability of a Chase combining HARQ system operating in the presence of an unknown source of CCI where we derive an accurate closed form expression for the Moment Generating Function (MGF) of the resultant Signal to Interference plus Noise Ratio (SINR). The accuracy of the derived result is verified using computer simulation.