Executive Summary : | Modern wireless communication scenarios with an enormous number of communicating devices do not ensure the presence of a direct link between the transmitter and the receiver. Intelligent reflecting (IRS) or reflecting intelligent surface (RIS), a channel modification technique, can convert the harsh channel conditions to the favourable case. IRS comprises several reflector elements such that when the signals from the transmitter impinge on the surface, they can be reflected with prefixed phases. The phases of the IRS elements are tuned so that all the incident paths add coherently to enhance the strength of the received signal. We plan to study two mathematical problems associated with IRS, which are discussed briefly in the following. First, the problem of phase optimization of the IRS elements over frequency-selective channel will be taken up. We have fewer angle variables to cancel the phases of all the channel coefficients. The complete phase cancellation by IRS is not possible in frequency-selective fading channels. In such a situation, we determine the IRS phases such that the received signal power is maximized for every channel realization. This optimization problem is non-convex at the outset. The objective is to convexify the problem and design an algorithm to determine the optimum IRS reflection angles. Secondly, we plan to find the distribution of the cascaded link (Base station to IRS then to User) in the IRS for generalized fading channels. Generalized fading distribution includes Rayleigh, Nakagami, Weibull, etc. The cascaded channel can be expressed as a sum of the product of two individual channel coefficients. The distribution of the cascaded channel is difficult to find even in the case when two individual channel coefficients are Rayleigh distributed. Here we plan to use several approximations to Bessel’s function to simplify the distribution. Based on the distribution of the cascaded link, the probability of outage can be computed. The outage analysis, in turn, provides a performance guarantee of the system. The distribution of the cascaded channel is useful for deriving the expressions for average bit error probability (ABEP) and the pair-wise error probability (PEP). The expressions of outage probability, ABEP, and PEP provide a holistic analysis of the IRS-aided system and provide insights to develop better phase optimization and receiver design. |