Assignment:
Consider a diversity scheme consisting of four branches as shown in Figure P15.2. Each branch is responsible for processing an independent Rayleigh faded signal. r(t). At a particular instant in time, the received signal can be expressed as a four branch vector r = r31, where r, represents the voltage signal at branch i. Also. the gain in the branches can be expressed with a four-branch vector r = [r1 r2 r3 ri where ri represents the voltage gain at branch i. Consider a moment in time when the measured values of r equal [0.87. 1.21, 0.66, 1.90], and the associated gains of G equal [0.5. 0.8, 1.0, 0.8]. The average noise power of each branch N is equal to 0.25.
(a) Calculate the SNR applied to the detector?
(b) It can he shown [1] that the SNR is maximized when the value of each Di is equal to ti/N. Based on this condition, determine the maximum achievable SNR.
Provide complete and step by step solution for the question and show calculations and use formulas.