The water-filling solution for the loading problem is defined by Equation (6.213) subject to the constraint of Equation (6.2 10). Using this pair of relations, formulate a recursive algorithm for computing the allocation of the transmit power P among the N sub channels. The algorithm should start with

(a) An initial total or sum noise-io-sign.al ratio NSR (i) = 0 for iteration i = 0, and

(b) The sub channels sorted in terms of those with the smallest power allocation to the largest.