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Existing routing and broadcasting protocols for ad hoc networks assume an ideal physical layer model. We apply the log-normal shadow fading model to represent a realistic physical layer and use the probability p(x) for receiving a packet successfully as a function of distance x between two nodes. We define the transmission radius R as the distance at which p(R)=0.5. We propose a medium access control layer protocol, where receiver node acknowledges packet to sender node u times, where u*p(x)≈1. We derived an approximation for p(x) to reduce computation time. It can be used as the weight in the optimal shortest hop count routing scheme. We then study the optimal packet forwarding distance to minimize the hop count, and show that it is approximately 0.73R (for power attenuation degree 2). A hop count optimal, greedy, localized routing algorithm [referred as ideal hop count routing (IHCR)] for ad hoc wireless networks is then presented. We present another algorithm called expected progress routing with acknowledgment (referred as aEPR) for ad hoc wireless networks. Two variants of aEPR algorithm, namely, aEPR-1 and aEPR-u are also presented. Next, we propose projection progress scheme, and its two variants, 1-Projection and u-Projection. Iterative versions of aEPR and projection progress attempt to improve their performance. We then propose tR-greedy routing scheme, where packet is forwarded to neighbor closest to destination, among neighbors that are within distance tR. All described schemes are implemented, and their performances are evaluated and compared.