We consider a network of n sender/receiver pairs, placed randomly in a region of unit area. Network capacity, or maximum throughput, is defined as the highest rate that can be achieved by each sender/receiver pair over a long time. It is known that without using relays (i.e., via only direct communication), the maximum throughput is less than O(1), that is, it strictly decays as n increases. The network capacity without relaying for static or mobile networks is not known. However, a known lower bound on this capacity is 0(\frac{{\log (n)}} {n}). Our goal is to find a higher achievable rate. We show, by demonstrating a simple coding and scheduling scheme that uses mobility, that O(\frac{{\log (n)}} {{n^{1 - \beta } }}) is achievable, where \beta > 0 is a constant that depends on the power attenuation factor in the wireless medium. For example, when power decays as d^-4 with distance d, 0(\frac{{\log (n)}} {{n \cdot ^{25} }}) is achievable. We assume channels to be AWGN interference channels throughout this work.