Millimeter wave communications will use large bandwidth and experience severe attenuation due to the pathloss. The two above conditions may force the communication system to enter the so-called wideband regime, where transmitted signals must be increasingly peaky in order to achieve a large fraction of the wideband capacity. This paper investigates noncoherent capacity of millimeter wave communications with average and peak power constrained inputs as a function of bandwidth. The impact of several parameters, in particular coherence block size and strength of the normalized specular component in line-of-sight propagation, is also studied. Capacity upper and lower bounds are provided and suggest that in practical scenarios the communication system may have to operate in the wideband regime. Paired with non-line-of-sight propagation, dense signaling is shown to limit the maximum achievable rate for typical users in the cell.