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Received ultrawideband (UWB) signals in most indoor environments are stochastic in nature, typically composed of abundant multipath components with random attenuation and arrival time. A commonly adopted detection strategy is to use a chosen deterministic template to correlate the received signal segment by segment, and only those segments having significant cross correlation with the template are selected, temporally synchronized, and cophased in their projections for coherent combining. Correlating a deterministic template with a random signal usually results in only partial energy captured by the receiver since a random signal is of multidimensions. In this paper, we construct a receiver with multiple orthogonal branches to fully capture the signal energy, in much the same way as a quadrature receiver does in conventional digital communications. The local reference signals are derived from the orthogonal expansion of UWB signals. The random projections of a UWB signal onto different orthogonal basis functions are noncoherently combined, leading to the concept of dimension diversity. Dimension diversity can be either used alone or alongside a Rake receiver to further exploit path diversity. The error performance of proposed receivers is analyzed, and their superiority over the conventional ones is examined by numerical results based on real UWB data.