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Considerable progress has recently been made in the theoretical analysis of the IEEE 802.15.3 a UWB channel model by treating it as a two-dimensional Poisson cluster process. Unfortunately, this only accounts for multipath arrival times and gains, not arrival angles. In this paper, it is shown that Spencer's extension of the channel model, which also accounts for arrival angles, can be accommodated in the cluster point process framework. Using this framework, closed-form expressions are derived for several quantities, including the power delay-angle profile and detectable-path delay-angle profile.