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In this paper a channel-averaged signal-to- interference-plus-noise ratio (SINR) is theoretically derived in closed-form for M-ary orthogonal balanced transmitted-reference (BTR) systems, considering the channel sparseness (i.e., no multipath component in a time bin) and cluster overlapping, often observed in realistic ultra-wideband (UWB) channels. The UWB channel here is a realistic and standard one with lognormal channel gain distribution and double independent Poisson arrival distribution of cluster and ray. The SINR expression derived is also valid when there exists the inter-pulse interference that arises due to a short inter-pulse distance between the reference and data pulses in BTR. Based on the channel-averaged SINR, the effect of the inter-pulse distance on the multiple access performance is fully investigated.