In time-hopping impulse radio, a number of frames are allocated for each information symbol. In each of these frames, one ultra-wideband pulse is transmitted. During demodulation of the received signal, these pulses need to be optimally combined in order to achieve the lowest bit error probability. For a single-user system over an additive white Gaussian noise channel, an optimal linear scheme is the one in which samples from the received pulses in different frames are added with equal weight. However, in multiuser and/or frequency-selective environments, the contributions from different frames should be combined considering the minimum mean square error (MMSE) criterion in order to obtain low bit error rates. Moreover, in frequency-selective environments, where the receiver obtains samples from different multipaths, those multipath components should also be combined optimally. In this paper, we consider optimal and suboptimal linear receivers for a given user in a frequency-selective multiuser environment. The optimal linear receiver combining all the samples from the frames and the multipath components, according to the MMSE criterion is designed. Due to the complexity of this receiver, two suboptimal receivers are considered: i) An optimal frame combining receiver, which optimally combines the samples from the frames, while combining different multipath components suboptimally. ii) An optimal multipath combining receiver, which combines the samples from different multipath components optimally, while combining the samples from the frames suboptimally. In this paper, these optimal and suboptimal linear receivers are designed and their performance is evaluated via simulations.