Four-dimensional signaling for bandlimited channels

In this paper we discuss multidimensional signaling for transmission over the satellite channel, i.e., a bandlimited radio channel with nonlinearities. We derive a set of basis signals that are orthogonal and whose bandwidth occupancy is minimal, in the sense that they maximize the power inside a fixed frequency interval (-B, B). Since we remove the assumption that the signals be confined in one symbol interval, the concept of orthogonality must be revisited. We design basis signals that satisfy the following requirements: (a) When passed through their matched filter, the sample sequence has no intersymbol interference; (b) when passed through the filter matched to another basis signal, the sample sequence has no interchannel interference, and (c) their bandwidth occupancy is minimum. The performance of four-dimensional signals designed according to this criterion is evaluated in terms of bandwidth occupancy and error probability over nonlinear satellite channels. Comparisons with two-dimensional modulation schemes (in particular QPSK) are also made