On destructive superposition of shaping pulses in band-limited linear modulation systems

We analyze pulse-shaped transmit signals with correlated input sequences in the framework of band-limited liner modulations. These signals are formed by superposition (convolution) of the shaping pulses and may have different amplitude statistics depending on the correlation properties of the input sequences. Hence, even if the sequences have a unit average power in discrete-time domain, the resulting transmit signals exhibit smaller (or larger) average power if there are many destructive (or constructive) superpositions produced by the correlated source. Since such a reduction of average transmit power does not change the amplitude of the underlying discrete-time sequence, one may expect the so-called shaping gain. We comprehensively analyze the shaping gain achieved by the correlation of the input sequences, and show that the use of a pulse shape, which convolves the sequence destructively, is capable of increasing the achievable information rate of the system.