Efficient chip design for pulse shaping

Pulse shaping is a crucial operation for every modem transceiver. It usually requires a large portion of the modem's computational power and, therefore, an efficient implementation can be very beneficial to the overall modem design. In particular, in the transmitter part where well defined signals are to be computed, the typical pulse shaping operation can be greatly simplified. While a standard filter design requires many mult/add operations, the transmitter pulse shaping filter could also be designed by a pure look-up table. However, for higher constellations and large pulse shaping filter lengths the look-up table can become too large to implement. This paper presents a new idea for implementing the pulse shaping filter for a modem transmitter. It is shown that for QPSK and other higher order modulations, like 16/32/64 QAM, no multiplication is required at all. Further, the number of multiplications for 8PSK (and 16/32 PSK) can be reduced to a very small number that is independent of the number of coefficients necessary for implementing the filter function.