Digital transmit and receive linear phase matched filters

The relationship between the causal real symmetric pulse and the linear phase characteristic is used for matched filter design. Real symmetric pulse transmission leads to a linear phase pulse shaping filter which is matched at both the receiver and the transmitter ends. This provides the potential for inexpensive system on a chip (SOC) design since the hardware implementation for transmit and receive filter is similar. The discrete time delayed raised-cosine pulse is considered for the causal real symmetric Nyquist pulse. A novel pulse shaping filter that retains a raised-cosine shape in the impulse response rather than the frequency response is considered in this paper. This design is completely different than the typical raised-cosine filter where the raised-cosine shape is maintained in the frequency response.The raised-cosine pulse used in our design has a finite number of transmission zero pairs; therefore, it can be perfectly reconstructed as the unit-sample response of the filter. Consequently, the transfer function of the shaping filter is exactly obtained from the z-transform of the pulse. This digital filter can be used at the receiver after the power amplification stage to achieve the desired amplification linearity in constant amplitude modulation systems. FIR filter design examples for various values of the delay parameter are described, and bit error rate simulation is also provided.