Digital Receivers and Transmitters Using Polyphase Filter Banks for Wireless Communications

This paper provides a tutorial overview of multichannel wireless digital receivers and the relationships between channel bandwidth, channel separation, and channel sample rate. The overview makes liberal use of figures to support the underlying mathematics. A multichannel digital receiver simultaneously down-convert a set of frequency-division-multiplexed (FDM) channels residing in a single sampled data signal stream. In a similar way, a multichannel digital transmitter simultaneously up-converts a number of baseband signals to assemble a set of FDM channels in a single sampled data signal stream. The polyphase filter bank has become the architecture of choice to efficiently accomplish these tasks. This architecture uses three interacting processes to assemble or to disassemble the channelized signal set. In a receiver, these processes are an input commutator to effect spectral folding or aliasing due to a reduction in sample rate, a polyphase -path filter to time align the partitioned and resampled time series in each path, and a discrete Fourier transform to phase align and separate the multiple baseband aliases. In a transmitter, these same processes operate in a related manner to alias baseband signals to high order Nyquist zones while increasing the sample rate with the output commutator. This paper presents a sequence of simple modifications to sampled data structures based on analog prototype systems to obtain the basic polyphase structure. We further discuss ways to incorporate small modifications in the operation of the polyphase system to accommodate secondary performance requirements. MATLAB simulations of a 10-, 40-, and 50-channel resampling receiver are included in the electronic version of this paper. An animated version of the ten-channel resampling receiver illustrates the time and frequency response of the filter bank when driven by a slowly varying linear FM sweep.