Modulation, Pre-Equalization and Pulse Shaping for PCM Voiceband Channels

For the past few decades, analog voiceband modems have been used extensively to carry digital information over the Public Switched Telephone Network (PSTN). Conventional voiceband modems treat the PSTN as an analog communication channel. However, today’s PSTN is mostly a digital network except for the basic telephone services provided via analog subscriber lines. The conventional model of analog voiceband channels is no longer adequate to characterize the physical connection between terminals with direct digital access to the network and voiceband modems connected to analog subscriber lines. Such a connection requires a different model in each direction. There are now international modem standards which support rates of up to 56 kbits/s for the down-stream channel. This dissertation examines the more challenging part of the voiceband communication channel, i.e., the up-stream direction connecting an analog subscriber to the digital network. The major source of distortion on the up-stream channel is quantization error caused by analog-to-digital conversion performed as part of the encoding to Pulse-Code Modulation (PCM) process. A bandpass filter prior to the PCM encoder restricts the bandwidth while the sampling rate of the PCM encoder is predetermined by the network. Signalling in the presence of such constraints lead to theoretical problems as well as practical concerns in modem design. Communication models that characterize PCM voiceband channels are developed. We investigate modulation design and related issues including index mapping, constellation design and constellation probability assignment to match the pre-determined structure of the detector at the receiver, i.e., the PCM encoder at the central office. We develop a framework for transmitter structures that can avoid or reduce Inter-Symbol Interference (ISI) at the receiver in order to sidestep the limited bandwidth of the up-stream channels and the fixed sampling rate of the up-stream channel. Techniques employed include linear filtering, spectral shaping and precoding to reduce the ISI, while limiting the average transmitted signal power. A filterbank structure for pre-equalizing channels with spectral nulls is also described. A new method for pulse shaping design is proposed. The new pulse shaping filters provide a compatible design that can be used for the up-stream PCM channel as well as to the cascade of the up-stream and the down-stream channels. Compared to conventional modem design, the proposed modulation and pre-equalization techniques together allow for an increase of the data transmission rates in the up-stream direction of up to 50%.