Sample Rate Conversion in Software Radio Terminals

Feasibility of Software Radio mainly depends on the availability of a suitable hardware platform. A basic feature of this hardware platform is the ability to process signals of different mobile communications standards, which are usually based upon a diversity of master clock rates. Hence, the conversion between different sample rates is an important functionality of a Software Radio receiver. Preferably realized digitally, sample-rate conversion is conventionally regarded as interpolation. It will be shown that interpolation does not fulfill the anti-aliasing requirement which is the very criterion to be obeyed. Based upon this idea anti-aliasing filters for sample rate conversion are proposed. These filters are realized by a multi stage system with different stages for integer-factor and fractional sample rate conversion. Introduction In the context of mobile communications systems the concept of software radio has become the subject of intensive study. Aiming for a universal receiver with virtually no restrictions regarding bandwidth, selectivity, frequency range and modulation schemes, the intended flexibility can only be achieved by digital signal processing while minimizing the number of analog components. All signal processing has to be realized on a fixed hardware platform, exclusively being controlled by software. This enables the adaptation of the terminal to present and future communications systems. A key component of a software radio receiver is the analog-to-digital converter (ADC) (Hentschel and Fettweis, 1999b). For reasons of simplification the AD-conversion is advantageously performed at a fixed clock rate as close to the antenna as possible. However, the different standards of operation require different symbolor chiprates usually not having common integer divisors or ratios with respect to the digitization rate. Therefore the sample rate of the digital signal has to be converted to a standard-specific rate (Hentschel et al., 1998; Buracchini and Mastroforti, 1999). In order to cope with the wide-band nature of the signals comprising several channels, sophisticated solutions to sample-rate conversion have to be found. While sample rate conversion (SRC) by integer factors can be realized without difficulty it is much more complicated to find efficient software-controlled algorithms for fractional SRC. Because of a necessarily high intermediate sample rate most of them are only suitable for low input rates. On the other hand, polyphase structures avoiding high intermediate sample rates render the implementation of more than two rate change factors on a fixed hardware platform nearly impossible. A solution to the problem could be a periodically timevariant implementation allowing a parameterizable sample rate conversion by arbitrary rational factors without any clock rate higher than the input sample rate. Starting with some fundamental considerations on SRC the important difference between anti-aliasing and antiimaging is elaborated. Usually being regarded as the very solution to the problem of SRC, the disadvantages of pure interpolation are worked out in the course of the paper. Finally, investigations regarding the implementation of sample-rate converters and thereby derived solutions are presented. Basics of Sample Rate Conversion (SRC) While sampling an analog time-continuous signal xa(t) with a period T the digital signal x(k) is obtained. Sample rate conversion means converting this sequence x(k) to another sequence y(m) as if it were obtained from sampling xa(t) with a period T . As a basic approach we use an analog interpretation: The time-continuous signal xa(t) will be reconstructed from x(k) by digital-to-analog-conversion followed by low-pass filtering with ha(t). Eventually, the reconstructed signal xa(t) is re-sampled with a period T (Crochiere and Rabiner, 1983). Thus the filter ha(t) has to fulfill two requirements: to reconstruct the signal xa(t), which corresponds to an interpolation of the signal x(k), and to perform band limitation, in order to avoid aliasing caused by the succeeding re-sampling. Assuming a rational ratio of T and T a direct digital approach can be found. This provides a means of replacing the ADC and analog filter ha(t) by the digital filter h(n) whose coefficients are obtained from sampling ha(t) with a period L = T M . Usually the digital filter h(n) will be implemented directly (figure 1). In this case the sample rate of the input signal is to be increased to an intermediate sample rate which the filter is clocked at. This intermediate samplerate is L T = L fin. It has to be observed that the sample rate of the input signal is generally relatively high in the context of mobile communications. This is due to the large bandwidth being occupied by the signals. Therefore the intermediate sample-rate quickly reaches values which real systems cannot cope with. Thus, the direct implementation of sample-rate conversion is not feasible. Interpolation by L Decimation by M h(n)