Holistic Biquadratic IIR Filter Design for Communication Systems Using Differential Evolution

Digital IIR filter implementations are important building blocks of most communication systems. The chosen number format (fixed-point, floating-point; precision) has a major impact on achievable performance and implementation cost. Typically, filter design for communication systems is based on filter specifications in the frequency domain. We consider IIR filter design as an integral part of communication system optimisation with implicit filter specification in the time domain (via symbol/bit error rate). We present a holistic design flow with the system's bit error rate as the main objective. We consider a discrete search space spanned by the quantised filter coefficients. Differential Evolution is used for efficient sampling of this huge finite design space. We present communication system performance (based on bit-true simulations) and both measured and estimated receiver IIR chip areas. The results show that very small number formats are acceptable for complex filters and that the choice between fixed-point and floating-point number formats is nontrivial if precision is a free parameter. 1. Introduction In signal processing, filters are building blocks removing unwanted signal components (often, but not exclusively, specified in the frequency domain). Design (i.e., identification of suitable structures and coefficients) of digital filters given some specification in the frequency domain (e.g., pass-band ripple, cutoff frequency, stop-band frequency, or stop-band attenuation) is a well-established field [1]. In many advanced systems, however, the ultimate goal is rarely specifiable in the frequency domain but is reflected in a more complex measure. Examples include bit error rate, peak power consumption, or power trace entropy. Designing efficient systems therefore requires embedding of the filter design process in a larger system design context. Implementation of digital filters requires identification of arithmetic units to be implemented, the choice of a specific number format for each arithmetic unit, and quantisation of filter coefficients. These actions alter the filter characteristics and, if not foreseen in the design process, can have a severe impact on the system’s performance. There is a vast literature on digital filter design and optimisation of resource usage under some constraints. All design approaches we are aware of have in common that the number format’s underlying error model has to be chosen in advance; that is, the designer has to take the decision if fixed-point or floating-point arithmetic is used prior to optimisation.