Complex Data Streams Research Articles

Efficient adaptive complex filtering algorithm with application to channel equalisation

The paper describes a means of efficiently implementing an adaptive complex transversal filter. Three real-coefficient filter sections are used to realise each transversal filter section of the complex equaliser, thus using one less filter than a conventional realisation. An adaptive algorithm is developed, in a manner similar to the least mean square algorithm, which allows the three filters to be trained independently and in parallel using real valued arithmetic. In this way, throughput can be maintained, whilst reducing the number of multipliers in both the filter and coefficient update sections by 25%. Using independence theory, it is demonstrated that the three filters converge to a solution consistent with the optimal Wiener-Hopf solution. The convergence speed is characterised in terms of the complex input data stream. The transient behaviour of the algorithm is examined using a simulation of a channel equaliser and is supported by analysis.

Flexible modulus residue number system for complex digital signal processing

The quadratic residue number system (QRNS) is often used for integer calculation on complex data streams. A finite polynomial ring mapping technique is presented that removes the 4k + 1 prime divisor restriction of the QRNS, albeit with an increase in independent processing channels from two to three.

A functional shell

One of the best features of the standard UNIX shell is the use of pipes to compose programs. A C language derivative is used for more complex program combinations involving looping or branching. This paper presents an alternative shell language based on natural extensions of the pipe concept. “Structured data streams” are introduced as a means of expressing potentially concurrent processing, and “labelled data streams” serve to route data to one of a pool of programs. These complex data streams are hooked together with functional operators much as simple data streams are hooked together with pipes. A generalized notion of “powers” provides for repetition of programs and also for systems that take an arbitrary number of input streams. This provides a uniform way of building complex tools from simple ones, as advocated by Kernighan and Plauger [8]. A major advantage of this new shell language is its program algebra, which facilitates system verification and analysis.