This Report was presented to the Faculty of the Graduate School of The University of Texas at Austin in partial fulfillment of the requirements for the degree of

Master of Science in Engineering

This research project entails an efficient numeric digital representation in communication systems design. A complex block floating-point format with box encoding is proposed to encode an array of complex numbers that has better numeric resolution than its IEEE-754 counterpart when the same number of bits are allocated to the dominant value in the array. It is estimated that at least 10% of bit savings could be achieved by the new complex block representation on a quad-precision IEEE-754 format. A further bits savings of up to 18% could potentially be achieved for complex blocks at half-precision and single-precision IEEE-754 representation.

The implementation cost of the proposed block floating-point format is evaluated in terms of memory usage, design of arithmetic units, and memory input/output rates for communications system modeling and block diagrams. Further analysis is performed on the limitation and quantization effects of this complex block format relative to complex IEEE-754 format. The coverage of the arithmetic units design include complex block adder and complex block multiplier. The appropriate systems that would be required to perform algorithms such as the fast Fourier transform

The proposed block floating-point format is simulated as a new numeric class defined and implemented in MATLAB simulation environment. The MATLAB simulation is divided into two major parts. The first part of MATLAB simulation targets the simulation of complex block addition and complex block multiplication units for arbitrary size of complex samples per input block. The reference output values of complex block arithmetic are those computed with similar precision in IEEE-754 format. The second part of MATLAB simulation is performed on the system model of the single-carrier modulation-based and multi-carrier modulation-based communication systems. The quadrature amplitude modulation (QAM) is the baseband modulation type targeted in this work. The specification identified in the system model is relevant to those specified in the Long-Term Evolution (LTE) Standards for Base Station, Release 12.