The effect of quadrature hybrid errors on a phase difference frequency estimator and methods for correction

Abstract

This thesis is concerned with the estimation of the frequency of a single sinusoid of fixed but unknown frequency and which has been corrupted by errors in a quadrature hybrid, coherent receiver system. The quadrature hybrid receiver has been employed to produce in-phase and quadrature baseband signal components which can be sampled and undergo an analogue to digital conversion. A simple, discrete frequency estimator is derived from the rate of change of signal phase between successive sampling instants after analogue to digital conversion. The statistical effects of the errors and imbalances, inherent in the quadrature hybrid, upon the discrete frequency estimator are studied. This study has been carried out in four stages forming the content of the four chapters : 2,3,4,5. In chapter 2, an analytic study of the estimation of the frequency of a single sinusoid, which has passed through a quadrature hybrid system, is carried out. This study is further subdivided so that each of the quadrature hybrid errors is examined individually. A summary of the results derived for each error case is provided, in tabular form, in appendix XII. In chapter 3, the quadrature hybrid and input signal are modelled as a computer simulation. This chapter is subdivided, as with chapter 2, so that each error case is simulated on an individual basis. In each case the error or imbalance is varied and the frequency of the input sinusoid is varied so that most of the possible error conditions and possible input frequencies are studied. Simulation results are presented in graphical form and compared with a similar graphical presentation of the theoretical results from chapter 2. In chapter 4, a real quadrature hybrid, receiver system is examined and the inherent system errors are measured. These measurements serve to support both the simulations and the theory. In chapter 5, techniques are derived in order to reduce the degradation of frequency estimation caused by the quadrature hybrid system errors and both simulation results and a real example are given. It is also demonstrated that the theoretical lower limit for frequency estimation in the presence of normally distributed noise (the Cramér-Rao lower variance bound) can be achieved for this system.