Graduation Year


Document Type




Degree Granting Department

Electrical Engineering

Major Professor

Arthur David Snider, Ph.D.

Committee Member

Paul Flikkema, Ph.D.

Committee Member

Vijay K. Jain, Ph.D.

Committee Member

Nagarajan Ranganathan, Ph.D.

Committee Member

Mourad Ismail, Ph.D.


signal processing, jammer nulling, GPS reception, exact gradient, Hilbert space gradient


A beamforming antenna array is a set of antennas whose outputs are weighted by complex values and combined to form the array output. The effect of the complex valued weights is to steer lobes and nulls of the array pattern to desired directions. These directions may be unknown and so the antenna weights must be adjusted adaptively until some measure of array performance is improved, indicating proper lobe or null placement.

An adaptive algorithm to adjust the complex weights of an antenna array is presented that nulls high power signals while allowing reception of GPS signals as long as the signals arrive from different directions. The GPS signals are spread spectrum modulated and have very low average power, on the order of background thermal noise. Simulations of the adaptive algorithm minimize the output power of the array to within 5 dB of the background noise level.

The adaptive algorithm, named the Hilbert-space-based (HSB) gradient method, is based on the steepest descent algorithm and implements an efficient, exact gradient calculation.

With M antennas in the array, only M − 1 weights are adjustable; one antenna weight is held constant to prevent the algorithm from minimizing the output power trivially by zeroing all weights thus preventing the reception of any signal by the array. It appears that M − 1 adjustable antenna weights can null M − 1 unwanted signals (jammers). However, in the course of the algorithm development, a few configurations of antennas and jammer arrival directions were found where this is not true. Even when the jammer arrival directions are known (‘oracle’) certain configurations are mathematically impossible to cancel.

The oracle solution has a matrix formulation and under certain conditions an exact solution for antenna weights to annihilate the jammers can be found. This provides an excellent comparison tool to assess the performance of other adaptive algorithms.

The HSB gradient adaptive algorithm and the oracle solution are both implemented in Matlab. Outputs of both are plotted for comparison.