Optimization of the Training Symbols for Minimum Mean Square Error Equalizer

摘要

The theory of Minimum Mean Square Error (MMSE) and Symbol Error Rate (SER) will be introduced and used as a parameter of analysis, we will find the optimized number of training symbols for different amounts of data. The training symbols are used in adaptive channel equalization where the communication channel is totally unknown, the training symbols are the data sent via the channel, the receiver already know which symbols it will receive, this way the equalizer can analyse the unknown channel and configure it's coefficients to improve the communication. Simulations of a communication channel made in Matlab together with the parameter SER will show the optimized settings for different amounts of numbers of symbols for different values of E_b/E_0 (the energy per bit to noise power spectral density ratio). After the simulations results, the settings will be implemented in a real hardware device (NI RF VSG PXI-5670 Vector Signal Generator and NI RF PXI VSA 5661 Vector Signal Analyzer) and the concepts of Modulation Error Ratio (MER) and Additive White Gaussian Noise (AWGN) will be used to evaluate the communication. The main purpose of this paper is verifying the theoretical assumptions concerning the impact of the number of training symbols on the quality of channel equalization in case of a real hardware in the form of software-defined radio (SDR). The real experiments brought the unique results, which can be used for the implementation of the feed-forward software defined equalization.