# Analysis and Implementation of Multipath Delay Estimation Using Matrix Pencil

In a wireless transmission scheme (e.g. wireless LAN) sophisticated techniques are used to mitigate the disturbing effects of the time-variant propagation channel. Intersymbol interference (ISI) which arises from the frequency selectivity of the channel can be combatted to enhance the error performance and thus increase the data-rate of the transmission. With the help of adaptive transmission schemes, it is possible to maximize the throughput of the application. All these techniques rely on the knowledge of the wireless propagation channel which underlies the transmission.

Measurement campaigns using different carrier frequencies are conducted in representative surroundings. The goal of these measurements is to gain insight into the propagation mechanisms of a wireless transmission scenario. Based on the acquired data, a model for the channel is then developed. This model can be used in real world applications to provide the above mentioned transmission techniques with the relevant parameters.

Frequency domain data from channel measurements is usually analyzed using the inverse Fourier transform (IFT) to yield the time domain response of the channel. However, due to the relatively low temporal resolution of the inverse Fourier transform, fine multipath delay cannot generally be extracted. To increase the resolution, the Matrix Pencil Method (MPM) can be applied to the frequency domain data. It estimates the time domain impulse response by fitting a sum of complex exponentials to the frequency domain data.

The objectives of the work will be the following:

• Getting acquainted with the technique of the Matrix Pencil Method and acquiring the mathematical background.
• Implementation of the method in a MATLAB environment.
• Comparison of the performance to the inverse Fourier transform. Real world measurement data will be provided as basis for these considerations.

As a result, the work will deliver an understanding of wireless propagation mechanisms and the mathematical intuition for working with the analyzed methods. Implementation of the algorithm in MATLAB will be a useful experience to enhance the understanding of this standard simulation and calculation software.

Subject area Wireless communication, Fourier transform, MATLAB 40% Software, 40% Theory and Algorithms, 20% System and Analysis Dr. Stefan Berger Prof. Dr. Armin Wittneben