Examination of Transmission Zeros in the MIMO Sensor-Based Propagation Environment Using a New Geometric Procedure

Area of Science:

• Electrical Engineering and Computer Science
• Applied Mathematics

Background:

• Transmission zeros are critical for modern communication systems.
• The classical Smith-McMillan factorization method for calculating transmission zeros is computationally intensive and time-consuming.
• There is a need for faster, more efficient methods to determine transmission zeros.

Purpose of the Study:

• To introduce a novel geometric procedure for calculating transmission zeros.
• To develop an efficient algorithm for multivariable telecommunication systems using a transfer-function approach.
• To reduce computational efforts and overcome technological limitations in transmission zero detection.

Main Methods:

• A new geometric-originated approach is proposed.
• The method is applied to multivariable telecommunication systems represented by transfer functions.
• Performance is evaluated through simulation examples, comparing computational time against the Smith-McMillan factorization.

Main Results:

• The proposed geometric method significantly reduces computational burden compared to Smith-McMillan factorization.
• For a 5x5 matrix, the new method was substantially faster than Smith-McMillan.
• Computational time savings increase with matrix dimension; for 100-element matrices, differences were substantial (QI=100, QII=60).

Conclusions:

• The new geometric approach offers a more efficient solution for calculating transmission zeros.
• This method overcomes limitations of existing techniques, particularly for large-scale systems.
• The findings confirm the potential of geometric methods in accelerating computations for communication system analysis.