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2 results

  • 5 - Linear Least-Squares Regression and Binary Classification

  • Jeffrey A. Fessler, University of Michigan, Ann Arbor, Raj Rao Nadakuditi, University of Michigan, Ann Arbor
  • Book:
    Linear Algebra for Data Science, Machine Learning, and Signal Processing
    Published online:
    01 November 2024
    Print publication:
    16 May 2024, pp 143-196

  • Summary

    Many applications require solving a system of linear equations 𝑨𝒙 = 𝒚 for 𝒙 given 𝑨 and 𝒚. In practice, often there is no exact solution for 𝒙, so one seeks an approximate solution. This chapter focuses on least-squares formulations of this type of problem. It briefly reviews the 𝑨𝒙 = 𝒚 case and then motivates the more general 𝑨𝒙 ≈ 𝒚 cases. It then focuses on the over-determined case where 𝑨 is tall, emphasizing the insights offered by the SVD of 𝑨. It introduces the pseudoinverse, which is especially important for the under-determined case where 𝑨 is wide. It describes alternative approaches for the under-determined case such as Tikhonov regularization. It introduces frames, a generalization of unitary matrices. It uses the SVD analysis of this chapter to describe projection onto a subspace, completing the subspace-based classification ideas introduced in the previous chapter, and also introduces a least-squares approach to binary classifier design. It introduces recursive least-squares methods that are important for streaming data.

  • Interference cancellation for higher harmonics of supply-modulated efficient RF power amplifier systems

  • Mohammad Omer, Farasat Munir
  • Journal:
    International Journal of Microwave and Wireless Technologies / Volume 9 / Issue 4 / May 2017
    Published online by Cambridge University Press:
    18 August 2016, pp. 729-739

  • In building highly efficient transmitters of today, one is forced to sacrifice linearity for efficiency. Some of the highest power amplifier efficiency figures are reported by envelope tracking (ET) amplifiers. These amplifiers can generate strong higher-order harmonics, which can lead to interference with receivers operating at the harmonic frequencies. Using non-linear interference cancellation, we can help to remove the interference being caused in those receivers. This paper looks at the problem of modeling the third and second-order harmonic emission from an ET amplifier. It derives the non-linear kernel for estimating such interference. This kernel has been rigorously expanded to show its correlation with the various harmonics and its effectiveness in predicting the harmonic content. We then set up an envelope amplifier test-bench to capture harmonic signal content and cancel it using the derived kernel model. The experiment yields excellent agreement with theory and provides a validation of the system and concept.