References & Further Reading

References

1. H. V. Poor, An Introduction to Signal Detection and Estimation, Springer, 2nd ed., 1994

   Chapters III and IV cover the matched filter, GLRT, and colored-noise detection in depth.

2. H. L. Van Trees, K. L. Bell, and Z. Tian, Detection, Estimation, and Modulation Theory, Part I, Wiley, 2nd ed., 2013

   Chapter 3 develops the detection of known and partially-known signals in noise.

3. S. M. Kay, Fundamentals of Statistical Signal Processing, Vol. II: Detection Theory, Prentice Hall, 1998

   The most widely used graduate reference for practical detector design, including GLRT and CFAR.

4. B. C. Levy, Principles of Signal Detection and Parameter Estimation, Springer, 2008

   Modern treatment connecting detection and estimation under a unified decision-theoretic framework.

5. J. M. Wozencraft and I. M. Jacobs, Principles of Communication Engineering, Wiley, 1965

   Classical signal-space development of digital communication; the continuous-time matched filter and Gram--Schmidt construction are foundational.

6. J. G. Proakis and M. Salehi, Digital Communications, McGraw-Hill, 5th ed., 2007

   Chapters 4 and 5 connect detection theory to modulation, giving the standard BPSK/QPSK performance derivations.

7. E. L. Lehmann and J. P. Romano, Testing Statistical Hypotheses, Springer, 3rd ed., 2005

   The statistical foundation for sufficiency, Fisher--Neyman factorisation, and UMP tests.

8. G. L. Turin, An introduction to matched filters, 1960

   The original tutorial introducing the matched filter to the IRE community.

9. J. Neyman and E. S. Pearson, On the problem of the most efficient tests of statistical hypotheses, 1933

   Foundational paper; indirectly motivates the matched-filter construction via the LRT.

10. A. D. Whalen, Detection of Signals in Noise, Academic Press, 1971

    Detailed treatment of continuous-time detection, including colored noise and deflection analysis.

11. L. L. Scharf, Statistical Signal Processing: Detection, Estimation, and Time Series Analysis, Addison-Wesley, 1991

    Unified linear-algebraic treatment of matched filtering, prewhitening, and sufficient statistics.

12. G. Caire, S. Saur, A. Bazzi, Information-theoretic foundations of integrated sensing and communication, 2023

Further Reading

• GLRT performance analysis

  Scharf & Friedlander, 'Matched Subspace Detectors', IEEE Trans. Signal Processing, 1994.

  Shows that the GLRT for subspace signals reduces to a ratio of energies on orthogonal subspaces --- the canonical architecture for radar and sonar.

• Locally most powerful tests

  Van Trees, Vol. I, §3.6

  When SNR is small and parameters are close to the null, LMP tests generalise the matched filter to locally optimal form.

• Karhunen--Loeve expansion

  Poor, §III.A

  Provides the rigorous $L^2$ underpinning for the continuous-time matched filter derivation via eigen-decomposition of the noise covariance.