Invariant Random Processes................................................................ 626

12.3.1. Introduction............................................................................ 626

12.3.2. Problem Statement................................................................. 628

12.3.3.1. SIRVs with Known Characteristic PDF............... 630

12.3.3.2. SIRVs with Unknown Characteristic PDFs ......... 631

12.3.3.3. Hankel Transform Approach................................ 632

12.3.4. Examples of Complex SIRVs................................................ 634

12.3.4.1. Examples Based on the Characteristic PDF ........ 634

12.3.4.2. Examples Based on Marginal

Envelope PDF....................................................... 641

12.3.4.3. Examples Using the Marginal

Characteristic Function......................................... 651

12.3.5. Significance of the Quadratic Form of the SIRV PDF......... 656

12.3.6. Conclusion ............................................................................. 664

12.4. Computer Generation of Simulated Radar Clutter

Characterized as SIRPs........................................................................ 665

12.4.1. Introduction............................................................................ 665

12.4.2. Preliminaries .......................................................................... 666

12.4.3. Two Canonical Simulation Procedures

for Generating SIRVs ............................................................ 670

12.4.4. Performance Assessment of the Simulation Schemes .......... 675

12.4.5. Conclusions............................................................................ 677

12.5. Distribution Approximation to Radar Clutter

Characterized by SIRPs ....................................................................... 680

12.5.1. Introduction............................................................................ 680

12.5.2. Definitions .............................................................................. 682

12.5.3. Goodness of Fit Test.............................................................. 682

12.5.4. Distribution Approximation................................................... 689

12.5.5. Parameter Estimation............................................................. 694

12.5.5.1. Estimation of Location and Scale Parameters ..... 695

12.5.5.2. Shape Parameter Estimation................................. 696

12.5.6. Assessing the Distributional Properties of SIRVs ................ 697

12.5.7. Distribution Identification of SIRVs ..................................... 700

12.5.8. Alternative Method for Parameter Estimation ...................... 704

12.5.9. Conclusions............................................................................ 705

12.6. Conclusions.......................................................................................... 705

12.6.1. General Remarks.................................................................... 705

12.6.2. Suggestions for Future Research ........................................... 706

The problem of weak signal detection in nonGaussian noise is of interest to

engineers in many disciplines such as, radar, sonar, digital communications, and

radio astronomy. In this research, we are interested in the detection of weak radar

targets in a strong clutter background. When a signal is transmitted by a radar, the

on the environment. Any return other than that from the target is an unwanted

signal and is defined as radar clutter.