Importance Sampling Book

	Preface
1	Elements of Importance Sampling	1
1.1	Rare events and simulation	1
1.2	Fast simulation	2
1.3	Optimal biasing	4
1.4	The simulation gain	8
2	Methods of Importance Sampling	9
2.1	Conventional biasing methods	10
2.2	Adaptive IS - optimized biasing	25
2.3	Combined scaling and translation	34
2.4	Other biasing methods	36
3	Sums of Random Variables	47
3.1	Tail probability of an i.i.d. sum	48
3.2	The g-method	49
3.3	The inverse IS problem	55
3.4	Approximations for tail probability	57
3.5	Asymptotic IS	61
3.6	Density estimation for sums	71
4	Detection Theory	85
4.1	The Neyman-Pearson lemma	85
4.2	Approximations for the error probabilities	88
4.3	Asymptotically constant error probabilities	91
4.4	Densities for the log-likelihood ratio	93
5	CFAR detection	97
5.1	Constant false alarm rate detection	97
5.2	IS for CFAR algorithms	99
5.3	Multiplier determination-adaptive optimization	101
5.4	Exponential twisting for CA-CFAR	101
5.5	Approximations for CA-CFAR	105
5.6	The GM-CFAR detector	107
5.7	Point of application of biasing	111
5.8	FAP decomposition for SO detectors: CA and GM	113
5.9	Examples in CFAR detection	121
5.10	STAP detection	132
6	Ensemble CFAR detection	137
6.1	Ensemble processing	137
6.2	The E-CFAR detector	139
6.3	Performance in nonhomogeneous clutter	145
6.4	Results for some ensembles	146
6.5	Randomized ensembles	153
6.6	Tuning the multipliers: homogeneous operating points	161
7	Blind Simulation	167
7.1	Blind biasing	167
7.2	Tail probability estimation	169
7.3	CFAR detection	174
8	Digital Communications	185
8.1	Adaptive simulation	185
8.2	DPSK in AWGN	187
8.3	Parameter optimization	190
8.4	Sum density of randomly phased sinusoids	194
8.5	M-ary PSK in co-channel interference	196
8.6	Crosstalk in WDM networks	211
8.7	Multiuser detection	223
8.8	Capacity of multi-antenna systems	230
	References	235
	Index	241