Book recommendations on DSP, statistical SP and signal detection
The Proakis and Manolakis book is good if you're looking for one book.

If you're looking for depth about statistical signal processing, I recommend the series of three by Steven M. Kay:


Fundamentals of Statistical Signal Processing Volume I: Estimation Theory
Fundamentals of Statistical Signal Processing Volume II: Detection Theory
Fundamentals of Statistical Signal Processing Volume III: Practical Algorithm Development


If you want some more advanced statistical signal processing books, then the ones by Harry L. van Trees might be more your style:


Detection, Estimation, and Modulation Theory (Part I)
Nonlinear Modulation Theory (Detection, Estimation, and Modulation Theory, Part II)
Detection, Estimation, and Modulation Theory, Radar-Sonar Signal Processing and Gaussian Signals in Noise (Part III)
Detection, Estimation, and Modulation Theory, Optimum Array Processing (Part IV)