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Foreword
In the survey estimation of the communication system of the latest research articles, I found CRLB (Cramer-Rao lower bound) appearance rate is very high. This also explains the concept that has long been proposed so far can follow their trend, it is worth to grasp. Therefore, simply wrote this article to outline the next CRLB estimation algorithm and Scientific Research.
Why should grasp CRLB
I always feel, before talking about a thing, we must first explain why to learn this stuff, the following brief description of the role and functions in the CRLB.
CRLB potential usage scenarios:Define the upper bound estimate of the performance of various types of algorithms
If you master the CRLB derivation can have the following advantages:
■ 1. algorithm similar to other papers, CRLB can be used as a contrast curve on simulation of FIG.
■ 2. As a theoretical upper bound, the distance CRLB line can define the pros and cons of the new algorithm proposed article.
■ 3. For many new algorithms framework, under which derive CRLB is itself a contribution to the point of the article.
■ 4. In the simulation, the gap value is reasonable CRLB can help find errors.
I think the biggest advantage is that CRLB, no matter what your estimation algorithm scene, what kind of problem, which is a kind of model can be replicated, a method of the generic.
Some recent estimation algorithm involving CRLB communication papers
CRLB brief introduction
Communication is the most important CRLB-- under Gaussian noise modeling
Because 99% of communications problems are based on the assumption of Gaussian noise, and this is very easy to assume that we derive necessary to solve CRLB PDF. Therefore, the algorithm for solving communication CRLB becomes relatively simple.
Vector circumstances CRLB
Real case
That is, first calculated Fisher information matrix, then the inverse, get CRLB.
In the Gaussian noise scenario, it can be further particular:
the majority of cases, when the variance has nothing to do with the estimated parameters, the equation can be further simplified as:
Complex situation:
Fisher information matrix (I) is given by the following formula.
Also, in the case of complex Gaussian noise, there may in particular be:
