Welcome to EDAboard.com

Welcome to our site! EDAboard.com is an international Electronics Discussion Forum focused on EDA software, circuits, schematics, books, theory, papers, asic, pld, 8051, DSP, Network, RF, Analog Design, PCB, Service Manuals... and a whole lot more! To participate you need to register. Registration is free. Click here to register now.

Maximum likelihood principle....

Status
Not open for further replies.

vkekk

Full Member level 3
Joined
Mar 30, 2007
Messages
159
Helped
5
Reputation
10
Reaction score
4
Trophy points
1,298
Activity points
2,211
What is meant by Maximum likelihood principle?

What is Zero forcing criteria and MMSE criteria ?
 

A.Anand Srinivasan

Advanced Member level 5
Joined
Oct 15, 2005
Messages
1,804
Helped
257
Reputation
514
Reaction score
39
Trophy points
1,328
Location
India
Activity points
10,680
maximum likelihood principle is selecting the most probable value.... MMSE is the way of selecting the values with minimum mean for square of the errors....
 

sinu_gowde

Full Member level 2
Joined
Nov 10, 2005
Messages
137
Helped
32
Reputation
64
Reaction score
12
Trophy points
1,298
Activity points
3,490
The maximum likelihood principle states that the set of model parameters that maximize the apparent probability of a set of observations is the best set possible. One rationale for this is that in the limit, such a choice approaches the true value of these parameters (assuming, of course, that the model is a valid one). This can be seen by the argument given below. Interestingly, maximum likelihood is equivalent to maximum compression. An alternative is the so-called maximum a posteriori approach (MAP) in which a Bayesian prior distribution on the parameters is assumed and the maximum is computed taking this prior into account. In terms of compression, MAP estimation correlates to minimizing the number of bits required to send a description of the observations and the model parameters. This formulation is also called the Minimum Message Length method.
 

eroica

Newbie level 4
Joined
Sep 7, 2007
Messages
7
Helped
0
Reputation
0
Reaction score
0
Trophy points
1,281
Activity points
1,329
ML is based on that all symbols are equally likely. It is nothing to do with a priori probability, which is used for MAP. However, if the priori probabilities are the same among symbols, then ML = MAP.


Zero forcing literally forces ISI to be zero. In other words, if H(z) is the channel TF(transfer function), designing a filter that has TF of 1/H(z) can restore the original signal making the frequency response flat over the frequency range because the overall response becomes H(z)(1/H(z)) = 1. However, SNR of the zero forcing is not that good since it also boosts noises of the signal. This is called noise enhancement.


MMSE uses least square algorithm. Let say we have a data comm model like following.

X(z) ---> C(z) ----> Y(z) -----> F(z) -----> + ------> e_k

where X(z)=z-domain version of the transmit signal x_k, C(z)=channel, Y(z)=channel output, F(z)=filter

If we put x_k, which is the original signal, in the adder such that e_k=x_k - z_k (z_k is the output of F(z)), then e_k=x_k - f_k*y_k, i.e., E(z) = X(z) - F(z)Y(z) in z-domain. So we determine F(z) by using E[E(z)Y(z)] = E[(X(z)-F(z)Y(z))Y(z)] = 0 where E[.] operator is statistical mean.
MMSE sense turns out to be better SNR than zero forcing because it has no noise enhancement.
 

Status
Not open for further replies.

Similar threads

Part and Inventory Search

Welcome to EDABoard.com

Sponsor

Top