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Questions tagged [maximum-likelihood-estimation]

Use this tag for any question regarding or utilizing the Maximum Likelihood (MLE / ML) method.

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Equivalence of ML and DFT Peak Finding for Single Tone Estimation

My understanding is Maximum Likelihood and DFT Peak Finding for a single tone produce the same results assuming the ML is restricted to the same frequencies as the DFT. I was wondering if there was ...
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805 views

Maximum Likelihood Detection of Signal Vectors in Gaussian Noise

Consider a binary-input additive white Gaussian noise channel. Let $\mathbf{x}_0 = (\sqrt{Es},\sqrt{E_s},⋯,\sqrt{E_s})$ and $\mathbf{x}_1 = (-\sqrt{E_s},-\sqrt{E_s},⋯,-\sqrt{E_s})$, be two codewords ...
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52 views

Why Isn't the ML Estimator (MLE) in MIMO Spatial Multiplexing Obtained by the Least Squares Solution?

In the simplest scenario of MIMO spatial multiplexing: $$\mathbf{y} = H\mathbf{s} + \mathbf{n}$$ where: $\mathbf{s}=[s_0,s_1,...s_{M-1}] \\\mathbf{y}=[y_0,y_1,...y_{N-1}]$ $\mathbf{n}=[n_0,n_1,......
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MLE parameter estimation — confusion regarding some terms in the pdf of complex normal r.v (Part 2)

This question is based on the application of the pdf which was an earlier question of mine asked here Confusion regarding pdf of circularly symmetric complex gaussian rv If $v \sim CN(0,2\sigma^2_v)$ ...
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MLE formulation — confusion regarding the terms in the equation (Part1)

If $v \sim CN(0,2\sigma^2_v)$ is a circularly complex Gaussian random variable which acts as the measurement noise in this model $$y_n = x_n + v_n \tag{1} $$ where $x \sim CN(0,2\sigma^2)$, then is ...
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203 views

Optimum Filter Signal Detection for Non AWGN Channels

I have been reading this question and it confirms that the matched filter is the maximum-likelihood receiver in the presence of additive white Gaussian noise. So in the AWGN channel it maximizes the ...
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1answer
332 views

Cramer Rao Lower Bound for Cross Correlation (Time Shift Estimation)

UPDATE 2 Okay, I think I understand now why the defined CRLB is not applying to my use case. In my use case, we have very high SNR, and the the first signal $x_1$ is always the same. So the classical ...
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99 views

Unable to understand what notations to use in formulating and example of Maximum likelihood estimation

The received noisy signal $y_n \in \mathbb{R}$ is expressed as: \begin{align} y_n = \mathbf{h}^\mathsf{T}\mathbf{u}_n + w_n. \tag{1} \end{align} $\mathbf{h} = [h_0,h_1,\ldots,h_{p-1}]^\mathsf{T} \in \...
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2answers
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Why maximum likelihood estimation method is taken as the benchmark for comparing with other methods?

In many research articles the performance of an estimation method is compared to that of the ML estimation performance. If the performance of the method does not achieve the ML estimation performance, ...
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346 views

Maximum likelihood estimator of active time delay and passive time delay

A typical time delay estimation problem has the model: $$ \begin{align} x_1(t) &= s(t)+ n_1(t) \\ x_2(t) &= a s(t-D) + n_2(t) \end{align} $$ Where $n_1$ and $n_2$ are considered to be ...
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520 views

Matlab : How to implement the likelihood expression

I need to check if the estimation algorithm has converged or not. I am using the Maximum Likelihood estimation method. For convergence check, we see if the log-likelihood has reached its maximum value ...
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286 views

Maximum Likelihood for Colored Noise

I have the following question about the maximum likelihood (ML) in presence of inter-symbol interference and colored noise. Assume the communication system is as follows. Information source, ...
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562 views

Matlab: Help in understanding if the example for Maximum Likelihood Equalizer is properly functioning

I am stuck in the part where I need to apply the MLSE Equalizer with Viterbi code. The equalizer is an optimal. I am using the Communication Toolbox http://www.mathworks.com/help/comm/ref/comm....
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1answer
657 views

What do we espect Likelihood function used for?

In my understanding, I let make a example. For example, you can see in the following picture. Consequently, We want to find ^sigma. and We have already known the observation data(which is random ...
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208 views

Maximum Likelihood Through a Noisy Channel

I have random variables $X_1, X_2, \cdots, X_m $, which can take $n$ values and is distributed iid according to $\Theta=(\theta_1, \theta_2, \cdots, \theta_n)$. That is $X_k$ can take values $\{1,2,\...
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986 views

Maximum Likelihood Estimation in Presence of Colored Noise

I am trying to test system identification in presence of measurement noise (1) A white Gaussian noise (2) Colored noise - pink, violet. When we are estimating parameters we do so in presence of iid, ...
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119 views

Maximum Likelihood Derivation

as you can see on page 314 the derivation of the ln[f etc.] equation is done via the matched filter that i have also provided below. i would like to know how this equation is used to derive the ln[f ...
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296 views

Minimum SNR Requirements for Maximum Likelihood Frequency Estimation

In certain applications, you have enough SNR available to, for example, perform an FFT and identify peak location and hence the signal frequency. If my understanding is correct, parameter estimation ...
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2k views

Differences using Maximum Likelihood or Maximum a Posteriori for Deconvolution / Deblur?

Are there any differences if you use Maximum Likelihood or Maximum a Posteriori to estimate the Point Spread Function for image deconvolution?