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Common Approaches for Commercial Denoisers Commercial denoisers are different than what you'd see on most papers. While on papers the results are mostly using objective metrics (PSNR / SSIM) and are evaluated vs. Additive White Gaussian Noise (AWGN) with high level of noise real world images are mostly with moderate level of noise with Mixed Poisson ...


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You have a set of message set $m_i$, $0 \le i \le N-1$. (For example, QPSK will be $N=4$). For the transmitted message $m_i$, the corresponding symbol vector is $\textbf{x}_i$, and the received symbol vector is $\textbf{y} = \textbf{x} + \textbf{w}$, where $\textbf{w}$ is the AWGN at the receiver. The above is a simplified baseband model assuming a simple ...


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Sorry for late reply .. I was little bit busy. you have mistakes in your code. Although mythology is right, you have mistakes in some parameters. Check this paper "Low-Complexity Equalization of Orthogonal Signal-Division Multiplexing in Double-Selective Channels" Then, Modify your code following part II in that paper. It's with details there, if you ...


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Traditionally, OFDM became popular in WiFi and LTE because the channel model consisted of multi-path. That is, the radio signal transmitted in 1-6GHz frequencies bounced from various obstacles (walls, trees, cars, humans) at the receiver. Of course this is time varying because obstacle position or transmitter/receiver position also changes. But to simplify ...


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Basically your problem is called Blind Deconvolution. It means we want to estimate both the operator and the input given the output. You model is Linear Time Invariant Operator so we have LTI Blind Deconvolution. In general blind deconvolution is ill poised problem. So we need to make assumptions about the model. The more assumptions the better the chance ...


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It is indeed possible to formulate this setting in terms of matrix-vector products. First, let us re-formulate your $x$ (notice throughout that I use bold letters for vectors and matrices): $$x = \begin{bmatrix}\mathbf{x}_1 & \mathbf{x}_2 & \ldots & \mathbf{x}_8\end{bmatrix}$$ where $\mathbf x_k$ is the $k$ column of $x$. I define the vertically ...


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Well, in your example, the channel isn't exactly sparse. It has been shown that $\ell_0$ minimization can recover any $K$-sparse vector $x$ from observations $\Phi x$ as long as $2K < {\rm spark}(\Phi) \leq M+1$, when $\Phi$ is $M \times N$ (so that $x$ is $N\times 1$), i.e., $K<M/2$ more or less. This is a necessary condition which means that if $K$ ...


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Basically I'd do something like: $$ \frac{ {\sigma}_{2}^{2} }{ {\sigma}_{1}^{2} + {\sigma}_{2}^{2}} {r}_{1} + \frac{ {\sigma}_{1}^{2} }{ {\sigma}_{1}^{2} + {\sigma}_{2}^{2}} {r}_{2} $$ This is the optimal weighing given knowledge of the Variance only (Well, linear). Basically it assumes the cross correlation is 0. Derivation There are many ways to derive ...


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Without more knowledge on $X$, we cannot say a lot. However, if it is IID with mean $\mu$ and variance $\sigma^2$, the sample mean $\hat{\mu} = \frac{1}{N}\left(\sum_{n=0}^{N-1}x_n\right)$ is unbiased, since: $$E[\hat{\mu}] = E\left(\frac{1}{N}\sum_{n=0}^{N-1}x_n\right) = \frac{1}{N}\sum_{n=0}^{N-1}E\left(x_n\right) = N\mu/N=\mu\,.$$ And its variance goes to ...


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The training sequence should be at the same spacing as the equalizer when considering its sampling at the input to the equalizer. Adaptive algorithms converge to the least square solution based on the error between the received sequence and the transmitted sequence (known when a training sequence is used). Further, the equalizer can only determine a solution ...


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It's a spurious artifact due to not referencing your phase generation to the center of your data window, and not doing an fftshift before the fft to place your phase reference point at fft input index 0. e.g. For varying frequencies, either you have to know, generate, or want the phase at location T/2 of your continuous sinusoid. The phase result of an ...


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There is a mistake int the conv function which you are using in your code. In ofdm, the channel must be convoluted with every symbol. the link provided in the above comments are ok, but you need to modify them according to your parameters. so replace the command of y = conv(x_ifft_p2s,h,'same'); by below command: for jj = 1 : n_ofdm_sym y(jj,:) =...


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The clue is that without zero-padding, the circulary shifted sequence is just a shifted version of the periodic continuation of the original sequence. That's why without zero-padding the magnitudes of the DFTs of both sequences are identical. When you use zero-padding, the two sequences cannot be obtained from each other by pure shifting. So the DFTs must ...


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For simplicity I will show an approach Id' use on 1D signal (A row of real world image). You will be able to extend it and I will add few remarks on how you can even gain from having 2D data. The general idea is as sketched in Estimate the Discrete Fourier Series of a Signal with Missing Samples. The trick here is to exploit prior information. In our case ...


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I'd do some small adjustments to your idea (You really nailed them). Assumptions The Signal Model - Signal + Additive White Gaussian Noise (AWGN) Probably we could generalize it more but this is beyond the scope of this question. The DFT of the signal contains Peaks with relatively small roll off This is important as we're almost saying the Signal is a ...


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There are indeed many peak detection algorithms, and no clear consensus on which ones are "good" or "bad". But for what it's worth, your approach makes sense. Using median or other quantiles to detect sparse signals is common, e.g. the "median clipping" stage in Lasseck (2014), Large-scale identification of birds in audio recordings. In effect, you're ...


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You can approach this problem as a special case of the "$k$-simple bounded signal" class described in (Donoho & Tanner, 2010 - Precise Undersampling Theorems ), see page 2, Example 3. Particularly, your signal is a "0-simple" signal, i.e. your values are either 0 or some constant. The problem can easily be scaled to 0 or "some constant" instead of 0 or 1....


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Maximium A Posteriori (MAP) and Maximum Likelihood (ML) are both approaches for making decisions from some observation or evidence. MAP takes into account the prior probability of the considered hypotheses. ML does not. This set of probabilities, known as "a priori" probabilities or simply "priors", is often known imperfectly, but even rough approximations ...


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Actually the first section of the notes in the link your provided are about the most likely value in the Bayesian Framework. So we have a comparison between the Minimum Mean Square Error (MMSE) Estimator and the Maximum a Posterior Estimator. Both are Bayes Estimator, namely they are a loss function of Posterior Probability: $$ \hat{\theta} = \arg \min_{a} ...


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Natural images can seem complicated. However, the set of humanly interpretable images is relatively limited, with respect to all possible images ($24^{x\textrm{millions of pixels}}$). There is a belief that their structure can be better summarized. Indeed, lossless compaction can achieve 2-3 factor ratios, and lossy compression about 8-16 with little ...


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Given no formal system model in the question, I will outline in words what each does and the relation between them. Matched Filter: The MF maximizes SNR when the signal is in additive Gaussian noise. You can go back and look at the derivation of the MF, but it does not include any mention of interference. During the derivation, there is a step where we say ...


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You can use various methods to interpolate the channel - Linear, Polynomial, Sinc Interpolation etc. But what you need to keep in mind is synchronization. You have to make sure that frequency and timing offsets are eliminated or accounted for. Otherwise you will see an error floor in the Channel Estimation Error. Means your Mean Square Error (MSE) for ...


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In both cases, you need to interpolate the channel between the pilots you've got. Both cases are typically suboptimal, since they'd only work perfectly for (a) actual block-fading (which is a convenient model, but doesn't look like reality) or (b) for a channel that is perfectly interpolatable from just a few points of observation in frequency (but that ...


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To expand on jithin's answer: The whole point of OFDM is, as they say, to avoid equalization in time domain! Equalization in time domain requires you to have the same amount of channel state information, but inherently reverses a convolution, and is hence quadratically complex with channel size (i.e. impulse response length in samples), whereas the OFDM ...


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A brief, non-mathy explanation: ML assumes that all hypothesis are equally likely. MAP does not make this assumption. MAP is the optimum criterion, but under some conditions ML is optimum too. When using BPSK, if the bits are independent and equally likely, then ML and MAP are equivalent and ML is optimum. If the bits are not equally likely, then you ...


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Perhaps transferable to your problem, one method from Olyha B., Rutledge J., "TrackPoint System Version 4.0 Engineering Specification", IBM, 1999: 2.2.3 DRIFT CORRECTION Due to the significant temperature sensitivity of the force sensors, it is necessary to recalibrate the zero force origin of each axis on a periodic basis. In order to properly ...


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The best fit time domain solution can be found by constructing two two basis vectors with your known frequency and calculate the coefficients directly. The magnitude and phase can then be directly determined from these values. Let C be a vector of cosine values over your frame and S be a vector of sine values. You then want to find $(a,b)$ so that $aC + ...


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If I understand your problem correctly, let us say $S_1$ and $S_2$ is the pair of signals, where, $W_1$ is the window segment from original signal and $S_2$ is the stretched version of the original signal. Since you do not know the stretching factor, you can only vary it over a reasonable range and check the auto correlation values. For each stretching ...


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Say you got two similar signals when one of them is stretched and you want to know the straching ratio... Seems like you can 1. guess the straching ratio 2. resample the short signal with a resampling ratio equal to your guessed straching ratio. 3. Find the max of the convolution between the signals. 4. Optimize the estimation of the straching ratio using a ...


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