New answers tagged estimation
1
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 ...
2
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 ...
1
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 ...
1
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 ...
1
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 ...
3
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 ...
4
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 ...
1
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 ...
3
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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