6 votes
Accepted

Nyquist noiseless channel capacity; how can bit-rate be two times the bandwidth?

I think you're confusing two different (but related) terms. Nyquist says that in a channel of bandwidth $B$ you can transmit up to $2B$ orthogonal pulses per second. So, $R_p \leq 2B$, where $R_p$ is ...
MBaz's user avatar
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6 votes
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Are capacity and spectral efficiency identical for a dicrete-time digital signal?

The capacity is a property of a channel. A channel can transport no more than a certain amount of information per channel use. When we use a fixed modulation and coding scheme ("discrete-time ...
Florian's user avatar
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4 votes

Are capacity and spectral efficiency identical for a dicrete-time digital signal?

I do not know where the 1/2 factor came from in the answer I linked, or why they've used variance of the discrete noise in the SNR, but it appears that capacity and spectral efficiency are the same ...
AlexTP's user avatar
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4 votes

What is the intuition explaining the Shannon-Hartley theorem?

Echoing what already answered: you are approaching this backwards. SNR is a concept that's very fundamental and applicable to way more things that just channel capacity. If you have a signal $y(t)$ ...
Hilmar's user avatar
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4 votes
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What is the intuition explaining the Shannon-Hartley theorem?

Fundamentally, the signal-to-noise-ratio (SNR or $S/N$) is the ratio of signal power to noise power and that power ratio and is usually expressed in $dB$. Shannon and Hartley (likely collaborating at ...
robert bristow-johnson's user avatar
3 votes
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Capacity and channel estimation algorithms: explanation of results

The channel capacity expression you cited is the one with CSI at receiver that means the receiver know perfectly the realization of fading channel, denoted $\mathbf{H}$, but not the realization of ...
AlexTP's user avatar
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3 votes
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Are there any techniques that can achieve higher transmission rate than Shannon capacity?

No, but the capacity formula you mentioned assumes a very specific channel. Other channels may have larger capacities (see "faster than Nyquist signaling", for example in this question). ...
MBaz's user avatar
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2 votes

Log-normal shadowing and mean power

I guess that the confusion was exactly that $$ \mathbb{E}[10^{P_\text{dBm}/10}] \neq 10^{\mathbb{E}[P_\text{dBm}]/10}. $$ Even though the expected dBm under normally distributed shadowing would be $0$,...
Mundo's user avatar
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2 votes

Are capacity and spectral efficiency identical for a dicrete-time digital signal?

With the help of comments and the other answer, you will certainly resolve your terminological confusion about spectral efficiency vs. capacity. In my answer, I address the "1/2 factor and ...
V.V.T's user avatar
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2 votes

Difference: Ergodic channel capacity and spectral efficiency

Loosely speaking: Capacity is the supremum of data rate that one can send data with arbitrarily small error probability over a given channel; ergodic capacity is also the supremum of rate with ...
AlexTP's user avatar
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2 votes

Achievable rate for MIMO channel with estimated channel matrix

I found the following relation which answers my question $$R=\log\det \left(\boldsymbol{C}_{MMSE}^{-1}\right)$$ where $\boldsymbol{C}_{MMSE}$ is the covariance matrix of the error in the data $\...
user3350919's user avatar
2 votes
Accepted

Concatenated Deletion & Sticky Channel Capacity

The identical and identically distributed (IID) binary deletion and sticky channels are both general repeat channels each characterized by a discrete probability distribution of repeating an input bit ...
Olli Niemitalo's user avatar
2 votes

Relationship between Nyquist and Shannon channel capacity

They become the same if $M = \sqrt{1+SNR}$ Nyquist simply says: you can send 2B symbols per second. Shannon extends that to: AND the number of bits per symbol is limited by the SNR. Shannon builds on ...
Hilmar's user avatar
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2 votes

Relationship between Nyquist and Shannon channel capacity

Well, I think both are unrelated unless you have some constraints. The Nyquist channel capacity says you can transmit $2B\log_2(M)$ bits per second for given channel bandwidth $B$. It does not say ...
jithin's user avatar
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1 vote

OFDM system capacity if we double the subcarriers

The capacity of $A$ is $W\log_2(1+\text{snr})/1.1/NW$ The capacity of $B$ is $2W\log_2(1+\text{snr}/2)/1.05/NW$ So the capacity of $B$ is larger than that of $A$.
c1119's user avatar
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1 vote
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Example of Entropy and Channel Capacity Computation

Since all transitions are equally likely, there is no information in the channel output about the source. Hence, the mutual information, and, consequently, the channel capacity, are zero in this case. ...
Matt L.'s user avatar
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1 vote
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Modulation with Maximum Likelihood decoder and capacity

You are correct that OFDM has several drawbacks, such as the required guard band, number of pilots, and its high PAPR. Many alternatives have been developed, with different sets of pros and cons. ...
MBaz's user avatar
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1 vote
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Assessing relative wireless channel quality using Capacity and Condition Number CDFs

What the CDF of the capacity tells you is how it distributes, which allows you to say something about the quantiles. Ergodic capacity tells you: what capacity will we see on average? Quantiles are ...
Florian's user avatar
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