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For lower-cardinality PSKs like the QPSK, the "classical" way is to take the signal to the $M$th power, $M$ being the number of constellation points. From the shape of an $M$-PSK modulation, it's clear that the constellation points are $e^{j2\pi \frac mM},\, m =0,1,\ldots,M-1$, and putting that to $M$th power yields $${\left(e^{j2\pi \frac mM}\...


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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 if these bits would be received reliably at the receiver in the presence of noise or channel distortion. I am assuming here that bandwidth limit is imposed by ...


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When we talk about linear phase in an LTI system we are talking about the phase of the FFT of the time domain system response. Thus the linearity is with respect to the frequency of the signal and not time shifts. This is where I think you have the confusion. The phase is linear in $\omega$, the frequency.


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For the classical baseband channel model for multipath, $h(t)=\sum_ka_k\delta(t-\tau_k)$, the frequency response $H(f)=\sum_k a_ke^{-j2\pi f\tau_k}$. If $K=1$, single tap the phase would have been linear $\phi(f)=2\pi f\tau_k$. But for different path incident on the receiver, there is no guarantee that phase is linear. But let us see how phase changes ...


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Does that mean awgn function behavior depends on the zero padding (length of the signal)? Yes, it does depend on the length of the signal. How does the 'awgn(input_signal,snr_db,'measured')' function calculates the input signal power? For an input signal of length $N$, $x[n]$, the awgn function calculates the power as $\frac{1}{N} \sum_{n=1}^N |x[n]|^2$. ...


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You are right, coherence bandwidth is the frequency domain counterpart of delay spread. However, to achieve diversity across antennas the spacing between the antennas is important "relative to the environment".Let me explain that a bit more. In a user mobile phone you would typically find the order of wavelengths seperation between antennas sufficient to ...


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Yes indeed it will be (although we could argue that it may not be necessarily for all distances since the phase is cyclical!). In free space the signal propagates at the speed of light, therefore this sets the wavelength in distance based on the frequency transmitted according to: $$\lambda = c/f$$ Where $c$ is the speed of light in meters/second (or ...


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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 Nyquist Nyquist doesn't really tell you the actual channel capacity since it only makes an implicit assumption about the quality of the channel. Shannon makes ...


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Because DMRS is only sent if there is data to transmit and, therefore, narrowband while SRS, as the term sounding suggests, is not associated to any data transmission and also wideband. For example, SRS can be used by base stations to choose the best portion of the UE channel bandwidth to schedule next PUSCH.


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OFDM subcarriers are packed relatively tightly together. If you look at the original OFDM signal in the frequency domain, you may wonder why adjacent subcarriers are not interfering with each other. The answer is that subcarriers are orthogonal to each other. Even adjacent subcarriers, have 0 influence on each other, and are independent in that sense. It ...


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Next, I receive the signal at two different locations with different distances from the receiver. Will the phase of the received signals be different for the two sites? It depends on the time reference used at the receiver. If it is perceived as being phase shifted, it needs to be with respect to a particular time reference. Phase of a received signal is ...


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Phase measurement depends on a reference time or point. If your time reference or clock sync is the same speed-of-light signal, then the phase of a signal with reference to itself is zero. If your clock or time reference is broadcast perpendicular to your Signal, then the phase could be different if the distance between the two points isn’t an exact ...


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In contrast to your previous question(Why multi-path channel has linear phase within the coherence bandwidth?), the coherence BW in mmWave may not be relevant considering delay spread alone. If you see eq (7) of the reference, the $H$ has contribution from all the $N_p$ paths, even though channel is mentioned as narrow band (flat fading). This is true till ...


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Looking at the equation you have posted, it seems $l$ is the variable for $N_p$ multipaths and for each path, there will be a constant delay $\tau_l$, an attenuation $\alpha_l$, a doppler shift in the carrier $\nu_l$ , angle of arrival at the receiver $\mathbb a_{\mathbf R}$ and angle of departure at transmission $\mathbb a_{\mathbf T}$. And both of these ...


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