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The Gardner Timing Error Detector is diagrammed in the graphic below, where two samples per symbol are used, and the error is determined using Prompt*(Late-Early), and when synchronized the center sample (Prompt) will be midway between two symbols. In contrast, an Early-Late approach uses (Late-Early), typically on a correlated symbol response, and when ...
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Yes, of course, you can sum them. The bandwidth of the resulting signal is simply the min/max of the individual signals. If we assume
$$z(t)=x(t)+y(t)$$
Then then bandwidth of $z(t)$ will simply be $[min(f_{min},g_{min}),max(f_{max},g_{max})]$, so in general the you will have $B_z > B_x$
Keep in mind that for any real valued signal $x(t)$ the spectrum ...
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How can I manipulate/control $R_S$?
You usually start with a desired pulse rate $R_S$. Then, the number of samples per symbol is $f_sT_S$, where $f_s$ is the sampling rate and $T_S = 1/R_S$. The resulting signal bandwidth will be $B = (1+\beta)R_S/2$, where $\beta$ is the excess bandwidth in the pulse you choose to use.
In other cases you have a desired ...
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In the case of BPSK, the data rate equals the symbol rate (one bit per symbol). One way to control $R_S$ is to change the modulation. For example, you can increase the number of bits per symbol by choosing a higher order modulation like 16-QAM which has 4 bits per symbol.
There is nothing wrong with your calculation. The plot is a single sided spectrum so ...
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Say you have the receive antennas very close together, like with spacing $\lambda/10$ or similar and they are uniformly spaced in a linear array. As you pointed out the the phase shifts between them will be fairly small, so what does it mean? It means that the spatial resolution of your beamformer will be poor. In the extreme case, consider something crazy ...
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Eventhough Laurent has given a broader sense of the answer, let me put here the communications theory sense ot it.
The concept of instantaneous freqency emerges when you consider Frequency Modulation or Phase Modulation systems, where the message is embedded into the change of the frequency or phase of a carrier signal.
This carrier is typically a single ...
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The notion of instantaneous frequency is (hopefully) consistent with the monochromatic wave model:
$$x(t)=a \cos 2\pi \nu t\,,$$
where $a$ is the amplitude and $ \nu$ the frequency. It would be tempting to compute a similar formula for evolving amplitude and frequency cases, something like:
$$x(t)=a(t) \cos \left(\phi(t)\right)\,.$$
However, this is not ...
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How can we measure the SINR of the nodes: as we do not have the Power x Gain product without the knowledge of Power and Gain of IoT nodes.
Not at all, you have zero information about the N in SINR, and without channel knowledge you also can't have any information on the S, nor the I, even if you knew the transmit powers (which you don't).
Is it right to ...
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no, frequency and phase are not independent quantities. phase is the integral of frequency. and in the VCO (or NCO) inside a PLL, there is an integrator. the frequency is proportional to the input of the VCO or NCO, but the phase (which is what goes into the phase discriminator) is the integral of that.
with feedback, a PLL is a servo-control mechanism. ...
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First you have to know that the vector in $U$ and the vector in $V$ are orthonomal,that is ,$\vec u \vec u^H=I$,and $\vec v \vec v^H=I$.
So now $H=U\Sigma V^H$,and $y=Hs+n=(U\Sigma V^H)s+n$
and $U^H y=\Sigma V^Hs+n$,see the $\Sigma V^Hs$,isn't it like " channel gain $\times$ beamforming $\times$ signal $s$ "?
Now you can also find that according to ...
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You need an estimate of the channel to receive the sequence but the zero-forcing equalizer does not need the channel response as an input. The zero forcing equalizer estimates the channel response. This can be done either with a training sequence, or can be decision directed when signal to noise ratios are high enough.
Given the received signal is the ...
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If the received signal can be written as
$$\mathbf{y} = \mathbf{H}\,\mathbf{x} + \mathbf{n}$$
where $\mathbf{H}$ is the channel matrix, $\mathbf{x}$ is the transmitted vector, and $\mathbf{n}$ is the AWGN of the channel, then a zero forcing equalizer is simply (assuming that the channel matrix is square, and it's estimated perfectly at the receiver)
$$\...
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Signal Processing First _ McClellan
Very readable introduction to signal processing.
Signals and Systems_Haykin
Probably the most readable undergraduate book on signals and systems.
Signals and Systems_Oppenheim
Classical text on upper undergraduate Electrical Engineering introduction to signals and systems. Not an easy read but definetely worth it. ...
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Everyone wants to minimize the power of their circuits, so there's nothing special about energy harvesting devices, at all.
Also, every paper about making communications more reliable while is about making the power usage lower, simply because if you want constant reliability, you can then achieve that with lower power.
Basically, all the research on ...
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