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I am currently implementing acoustic FSK modulation and demodulation. I am not a signal processing guy… Since you say you have matched filters, and you mention non-coherent detection, I think you're pretty much of a digital communication person already – the step to being a DSP person is pretty small :) The fully-fledged synchronizer SDR approach So, the ...


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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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There is an optimum loop BW that maximizes the SNR, and this applies to both Symbol Timing Recovery as you inquire about as well as Carrier Recovery. The specific answer depends on the characteristics of the noise source involved in your system, such as clock jitter and phase noise, and the modulation you are using; specifically how the signal energy is ...


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In general the ISI is never severe enough for the symbol timing recovery algorithm not to work, but it does degrade its achievable performance on the $P_{be}$ vs. $\dfrac{E_b}{N_0}$ curve. In other words, for the same error rate, you need better SNR to make up for the ISI. ISI will degrade the S-curve of the Timing Error detector, causing it to flatten a ...


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An easy way to see what's going on is by plotting the signal's eye diagram. With low roll-off factors, the eye diagram will show you that deviating a small amount from the optimum sampling time will decrease the error margin. Note that the signal peaks are not the ideal sampling points. This is the eye diagram of a sinc pulse (zero roll-off): With larger ...


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One approach could be to perform an FM-detection step (e.g. an atan2() operation followed by a first-order difference) to transform the waveform to measurements of the approximate received frequency versus time. Your FSK signal should then look like a binary-modulated baseband waveform. Then you can apply a nonlinearity to the signal to induce a discrete ...


2

The nonlinear trick is in fact often used to recover the symbol clock of $\frac \pi {2N}$ phase-shifted signals, e.g. BPSK, QPSK: Squaring samples $x[n]$ (or even taking $x^4$) leads to a removal of phase information, and you can then optimize timing with something that is pseudo-derivate based like Müller&Muller. Now, the problem with QAM is usually ...


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If you postulate that receiever's clock is perfect, then you want to make the transmitter send symbols every $T_s \pm \varepsilon$ seconds, where $T_s$ is the symbol period according to the receiver. This is easily achieved by using a very high sampling rate in the transmitter. Let's assume $T_s=1$ and you need a deviation of $\pm 0.01$. This deviation ...


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Preamble: This answer is about timing recovery in a sense of symbol synchronization, i.e. finding the proper sampling phase of a baseband signal. Based on the stated requirement of only 8 samples per symbol, I will assume that you are employing a fully digital approach to timing recovery. That means that you have no control over the times of sampling by ADC. ...


1

The Symbol Synchronizer block is a PLL-based synchronizer that is trying to estimate the symbol clock period and symbol clock phase (aka timing offset) based on the samples coming in that represent the data symbols. Being a PLL configured with static parameters, there is a fundamental trade off between acquisition speed and tracking stability of the symbol ...


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Below is the constellation diagram of 8 QPSK, The circles you see below are modulation symbols. The alphabet A here is the set of all these 8 possible symbols that are equally likely to be transmitted. Each symbol represents a bit pattern as you see in the diagram. each time a symbol is transmitted that bit pattern is essentially transmitted


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Your results are not showing that the data is being "filtered out" necessarily but that you are using a non-linear phase filter resulting in group delay variation over your passband, as evidenced by the spread in phase. Don't use a Butterworth filter to model this. Instead use filters derived from either firls or firpm (remez in Octave) which are linear ...


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Are there any superior ways of doing symbol sync? Yes! As you've noticed, your initial estimation of timing isn't "valid" forever. This might be caused by clock jitter, or simply remaining sampling rate offset. It's a very common problem in communication receivers. What you can of course do is that you simply do the same estimate you did at the beginning ...


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For PAM signals, the squaring creates a spectral component at $\dfrac{1}{T}$. Consider the following trigonometric identity to understand why this is the case: $$\cos^2\left(2\pi \dfrac{1}{2T}\right) = \dfrac{1}{2}+\dfrac{1}{2}\cos\left(2\pi \dfrac{1}{T}\right)$$ The phase of that spectral component at frequency $\dfrac{1}{T}$ is a measure of the evenness ...


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The answer is to NOT down-select to one sample per symbol until after using the Gardner Timing recovery since the TED requires 2 samples per symbol. If the equalizer is running at 2 samples per symbol, that is perfect for use with the Gardner; why would you down-select to one sample per symbol after the equalizer? You can downselect after timing recovery ...


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You are mixing up two different notions of sampling. In a digital communications system, the received (analog, continuous-time) signal is passed through an A/D converter so that the needed further processing (e.g. matched filtering) can be implemented on a programmable DSP processor or as a MATLAB or C++ program or on a special purpose ASIC. The sampling ...


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