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The Gardner Timing Error Detector (TED) when at zero error positions the samples as follows related to the equation for the timing error: Specific to the use of the Gardner TED for higher order QAM I offer the following from my own experience in using it successfully for this purpose: First we note that the Gardner TED can be viewed as a form of the Maximum ...


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The gardner detector, if defined as $T =\mathbb{E}\left[(x_{2i-1} - x_{2i+1})x_{2i}\right]$ is equivalent to $\mathbb E[x_{2i-1} x_{2i}] - \mathbb E[x_{2i+1} x_{2i}]$ Assuming the channel input response is symmetric, and the transmitted data uncorrelated. If the sampling occurs before the correlation between $x_{2i}$ and $x_{2i-1}$ will be stronger than the ...


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Using the formula you would arrive at 5Rs. Pay attention to the spacing given in the formula and the spacing of your actual carriers. The 4-orthogonal FSK system is not at the minimum frequency separation; you could actually fit in 3 more carriers that would still be orthogonal and thus have the same bandwidth as a 7-orthogonal FSK system.


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Doing the summation is the necessary low pass filter step prior to decimation, and an ideal decimation approach when the noise is white (evenly spread across frequency). What this does is ensure that every signal component of every sample is included while the noise gets reduced through averaging (summing is averaging just without the scaling by dividing by ...


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One particular advantage of pi/4 QPSK and pi/4 DQPSK is that there is always a transition between symbols, making demodulation simpler. Differential - PSK (such as DQPSK) can be demodulated without a local oscillator (by comparing previous symbols to the current ones), making for extremely low cost receivers at a modest expense in performance (sensitivity).


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Method 1 is close and Method 2 is even more off. There are a few mistakes: The dB is a relative value, it is always calculated from a ratio of something. It is up to you to know what the reference is. You cannot convert direct values to and from dB and apply them correctly without keeping track of how those values were calculated in the first place. Method 1 ...


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10log(165) - 10log(1) is wrong; 1W is reflected; remember, subtraction of logarithm yields the same as division of numbers the logarithm is taken from. By the way, log(1) is always 0, so this should be a giveaway that this operation can't be right. So, 1.3 dB = 1.3489 W no. Definitily not. 1.3 dB is a unitless factor. You need to refresh what a decibel is,...


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If your error vector magnitude is below the decision threshold between adjacent symbols then there would be no impact on the BER. Thus there will be a point where you can continue to reduce the error vector while not see a change in BER. Ultimately our objective is to minimize the error vector regardless, to maximize performance in lower SNR conditions. Also ...


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In order to measure the ICI power on a subcarrier x (ICI that is caused by all other subcarriers). Simply, consider an ideal system without any source of noise, keep all subcarriers turned on (activated) and turn off subcarrier x (through power loading or bit loading) so that subcarrier x does not convey any data. At the receiver, after FFT, the power on ...


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Since the OP mentions an index of frequency I assume a missing step not shown is an FFT is computed on the M samples, and the algorithm is to determine the maximum frequency. I would not recommend such an approach to determine Doppler offset and fine frequency tuning except for initial acquisition (course tuning), given the computation involved in the FFT ...


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I can't simply just add Asn1 and Asn2 to calculate the total noise, because some signal samples will have opposite phases. On the contrary! Uncorrelated noise is the only thing where adding the noise simply leads to noise with twice the power. So, yes, you simply add the noises, and if you're doing it right, then the resulting noise will have variance ...


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Your signal is 8 samples per symbol. After reviewing your eye diagram it also appears that the signal is only root-raised cosine filtered. It should go through one more root raised cosine filter before final decision (the matched filter in the receiver) for optimum performance in the presence of noise.


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This is numerical noise. You are using floating point math which is never "exact" but only approximate. The problematic line here is ph_ref=wrapToPi(2*pi*f_mix*t);%phase ref for comparison with accumulated phase The argument into your phase wrapping function can get large and the larger the argument, the larger the phase wrapping error will be. You ...


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I suspect the OP is referring to a frequency offset and not a static time offset. If the 1ppm is a frequency offset of the clock frequency and not a static time offset, this could be introduced with an numerically controlled oscillator (so in Matlab this is simply multiplying the datapath signal by $e^{j\Delta f t}$). If that clock is a reference to other ...


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In the Gardner Timing Error Detector (TED), "self-noise" is induced from the zero-crossing jitter caused by the inter-symbol interference (ISI) at these locations due to the pulse shaping filter. The "zero-ISI" pulse shaping filters reduce bandwidth with zero-ISI at the symbol sampling locations for data decision, but this is at the ...


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Self-noise in TED is the effect of pulses that are longer than the symbol period $T$. Consider a noise-free system. If bandwidth is not a concern, you can use short pulses. For example, a (time-domain) raised cosine, or a half-sine pulse. In this case, the duration of each pulse is $T$ and pulses don't interfere with each other; there is no self-noise and ...


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Honestly, I have never read about self-noise in contest of TED algorithm. I think that was introduced as the difference between the error observed by the detector and the expected timing error. For details: I think N. A. D'Andrea and M. Luise, "Design and analysis of a jitter-free clock recovery scheme for QAM systems," in IEEE Transactions on ...


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The noise is colored. If we are to talk of spectral densities (color) then we would best refer to phase noise and not jitter (jitter is the result of integrating the phase noise, and typically after a high pass function given by the typical cycle-cycle jitter measurement). The PLL's phase noise would be a low pass filter of the phase noise from the reference ...


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I work in the field of time and frequency in the design of atomic clocks, and there the notion of the instantaneous frequency for a sum of two tones is very clearly defined and useful. Fat32 touched on this with reference to communications (where I spent most of my career), but it extends far beyond that in more general cases starting with the clear ...


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If you have a 2 dimensional signal with orthogonal components, then sure. Just call one of the dimensions the imaginary component from the complex result of an inverse FFT or DFT. This can be a close approximation to many pairs of physical measurements, such as voltage and current in certain topologies of AC electrical circuits, or single-sideband baseband ...


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As @Bob said, it depends of your definition of "in reality". I am going to ignore images on this post and focus on signals as a function of time. One-dimensional signals always have a symmetrical magnitude spectrum. Examples are the voltage or current on a wire, or a sequence of real numbers stored in digital memory. Two-dimensional signals may ...


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If by "signal in reality" you mean a real signal, than the answer is no. You can just look at the definition of the Fourier transform $$ X(\xi) = \int x(t) e^{-j \xi t} dt$$ and see that $X(-\xi)$ is the complex conjugate of $X(\xi)$, therefore, the frequency response will be symmetric. If by "signal in reality" you mean a physical signal,...


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Does the number of taps affect a cost of implementation of FIR? Well, insert your definition of "cost", and your question should really answer itself. FIR filters belong to the class of linear filters, the combination of N lower order filters can create the desired FIR filter of the higher order. So I was thinking If it makes sense to implement ...


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