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Are there any modulation schemes (or other situations) where sampling at or very near twice the carrier frequency would be better than IQ or quadrature sampling using a local oscillator at or near the carrier frequency for SDR demodulation?

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  • $\begingroup$ I'm asking in regards to the comments on this answer: electronics.stackexchange.com/questions/39796/… $\endgroup$ – hotpaw2 Feb 13 '14 at 1:01
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    $\begingroup$ It depends on how well the modulation scheme deals with IQ imbalance and DC offset. $\endgroup$ – John Feb 13 '14 at 2:16
  • $\begingroup$ I can envision advantages (or rather convenience) in doing this for lower IF signals certainly, as long as the sampling rate is significantly higher than the signal bandwidth to contain the phase dispersion you would get with this approach (I commented on your answer there as well @hotpaw2 for clarifications on your answer.). An implementation can be much more lower cost in the analog with a single mixer/ADC front-end for example. This becomes less feasible at higher carriers where nonlinear noise contributions can start to dominate (relative SFDR in ADC's for example). $\endgroup$ – Dan Boschen Feb 15 '17 at 13:02
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I can envision advantages (or convenience) in doing this for lower IF signals certainly, as long as the sampling rate is significantly higher than the signal bandwidth to contain the phase dispersion you would get with this approach. An implementation can be lower cost and simpler in the analog with a single mixer/ADC front-end for example. This becomes less feasible at higher carriers where nonlinear noise contributions can start to dominate (relative SFDR in ADC's for example).

To further comment on cautions with an approach of sampling at "twice the carrier frequency". I assume in this statement that the approach is to approximate the baseband IQ samples by demultiplexing the samples: I1 Q1 I2 Q2 I3 Q3, etc. It should be pointed out that this is just an approximation, with large errors as the signal bandwidth becomes large relative to the entire digital bandwidth. This is because in this approach the 90° shift is being emulated by a delay, but a delay would only be 90° at ONLY the center frequency of the signal (and varies linearly with frequency everywhere else). To do IQ sampling without delay distortion requires a Hilbert transform which is 90 degrees at all frequencies within the bandwidth of the signal. Note this is of minimal consequence when the bandwidth is significantly smaller than the sampling rate, which would apply to most direct carrier sampling schemes, but is mentioned since the real application to do 2x carrier sampling would not be such cases but lower IF carriers where analog cost and performance is less affected.

So that said, I would likely never sample at twice the carrier frequency, but if the intention is to sample close to that (for some reason), I would choose either 2/.75 = 2.66x or 2/1.25 = 1.6x. Let me explain why below:

So how to do something close to the intention of 2x carrier sampling (which is to sample at a different frequency closest to fs with a single ADC and avoid having to do any IQ in the analog). Obviously we can envision approaches of sampling with a much higher rate to a digital IF and processing IQ in the digital, but to quantify a specific approach that has no additional inaccuracies beyond the analog hardware is to to the following:

Sample the analog signal following all rules of Nyquist (including anti-alias bandpass filtering), meaning ensure the sampling rate is twice the bandwidth of the anti-alias filter, with the additional conditions:

Sample the analog signal such that the resulting digital signal resides at $F_s/4$ where $F_s$ is the sampling rate or any integer fraction of the actual sampling rate.

This means the signal can be centered in the analog prior to sampling at $nF_s/4$ where n = 1,3,5,... Which n is used is referred to as which "Nyquist Zone". n=1 is the first and primary Nyquist zone, for example.

Once digitized, the signal can be complex down-converted to baseband if complex IQ samples are still desired. What is great about positioning the signal at $F_s/4$ is that the complex downconverter reduces to multiplying the signal by the following to generate I and Q:

Since the complex rotator to do $Fs/4$ downconversion to baseband is multiplying by $e^{-jn\pi/4}$ = +1, -j, -1,+j,... then the I samples for this multiplier are +1,0,-1,0,... and the Q samples are 0, -1, 0, +1 ... So baseband I and Q is created by doing the following to the sampled sequence:

$$I = +1x_1 + 0x_2 -1x_3 +0x_4 + 1x_5 ...$$

$$Q = 0x_1 - 1x_2 +0x_3 +1x_4 + 0x_5 ...$$

Very convenient: demultiplex and multiply each by +/-1!

Note, if even Nyquist zones are chosen for the analog downconversion, spectral inversion will result. This is easily resolved by rotating the other way: $e^{+jn\pi/4}$.

$$I = 1x_1 + 0x_2 -1x_3 +0x_4 + 1x_5 ...$$

$$Q = 0x_1 + 1x_2 -0x_3 -1x_4 + 0x_5 ...$$

Note how this is done just by changing the sign of the Q.

Now if the complex rotator is used for carrier tracking (which is entirely likely) then we would not use the reduction down to +/-1's in the multiplier, but still benefit by the ideal placement of fs/4 which optimizes the analog anti-alias filter design by centering the signal within the bandwidth from the edges where aliasing would otherwise occur.

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