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#### AWR Version 13

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### Design Notes

IF Subsampling Example

This example shows how to model IF subsampling in VSS. An exaplanation of Nyquist zone subsampling can be found at the following link:

A graphical illustration of Nyquist zone folding is shown below:

In this example, the signal source has a symbol rate of 0.125 MHz and the simulation sampling rate is set to 8 MHz, yielding an oversampling rate of 64 samples per symbol.

The signal is assumed to be at IF, which is 2.75 MHZ. The system employs an ADC with sample rate of 1 MHz, so it is subsampling the IF.

We can take advantage of the fact that higher Nyquist zones fold into the first Nyquist zone when subsampling occurs (i.e., we sample an alias of the signal).

In this project the IF frequency is defined by variable IF and ADC sampling frequency by Fs. The subsampling design uses the following relationship between IF frequency and ADC sampling rate:

IF = (2n+1) Fs / 4

For the values defined in this project:

Fs = 1 MHz (1MSPS)

n = 5

IF = 2.75 MHz  =11/4 Fs

11/4 Fs falls in the 6th Nyquist zone; the first zone corresponds to Fs/2 (n = 0)

When the IF envelope is subsampled with a single ADC the data stream forms an interlaced sample stream consisting of I-Q-I-Q... We use an ideal DAC following the ADC to convert the quantized digital signal (digital 0/1 values) to a quantized real signal for further processing.

The NCO forms a digital local oscillator as 1010...  or 0101..., which correspond to sampling sin or cos waveforms at 4 points per period. The NCO forms a downconversion by factor of two and “unzips” the data into the separate I and Q streams:

IQIQ*1010 = I 0 I 0

IQIQ*0101 = 0 Q 0 Q

Now the data must have the zeros removed and retimed to align I and Q.