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QPSK Spreading - Receiver Statistics

The QPSK version of the modulator duplicates the BPSK structure, but with a quadrature RF carrier applied (Figure 1).

Figure 1. QPSK direct sequence modulator.

The channel model is the same as the BPSK case (Figure 2).

Figure 2. Channel model.
The demodulator also duplicates the BPSK demodulator with a quadrature local oscillator (Figure 3). The sign changes in the quadrature channel can be thought of as conjugating the complex carrier and spreading sequence amplitudes.
Figure 3. QPSK direct sequence demodulator.

We can shortcut most of the math here by noting that each of the QPSK channels, I and Q, is exactly like the BPSK model, except that half the signal energy appears in each channel, so we replace with /2. The noise and interference, on the other hand is the same in each channel, so those expressions are unchanged. The detection amplitude means and variances are now
The message here is that the signal-to-noise ratio

is unchanged. The reason for the quadrature spreading is really to make sure that the mutual interference between users and between stations is uniformly distributed in phase. It otherwise contributes nothing to performance.

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