# Quadrature Amplitude Modulation: I and Q Same

I am trying to understand a previous design that uses Amplitude Modulation. Instead of just using the real part of the signal, the designers put the voice signal on both I and Q. Both I and Q have the same data.

How would this affect the spectrum of the resulting AM signal and how would this affect the performance of the demodulator (assuming we are demodulating using a simple envelope detector)?

It doesn't really affect anything at all. If you modulate a signal on the I channel only, then it would look something like:

$$x_1(t) = m(t) \cos(2\pi f_c t)$$

If it were on the Q channel only, then it would look like:

$$x_2(t) = m(t) \sin(2\pi f_c t)$$

$x_1(t)$ and $x_2(t)$ only differ by a phase shift of 90 degrees on the carrier. Likewise, if you were to split the signal evenly in power across the I and Q channels, it would look like:

$$x_3(t) = \frac{1}{\sqrt{2}} m(t) \cos(2\pi f_c t) + \frac{1}{\sqrt{2}} m(t) \sin(2\pi f_c t)$$

Again, in the complex baseband form that is often used for analyzing signals, this corresponds to just a phase shift of 45 degrees from the original signal $x_1(t)$. In most systems, you will have a random phase shift between the transmitter and receiver anyway; this should not have any effect on the performance of your receiver.

• When demodulating, would it increase SNR? I'd think with an envelope detector, you'd get a gain from having the same data on I and Q. – jeremy Jun 28 '17 at 0:16
• @jeremy Yes, you're right. If the data is on I and Q, then you do get an SNR improvement. However, there's no free lunch here: this just corresponds to transmitting the signal with greater power. You could do the same thing by just using either I or Q and applying a gain factor to the signal. Summary: yes, this increases SNR, but only because you're increasing the signal power by doing so. – Jason R Jun 28 '17 at 15:24