Transmitting Data
The resultant coded signal next modulates an RF carrier for transmission using
Quadrature Phase Shift Keying (QPSK). QPSK uses four different states to encode each
symbol. The four states are phase shifts of the carrier spaced 90_ apart. By convention,
the phase shifts are 45, 135, 225, and 315 degrees. Since there are four possible states
used to encode binary information, each state represents two bits. This two bit “word” is
called a symbol. Figure 3 shows in general how QPSK works.
First, we’ll discuss Complex Modulation in general, applying it to a single channel with
no PN-coding (that is, we’ll show how Complex Modulation would work directly on the
symbols). Then we’ll discuss how we apply it to a multi-channel, PN-coded, system.
Complex Modulation
Algebraically, a carrier wave with an applied phase shift, _(t), can be expressed as a
sum of two components, a Cosine wave and a Sine wave, as:
I(t) is called the real, or In-phase, component of the data, and Q(t) is called the imaginary,
or Quadrature-phase, component of the data. We end up with two Binary PSK waves
superimposed. These are easier to modulate and later demodulate.
This is not only an algebraic identity, but also forms the basis for the actual
modulation/demodulation scheme. The transmitter generates two carrier waves of the
same frequency, a sine and cosine. I(t) and Q(t) are binary, modulating each component
by phase shifting it either 0 or 180 degrees. Both components are then summed together.
Since I(t) and Q(t) are binary, we’ll refer to them as simply I and Q.
The receiver generates the two reference waves, and demodulates each component. It is
easier to detect 180_ phase shifts than 90_ phase shifts. The following table summarizes
this modulation scheme. Note that I and Q are normalized to 1.
Symbol I Q Phase shift
00 +1 +1 45
01 +1 -1 315
10 -1 +1 135
11 -1 -1 225
For Digital Signal Processing, the two-bit symbols are considered to be complex
numbers, I +jQ.