QPSK

Starting from BPSK

Remember BPSK? We used 2 phases to represent bits:

With 2 phases, we have 2 possible symbols. Each symbol carries 1 bit.

What If We Used More Phases?

If we use 4 phases instead of 2, we have 4 possible symbols.

How many bits can 4 symbols represent?

$\text{bits per symbol} = \log_2(\text{number of symbols}) = \log_2(4) = 2$

4 phases = 4 symbols = 2 bits per symbol

QPSK: Quadrature Phase Shift Keying

QPSK uses 4 phases, spaced 90° apart:

Instead of sending bits one at a time, we send them in pairs.

The Constellation Diagram

A constellation diagram shows all possible symbols as points on a 2D plane.

• Each dot is a symbol
• The angle from center is the phase
• The label shows which bits that symbol represents

The Waveform

When we transmit QPSK, the wave shifts between 4 different phases based on the bit pairs:

Notice how each symbol period carries 2 bits. The phase of the wave tells the receiver which pair was sent.

Why Is This Better?

Same bandwidth, double the data rate.

You’re transmitting twice as much data in the same time, using the same bandwidth.

The Tradeoff

With 4 phases instead of 2, the symbols are closer together on the constellation.

If noise pushes a received signal slightly, it might land closer to the wrong symbol.

QPSK is slightly more vulnerable to noise than BPSK, but the efficiency gain is worth it.

Where Is QPSK Used?

QPSK is everywhere:

• WiFi (802.11)
• LTE / 4G / 5G
• Satellite communications
• Digital TV

It’s the sweet spot between simplicity and efficiency.

What’s Next?

QPSK only changes phase. All symbols have the same amplitude (same distance from center).

What if we also varied amplitude? Then we could pack even more symbols into the constellation.

That’s QAM (Quadrature Amplitude Modulation), where 16-QAM gives us 16 symbols = 4 bits per symbol.