How it works
QPSK maps 2 bits per symbol to four phase states: 00→+45°, 01→+135°, 11→−135°, 10→−45° in Gray-coded assignment. The I and Q axes each carry ±1/√2 of the total symbol energy. QAM combines amplitude and phase modulation — 16-QAM has a 4×4 grid of 16 constellation points, each carrying 4 bits; 64-QAM has an 8×8 grid of 64 points, each carrying 6 bits. Gray coding ensures adjacent constellation points differ by only 1 bit, minimising BER when symbol errors occur. BER of QPSK = Q(√(2E_b/N₀)), identical to BPSK at the same E_b/N₀.
Key points to remember
QPSK bandwidth efficiency = 2 bits/s/Hz; 16-QAM = 4 bits/s/Hz; 64-QAM = 6 bits/s/Hz. Higher-order QAM requires higher SNR to achieve the same BER — 64-QAM needs about 5–6 dB more SNR than QPSK for the same BER. Minimum Euclidean distance between constellation points decreases as order increases (for fixed average power), explaining the SNR penalty. OFDM combined with 64-QAM is the core physical layer of LTE and Wi-Fi 802.11n. Differential QPSK (DQPSK) encodes data as phase changes between symbols, eliminating the need for absolute phase reference at the cost of about 3 dB SNR penalty.
Exam tip
The examiner always asks you to draw the 16-QAM or QPSK constellation diagram with Gray coding and calculate spectral efficiency — label all constellation points with their 2-bit or 4-bit binary labels and use Gray code, not natural binary.