Lab 8.8 — QPSK modem, impairments and BER

Goal

Extend the BPSK path to QPSK with two bits per symbol and verify two implementation levels:

1. a synthesizable QPSK modem that recovers a complete frame at BER = 0 in ideal HDL loopback;
2. an AWGN/CFO channel model that shows how impairments affect the constellation and BER.

Modem and verification

QPSK uses two orthogonal BPSK axes. The mapper creates Gray-coded points before the shared chain performs upsampling, RRC filtering, symbol sampling and hard decisions:

dibit source → QPSK mapper → upsampler → RRC TX → loopback →
RRC RX → symbol sampler → hard decision → BER counter

The tb_qpsk_zynq_ber_top testbench checks 140 symbols / 280 bits at BER = 0.

Impairments

• AWGN spreads the four clusters and eventually moves samples across decision boundaries.
• CFO rotates the constellation from symbol to symbol and turns the four points into a ring without correction.
• Gray QPSK has the same theoretical per-bit error probability as BPSK: Q(√(2·Eb/N0)).

Reproduce

python blocks/block_08_modulation_and_synchronization/python/qpsk_impairments_ber.py
python tools/run_block5_hdl_smoke.py

Expected result: the simulated BER curve follows theory, HDL loopback passes without errors, and the CFO case demonstrates why carrier recovery is required.

Next step

Lab 8.9 closes the CFO problem with a Costas loop and known-preamble resolution of the 90° ambiguity.