Lab 7.3 — TX/RX Loopback Metrics¶

Goal¶

Build a compact synthetic QPSK TX/RX loopback experiment and compute the core metrics used later for real RF captures: EVM, SNR and BER.

The lab answers the practical question:

How do we validate a complete TX/RX chain using constellation plots and numeric metrics before moving to RF hardware?

Executable files¶

Environment	File	Output
Python	`blocks/block_07_tx_rx_chains/python/lab_7_3_tx_rx_loopback_metrics.py`	spectra, constellation plots and metrics JSON in `docs/assets`

Run from the repository root:

python blocks/block_07_tx_rx_chains/python/lab_7_3_tx_rx_loopback_metrics.py

Generated artifacts:

docs/assets/lab73_tx_rx_loopback_spectrum.png
docs/assets/lab73_tx_constellation.png
docs/assets/lab73_rx_constellation_after_ddc.png
docs/assets/lab73_tx_rx_loopback_metrics.json

Processing chain¶

flowchart LR
    BITS[Random bits] --> MAP[QPSK mapper]
    MAP --> TX[TX samples]
    TX --> SHIFT[TX frequency offset]
    SHIFT --> CH[Noise / loopback channel]
    CH --> DDC[DDC correction]
    DDC --> SYM[Symbol sampling]
    SYM --> DEC[Hard decisions]
    DEC --> METRICS[EVM, SNR, BER]

Model assumptions¶

This lab is intentionally compact:

QPSK symbols use a deterministic random seed;
rectangular pulse shaping is used as an educational placeholder;
timing is assumed known;
DDC shift exactly compensates the synthetic TX offset;
scalar gain/phase alignment is applied before EVM and BER estimation;
synchronization algorithms are introduced later in Block 8.

Metrics¶

Metric	Meaning
EVM	RMS distance between aligned RX symbols and TX reference symbols
EVM dB	`20*log10(EVM_rms)`
SNR estimate	approximately `-EVM_dB` in this simplified model
BER	bit errors divided by compared bits
estimated offset before/after DDC	carrier-offset estimate before and after digital downconversion
residual frequency error	estimated residual carrier offset after DDC

Expected plots¶

RX spectrum before and after DDC;
TX reference constellation;
RX constellation after DDC and scalar alignment.

What to expect¶

With the default configuration (4096 QPSK symbols, 4 samples/symbol, 100 kHz TX offset) a correct run prints:

Symbols: 4096
Samples per symbol: 4
TX offset: 100000.000 Hz
DDC shift: -100000.000 Hz
Estimated offset before DDC: 99908.589 Hz
Estimated offset after DDC: 91.568 Hz
Residual frequency error: 91.568 Hz
EVM: 8.526 % (-21.39 dB)
SNR estimate: 21.39 dB
BER: 0.000000e+00 (0/8192)

Read these together:

The DDC removes the offset. The estimator sees about 99.9 kHz before the downconversion and about 92 Hz after it: the residual is under 0.1 % of the original offset. The remaining ~92 Hz is the estimator's own bias, not a channel effect.
EVM 8.5 % corresponds to SNR ≈ 21.4 dB through SNR ≈ −EVM_dB, which is the approximation this simplified model uses. It is an estimate of SNR from the constellation, not an independent measurement.
BER = 0 over 8192 bits, but EVM is not zero. This is the normal picture for QPSK at ~21 dB: decisions are still correct while the constellation clouds already have a visible spread. BER alone would hide the noise level, which is why the metric set always includes EVM (compare Lab 8.7).

Why this lab matters¶

This lab connects several earlier course blocks:

Earlier block	Used here
Block 3 DSP basics	FFT, mixer, spectrum reading
Block 4 fixed-point thinking	Q-format and EVM/error interpretation
Block 6 RF frontend	frequency offset and capture-style analysis
Block 7 TX/RX chain	end-to-end metrics

Transition to real RF captures¶

The same metric pipeline can be reused with real IQ data:

real capture.ci16 + metadata JSON -> DDC -> symbol timing -> alignment -> EVM/SNR/BER

The synthetic model avoids the hardest real-world steps at first:

carrier frequency offset estimation;
timing recovery;
frame synchronization;
IQ imbalance;
DC offset;
gain drift;
phase noise.

These are introduced in Block 8.

Report checklist¶

State modulation type and symbol count.
State sample rate and samples per symbol.
State TX offset and DDC shift.
Include RX spectrum before/after DDC.
Include TX and RX constellation plots.
Report EVM, SNR estimate and BER.
Explain why the synthetic model is easier than real RF.
State which synchronization steps are still missing.

Engineering conclusion template¶

The synthetic QPSK loopback used ____ symbols and a TX frequency offset of ____ Hz.
After DDC, the residual frequency error was ____ Hz. The measured EVM was ____ %,
the SNR estimate was ____ dB and BER was ____.
The chain is / is not ready for real RF captures because ______.