Lab 11.34 — Continuous QPSK Gardner timing recovery

Goal

Replace the burst-only fixed-phase sampler with a continuous timing loop that can follow sample-clock mismatch, while retaining a runtime-selectable baseline in the same bitstream. The live experiment is now complete. It demonstrates a large lock-rate gain, but the predeclared clean-attempt gate does not pass over the full CFO sweep, so the fixed sampler remains the default rather than turning a near-tie into a success claim.

Why a loop, after Lab 11.33 rejected a timing change

Lab 11.33 disproved one narrow hypothesis: timing walk inside a 140-symbol retained frame was not the immediate cause of the observed failure. It did not make a fixed sample phase a sound long-duration receiver. A feedforward picker chooses one of eight phases once; independent sample clocks continue to move after that choice. The new block therefore estimates timing error continuously and adjusts a fractional sampling phase instead of periodically choosing a new integer tap.

Architecture

qpsk_symbol_timing_recovery.v implements a complex sign-Gardner loop:

1. A Q16 modulo-one NCO produces two interpolation strobes per symbol.
2. A linear interpolator forms the sample at the fractional phase between adjacent matched- filter samples.
3. Even strobes are on-time symbol outputs; odd strobes are mid-symbol samples.
4. The timing-error detector combines both axes:

e = sign(sign(I_mid) * sign(I_now - I_prev) + sign(Q_mid) * sign(Q_now - Q_prev))

1. A PI loop updates omega, with explicit clamps around the nominal 2/SPS step.

The first hardware candidate used K1=1/256 and K2=1/4096. Its live debug telemetry showed omega_q16 spanning 15,600...16,848 around the nominal 16,384, much more movement than the physical sample-clock mismatch requires. The retuned candidate halves both gains to K1=1/512 and K2=1/8192; it keeps the model's zero-error drift cases and narrows the live full-sweep range to 16,088...16,672.

The detector is deliberately amplitude-independent and contains no general divider. With SPS=8, mu/omega reduces to the bounded fixed-point operation used by both the Python model and RTL. The model mirrors Verilog nonblocking semantics: an omega update affects the NCO on the following valid input sample, not the current edge.

Runtime contract

The bridge compiles both timing methods and selects them with gp_ctrl[14]:

gp_ctrl[14]	Timing path	Phase picker
0	legacy fixed-phase sampler	available through its existing enable
1	continuous Gardner loop	forced to bypass

While bit 14 is set, gp_adc_input_debug exposes {omega[15:0], mu[15:0]} and the capture debug word exposes the signed three-level TED error. The runtime mux is followed by one registered valid/I/Q boundary. That register is functionally a uniform one-clock delay and physically prevents the synchronized control bit from feeding through the mux and two coarse-CFO DSP levels in one 8 ns divide-select cycle.

The accepted Lab 11.33 behavior remains the runtime default. Gardner is still selectable for diagnostics and follow-up experiments, but the live result below does not promote it.

Floating-point and fixed-point evidence

Run the executable model:

python blocks/block_05_fpga_hdl_flow/python/qpsk_timing_recovery_model.py

For the 140-symbol course frame, the best start-offset sweep produced:

Observed samples/symbol	Float Gardner errors	Fixed Gardner errors	Fixed-phase errors
8.000	0	0	0
8.030	0	0	0
8.060	0	0	14
7.970	0	0	0
7.940	0	0	12

The intentionally large short-frame mismatch makes the failure visible without a long simulation. A separate 12,000-symbol test uses a realistic ±100 ppm sample-clock mismatch:

Observed samples/symbol	Fixed Gardner	Best fixed phase
8.0008 (+100 ppm)	0 / 12,000 symbol errors	1,790 / 12,000
7.9992 (−100 ppm)	0 / 12,000 symbol errors	1,789 / 12,000

This is the distinction the old picker cannot erase: it can find a good initial phase, but it cannot follow the accumulated clock error.

RTL evidence

The canonical smoke runner now generates vectors and exercises four new benches:

python tools/run_block5_hdl_smoke.py `
  --test tb_qpsk_symbol_timing_recovery `
  --test tb_qpsk_timing_recovery_chain `
  --test tb_qpsk_timing_recovery_mux `
  --test tb_qpsk_timing_recovery_retained

Current results:

• the standalone RTL block is bit-exact against the integer model for 140 symbols at SPS=8.06, with zero sample mismatches;
• the full drifted chain recovers 0/280 bit errors, while the fixed sampler has 15/280;
• the runtime mux preserves the same 0/280 versus 15/280 comparison;
• on the retained two-board +30 kHz capture, Gardner preserves the known clean result at offsets 3, 4, and 7; the full legacy QPSK top and bridge loopback remain BER=0.

Physical implementation gate

The first implementation exposed an XDC coverage error, not an algorithmic failure. The existing timing-recovery multicycle matched only the BPSK hierarchy, leaving the new QPSK recurrence single-cycle. Its worst path was 24.836 ns and failed the 8 ns divide-select clock by 17.340 ns. Extending the same setup/hold 4/3 constraint to the QPSK hierarchy removed that false single-cycle requirement.

The next route reached WNS=-0.188 ns, TNS=-6.084 ns, with clean hold timing. Its worst path was no longer the Gardner recurrence; it ran from synchronized gp_ctrl[14] through the runtime mux into the coarse-CFO DSP datapath. Post-route physical optimization improved only 0.002 ns, so the mux output was registered instead of weakening the timing constraints.

The first registered candidate closed the physical gate at WNS=+0.049 ns and was used to discover excessive live loop movement. After retuning the PI gains, a fresh implementation plus post-route physical optimization closes the final candidate:

• WNS=+0.003 ns, TNS=0.000 ns;
• WHS=+0.041 ns, THS=0.000 ns;
• all 77,389 routable nets are fully routed, with zero routing errors;
• bit generation completed with zero errors and zero critical warnings.

The tested raw boot image is tmp/snapshot_impl_sweep/lab1134_retuned_postroute/system_top.bit; its SHA-256 is 2493b26225b76768ccff985359570761a424a0b6522a70ef4d7e111bbc5ef380. It clean-boots board B, probes the AD9361 successfully, and reports the expected course core ID 0x4250534B.

Live two-board A/B result

The conducted stand used board A as the vendor cyclic-DMA transmitter and board B as the course receiver at 915 MHz through the 30 dB attenuator, with TX at −30 dB and RX at +50 dB. Both modes used the same bitstream, CFO grid, offsets and retry budget; no-lock attempts stayed in the denominator.

Campaign	Mode	Full frames	BER=0 attempts	Aggregate BER in full frames
+30 kHz, 80 attempts	fixed	54/80 (67.5%)	21/80 (26.25%)	0.192196
+30 kHz, 80 attempts	retuned Gardner	72/80 (90.0%)	22/80 (27.5%)	0.106597
0…55 kHz, 288 attempts	fixed	193/288 (67.01%)	72/288 (25.00%)	0.137435
0…55 kHz, 288 attempts	retuned Gardner	246/288 (85.42%)	71/288 (24.65%)	0.119178

The focused +30 kHz gate passes: Gardner improves clean attempts by one and adds 18 full frames. The larger sweep is the decisive check. Gardner reaches BER=0 at all 12 CFO points and adds 53 full frames, but produces one fewer clean attempt than fixed sampling. Under the predeclared point-estimate rule (clean_rate_improved && lock_rate_preserved), that is a reject. The difference is too small to infer that Gardner is intrinsically worse, but it is also not evidence for replacing the baseline. A longer, higher-power comparison would be a new experiment with a statistical margin, not a reinterpretation of this one.

The Lab 11.32 hardware runner now has a --timing-recovery switch, so the two campaigns use the same acquisition code and differ only by gp_ctrl[14]. Assemble the evidence with the Lab 11.34 post-processor:

python blocks/block_11_integrated_sdr_project/python/lab_11_32_two_board_fabric_coarse_cfo.py `
  --json-out tmp/lab1134_fixed.json
python blocks/block_11_integrated_sdr_project/python/lab_11_32_two_board_fabric_coarse_cfo.py `
  --timing-recovery --json-out tmp/lab1134_gardner.json
python blocks/block_11_integrated_sdr_project/python/lab_11_34_continuous_qpsk_timing_recovery.py `
  --baseline tmp/lab1134_fixed.json --gardner tmp/lab1134_gardner.json

The post-processor rejects mismatched CFO grids, offsets, or retry budgets and keeps every attempt in the reported lock and clean-frame rates. Raw attempts, timing telemetry and the comparison plots are stored in docs/assets/lab1134_*_live_20260721.*.

The honest conclusion is: continuous QPSK timing recovery is implemented, model/RTL qualified, timing-closed and measured on the live conducted link. It substantially improves full-frame lock, but does not pass the full-sweep clean-attempt acceptance gate, so the fixed sampler remains the default pending stronger evidence.