46 lines
2.1 KiB
Markdown
46 lines
2.1 KiB
Markdown
# Fixed-point plan
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The fixed framework represents signed two's-complement integers with declared
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total/fractional widths. Every quantizer selects saturation or wrap and nearest,
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truncate, or convergent ties-to-even rounding. Quantizers count overflow and
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accumulate RMS/peak quantization error.
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Proposed starting points (not final widths):
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| Stage | Width | Fraction | Policy |
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| input sample | 8 | 7 | saturate |
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| sine/cosine | 16 | 15 | saturate |
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| mixer output | 18 | 15 | saturate |
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| FFT input | 18 | 15 | saturate |
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| FFT twiddle | 16 | 15 | convergent |
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| FFT stage | 20 | 15 | configured scaling |
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| correlation product | 36 | 30 | full precision then requantize |
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| IFFT output | 28 | 15 | saturate |
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| coherent accumulator | 40 | 15 | saturate |
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| noncoherent accumulator | unsigned 56 | 20 | saturate |
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| carrier phase | unsigned 32 | 0 | natural wrap |
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| code phase | unsigned 48 | 32 | natural wrap |
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| loop state | 32 | 20 | saturate |
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| FCW | signed 32 | 0 | wrap in phase accumulator |
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| discriminator | 24 | 18 | saturate |
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`FixedNco` and `FixedCorrelator` are integer bit-true models. Fixed PCPS models
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declared quantization at input, normalized FFT output, pointwise product, IFFT
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output/power, and accumulation. Exact butterfly-level identity depends on the
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chosen streaming FFT IP scaling schedule and is explicitly unresolved until an
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RTL FFT architecture is selected.
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`FixedRadix2Fft` supplies a fully stage-quantized power-of-two oracle with
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quantized twiddles, convergent butterfly rounding, saturation counters, and one
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bit of scaling per stage. It is used for standalone RTL FFT vectors. The
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runtime PCPS boundary model remains able to use arbitrary transform lengths;
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matching a vendor FFT at those lengths requires configuring that core's exact
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schedule.
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The sweep utility varies input/FFT widths and reports mean absolute/relative,
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RMS, peak error, acquisition decision, Doppler bin, code phase, and overflows.
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Tracking qualification additionally compares convergence, steady-state jitter,
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and loss-of-lock decisions; these metrics must become release gates once loop
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state formats are frozen.
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