MODCOD | Modulation & Coding

What this tool is

MODCOD3 is a trade‑study visualiser for selecting modulation and coding under a given channel model. It sweeps Eb/N0 and produces analytic/parametric estimates of BER, SER, PER, envelope CCDF/PAPR, and the implied throughput and goodput.

Important: results are engineering estimates intended for comparison and intuition. They are not a bit‑accurate link‑level simulator for any one standard. Use presets (DVB‑S2X/CCSDS/LTE/NR) as convenient starting points, then adjust assumptions and margins to match your system.

Key definitions

Eb/N0 (dB): energy per information bit to noise spectral density. For AWGN, it is a primary performance axis.
BER: bit error probability at the detector/decoder output.
SER: symbol error probability (post‑detector / post‑decoder proxy).
PER: packet error probability. MODCOD3 uses a block‑error approximation from BER and packet length.
Throughput: raw delivered information bit‑rate (PHY rate) for the chosen parameters; fixed MCS → independent of Eb/N0.
Goodput: successful payload bit‑rate; decreases with PER (and payload/header/CRC overhead).
CCDF/PAPR: complementary CDF of instantaneous power relative to mean; used for PA back‑off design.

Typical workflow

Select a preset closest to your scenario (DVB‑S2X/CCSDS/LTE/NR) or choose parameters manually.
Set the channel model and any implementation margin to reflect real‑world losses.
Adjust packet size and overhead (header/CRC, CP/pilots for OFDM).
Run a sweep and inspect BER/PER and the required Eb/N0 at the target error rate.
Use the Trade‑off summary to compare candidates: spectral efficiency, Shannon gap, PAPR, goodput.

Inputs

Standards profiles (LTE/NR/DVB-S2X/CCSDS)
Set Profile to enable standard MODCOD selectors. In these modes the tool uses the standard CQI/MCS/MODCOD tables for modulation order and nominal code rate, and models BLER/PER using a capacity-gap abstraction (set by “Coding gap to capacity”). Use Target BLER/PER (often 10% for LTE/NR with HARQ) and Channel BW to obtain believable throughput/goodput and required Eb/N0. The manual “Decoding and coding chain” fields are disabled and ignored in standards mode.

Every input affects either (a) the error‑rate curves, (b) the throughput/goodput scaling, (c) PAPR/CCDF, or (d) the summary metrics.

Modulation

Control	Meaning	Effect in the tool
Modulation	Selects the signaling family (PSK/QAM/APSK/FSK/GMSK/OFDM).	Sets constellation size (bits/symbol), the uncoded BER/SER model, and which UI fields are relevant/enabled.
Roll‑off α	RRC excess bandwidth (raised cosine). α=0 → Nyquist, α>0 increases occupied bandwidth.	Affects spectral efficiency (η) in the summary. Also used as part of PHY efficiency factors.
Symbol rate (Msym/s)	Absolute symbol clock.	Scales throughput and goodput in Mb/s. Error rates vs Eb/N0 are normalized and largely independent of symbol rate.
RRC span (symbols)	Filter length (impulse response truncation) for pulse shaping.	Used in the waveform assumptions; longer spans imply “cleaner” shaping. (Does not attempt full ISI optimisation.)
OFDM sub‑mod	Constellation on each active subcarrier (e.g. QPSK/64QAM/256QAM).	Determines bits/symbol on subcarriers; drives BER/SER and rate metrics while the overall modulation is OFDM.
OFDM Nfft / Used	FFT size and number of occupied tones.	Used to compute occupancy/guard‑band efficiency and to parameterise PAPR statistics (more tones → higher PAPR tendency).
OFDM CP / pilots (%)	Cyclic prefix and reference/pilot overhead as percentages of the time‑frequency resources.	Reduces throughput/goodput and η. Does not directly change BER model (treated as overhead, not as additional SNR penalty).
FSK h / tonespace	Modulation index `h` and tone spacing factor for FSK/MSK family.	Used to shape the FSK/MSK error model and tagging as near‑constant envelope.
GMSK BT	Gaussian filter bandwidth‑time product (typ. 0.3 in GSM‑like systems).	Controls the GMSK spectrum/ISI trade and the waveform characterisation; envelope is treated as near constant.

Decoding and coding chain

Control	Meaning	Effect in the tool
Soft decoding	Whether the decoder uses soft metrics (LLRs) vs hard decisions.	Soft decoding increases estimated coding gain and improves the waterfall region.
1st stage decode / rate / iterations	Primary FEC (e.g. LDPC/Turbo/Viterbi) with code rate and iteration count.	Contributes multiplicatively to net code rate and to estimated coding gain (iterations improve gain with diminishing returns).
Stage 1 gain override (dB)	Manual adjustment to the estimated coding gain for stage 1.	Adds (positive or negative) dB to the coding gain model to match a known implementation.
Interleaver type	Interleaving strategy (block/convolutional/random/etc.).	Improves robustness to burst/frequency‑selective impairment via an additional “burst mitigation” gain term.
Depth / span, rows / cols	Interleaver sizing parameters.	Used to scale the burst‑mitigation term: deeper interleaving reduces correlation of errors.
2nd stage decode / rate / iterations / gain override	Outer code (e.g. BCH/RS/CRC) or a second FEC stage.	Multiplies net code rate and adds to estimated coding gain (or detects errors if CRC‑only).

Packet (bits)

Control	Meaning	Effect in the tool
Packet length (bits)	Payload size.	Sets payload fraction and PER sensitivity. Larger packets: PER rises for the same BER.
Header / CRC (bits)	Non‑payload bits per packet.	Reduces payload fraction and increases total bits used in the PER approximation.
Target BER	Design threshold for “acceptable” BER.	Used to compute required Eb/N0 at target BER and to evaluate throughput/goodput at that operating point.

Channel

Control	Meaning	Effect in the tool
Fading type	Selects AWGN, Rayleigh, Rician, Nakagami‑m, shadowing, burst, or frequency‑selective severity.	Introduces an Eb/N0 penalty term relative to AWGN; interleaving can reduce the burst penalty.
K‑factor (Rician)	Ratio of LOS to scattered power (dB‑like parameter but entered linearly here).	Higher K → less severe fading penalty (approaches AWGN as K increases).
Nakagami m	Fading severity parameter: m=1 Rayleigh, m>1 milder, m<1 more severe.	Scales the fading penalty term.
Shadowing σ (dB)	Lognormal slow fading standard deviation.	Acts as an additional margin/penalty on the required Eb/N0.
Burst len / depth	Parameters for bursty error processes (correlated fades).	Used with the interleaver model to determine how much burst‑mitigation gain is realised.
Freq‑selective severity	Proxy for multipath delay spread / selectivity / channel estimation stress.	Applied as an implementation penalty term (especially relevant for OFDM presets).
Implementation margin (dB)	Catch‑all margin for non‑idealities (phase noise, quantisation, PA distortion, channel estimation loss, etc.).	Subtracts directly from effective coding gain (i.e., shifts curves to require higher Eb/N0).

Sweep and display

Control	Meaning	Effect in the tool
Eb/N0 sweep (dB)	Min / max / step for the x‑axis sweep.	Determines resolution and the ability to read required Eb/N0 accurately (smaller step → more precise).
Constellation Eb/N0 (dB)	Operating point used when generating the constellation sample.	Higher values show tighter clusters; lower values show more scatter.
Constellation symbols	Number of points plotted in the constellation view.	More points give better visual density but can be heavier for the browser.
CCDF samples (k)	Number of time‑samples used for CCDF estimation (in thousands).	Higher values reduce Monte‑Carlo noise in the CCDF tail.
CCDF oversample	Oversampling factor used for envelope statistics (important for OFDM peaks).	Higher oversampling finds higher peaks → higher estimated PAPR (more realistic PA sizing).
Show uncoded refs	Overlay uncoded BER/SER references on the BER plot.	Useful to visualise coding gain (horizontal shift) and the waterfall/floor behaviour.

Plots

BER / SER vs Eb/N0

Shows analytic BER and SER estimates versus Eb/N0 for the selected effective modulation (for OFDM: the sub‑carrier modulation). If Show uncoded refs is enabled, uncoded references are overlaid for comparison.

Interpretation: coding generally appears as a left‑shift (coding gain) and a steeper waterfall. Floors and residual terms approximate finite‑length/implementation effects.

PER vs Eb/N0

PER is derived from BER using a block‑error approximation over the total packet bits (payload + header + CRC): PER ≈ 1 − (1 − BER)^{N}, where N is the total packet bit count. Larger packets therefore require lower BER to reach the same PER.

Constellation sample

Displays a noisy constellation at the selected Constellation Eb/N0. It is a visual diagnostic of Euclidean distance, SNR, and modulation order. For OFDM, the plot represents a representative sub‑carrier constellation rather than time‑domain OFDM samples.

Envelope CCDF / PAPR

Plots the complementary CDF of instantaneous power normalised to mean: CCDF(x) = P(P/mean(P) > x). The x‑axis is in dB relative to mean (so 0 dB corresponds to mean power).

Constant‑envelope waveforms (e.g. FSK/MSK/GMSK) should sit near the floor for x ≥ 0 dB (PAPR ~ 0 dB).
OFDM has a heavy tail and requires PA back‑off; more tones and higher oversampling typically increase peak capture.

The summary reports PAPR @ CCDF = 1e‑6, a common PA‑sizing metric (tail probability).

Goodput / Throughput vs Eb/N0

Throughput is the raw PHY rate implied by symbol rate, bits/symbol, coding rate, and overhead factors (for OFDM: occupancy, CP, pilots). With a fixed MCS, it is essentially independent of Eb/N0 (horizontal line).

Goodput accounts for packet success: Goodput ≈ Throughput × payload_fraction × (1 − PER). At high Eb/N0, PER → 0 and goodput saturates at the payload‑limited maximum.

Trade‑off summary metrics

The summary panel aggregates the most decision‑relevant quantities for MODCOD selection. Values are computed from your current settings and the modeled curves.

Metric	Meaning / how to use it
Bits / symbol	Log2(M) of the effective modulation (for OFDM: per sub‑carrier). Drives η and throughput.
Net code rate	Product of stage‑1 and stage‑2 rates. Lower rate → more redundancy → better sensitivity but reduced throughput.
Net η (b/s/Hz)	Effective spectral efficiency after overhead factors (roll‑off, OFDM occupancy/CP/pilots). Used for Shannon limit comparison.
Overhead (%)	Non‑payload fraction from packet header/CRC and PHY overhead (e.g. CP/pilots). High overhead reduces goodput even at high Eb/N0.
Req Eb/N0 @ target BER	The first Eb/N0 point where modeled BER ≤ Target BER. Used as a sensitivity comparator.
Req Eb/N0 @ target PER	Equivalent operating point for a PER target derived consistently from the Target BER and packet length.
Shannon limit	Theoretical minimum Eb/N0 for the given η in AWGN with ideal coding and infinite length. Used as a lower bound only.
Gap to Shannon	`Req Eb/N0 − Shannon`. Smaller gap generally indicates a stronger coding/modulation choice under the assumptions.
Est coding gain	Modelled horizontal shift versus uncoded reference attributable to the selected decoders and iterations (plus any overrides).
PAPR @ CCDF=1e‑6	Peak‑to‑average power ratio at a tail probability of 1e‑6. Drives PA back‑off and efficiency. Lower is better.
Throughput @ target BER	Raw PHY rate at the target BER operating point (in practice constant with Eb/N0 for fixed MCS).
Goodput @ target BER	Payload success rate at target BER, accounting for PER and packet overhead.

Design tip: You rarely optimise one metric. Typical constraints: (i) BER/PER at a required availability, (ii) goodput target, (iii) PA back‑off (PAPR), (iv) occupied bandwidth. MODCOD3 is intended to make these trade‑offs visible in one place.

Models & assumptions

MODCOD3 uses a combination of closed‑form error‑rate expressions (uncoded) and parametric “coding gain / waterfall / floor” shaping for coded performance. Channel types introduce penalty terms relative to AWGN, and the interleaver reduces burst penalties.

Uncoded BER/SER

PSK/QAM use standard analytic approximations versus Eb/N0 (including Gray‑coded QAM style fits).
APSK is approximated as a QAM/PSK‑like effective distance model (trade‑study accuracy, not standard‑exact).
FSK/MSK/GMSK are treated as near‑constant envelope families with appropriate error‑rate scaling.
OFDM uses the sub‑carrier modulation for BER/SER; OFDM overhead and PAPR are treated separately.

Coding performance

Selected decoders contribute an estimated coding gain that grows with iterations and soft decoding.
Residual/error‑floor behaviour is included as a low BER floor plus a waterfall slope term.
Gain override fields exist to calibrate against known link‑level or lab results.

Channel penalties

Fading/shadowing/burst/frequency‑selective selections are translated into an Eb/N0 penalty relative to AWGN.
Implementation margin is treated as an additional required Eb/N0 (subtracts from effective gain).

PER model

PER is derived from BER using an i.i.d. bit‑error assumption over the packet bit count. Real systems with burst errors can deviate; use burst/fading plus interleaver settings to explore sensitivity.

CCDF/PAPR model

OFDM CCDF is generated from oversampled time‑domain synthesis (peak capture improves with oversampling).
Constant‑envelope families are represented as near‑constant envelope (PAPR ~ 0 dB).

Calibration: If you have a reference curve (e.g. 3GPP link‑level BLER), tune Implementation margin and Gain overrides until the modeled required Eb/N0 matches your reference, then use the tool comparatively across candidate MODCODs.

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