DMR End to End, Part 1: The 4FSK Carrier & the Tier Family

By Matt Cheramie · September 17, 2026

Part 1 of DMR End to End, a 14-part deep dive that follows the world’s most widely deployed digital PMR protocol through GopherTrunk — from a 4FSK carrier to two simultaneous recorded calls, direct-mode handhelds, and decrypted Enhanced Privacy voice. TETRA End to End followed a carrier whose information rode in phase transitions; P25 End to End followed the amplitude-carried twin family. DMR borrows P25’s physics and TETRA’s time-slicing, and adds the thread that runs this whole series: one carrier carries two of everything — two slots, two sync polarities, two tiers of trunking, two decode cadences — and the receiver only works when it knows which one it is looking at. This opener is the physical layer everything else stands on.

TL;DR: DMR is 4FSK at 4800 symbols/s in a 12.5 kHz channel — the same four-level family as P25 Phase 1, with outer symbols at ±1944 Hz and inner ones at ±648 Hz (DeviationHz: 1944.0 in internal/scanner/ccdecoder/pipelines.go). Unlike P25 the transmit pulse is a root-raised-cosine (α = 0.20, RolloffAlpha); unlike TETRA the carrier is time-sliced — two 30 ms slots per 60 ms frame, each holding one 27.5 ms burst of 132 dibits. GopherTrunk channelizes it to 48 kHz — 10 samples/symbol (ddcTargetForProtocol, internal/scanner/ccdecoder/ddc.go), and the receiver (internal/radio/dmr/receiver, imported as dmrrx) is a discriminator → carrier gate → RRC matched filter → Mueller-Müller → post-clock CoarseAFC → symbol AGC → slicer → SymbolToDibit chain. Three tiers ride the same dibits — dmr-tier1, dmr-tier2 and dmr (Tier III) — differing only in which sync words they hunt and which state machine reads them.

Key takeaways

• DMR asks P25’s absolute question on TETRA’s clock. After the FM discriminator a symbol is a level, so the chain needs level calibration and offset control — but the carrier is TDMA, so every tracker must also survive gaps a repeater never shows and a handheld always does.
• DMR is the RRC-matched member of the 4800-baud family. P25 shapes with raised-cosine plus inverse-sinc; DMR shapes with a plain RRC at α = 0.20, so the textbook matched filter is correct here.
• The tier is a reader, not a waveform. Tier I, II and III pipelines build the same dmrrx.Receiver at the same 1944 Hz deviation; they differ in the sync alphabet and in what drives the grant.
• 48 kHz is a design rate, shared five ways. Ten samples per symbol sizes the matched filter, the timing-loop gain and the AGC window for P25, DMR, NXDN, dPMR and YSF alike.

Cheat sheet

Concern	What it does	Where it lives
On-air constants	4800 sym/s, RRC α = 0.20	internal/radio/dmr/receiver/receiver.go (SymbolRate, RolloffAlpha)
Deviation calibration	slicer scale = 2π·1944/48000	receiver.go (Options.DeviationHz), set in ccdecoder/pipelines.go
Channel rate	48 kHz for the 4800-baud family	internal/scanner/ccdecoder/ddc.go (ddcTargetForProtocol)
Symbol AGC	mean|x| → slicerScale·2/3	internal/dsp/demod/symbol_agc.go (C4FMAGCTarget)
Carrier-offset control	post-clock CoarseAFC + coarse acquirer	receiver.go, receiver/coarse_carrier.go
Dibit mapping	{+1,+3,−1,−3} → 00, 01, 10, 11	receiver.go (SymbolToDibit)
Tier pipelines	one receiver, three readers	ccdecoder/pipelines.go (newDMRTier1Pipeline, newDMRTier2Pipeline)

In this post

• Where DMR sits — amplitude-carried like P25, time-sliced like TETRA.
• The deviation ladder, DMR edition — ±1944/±648 Hz, the RRC that is right this time.
• One carrier, two slots — the 60 ms frame, the 27.5 ms burst, the gaps.
• The tier family tree — Tier I, II and III as three readers of one dibit stream.
• 48 kHz and the receiver in one pass — IQ to dibits, and why the AFC sits after the clock.

Where DMR sits

The two earlier series each opened with a table; here it is with all three columns, because DMR borrows from both sides:

Axis	P25 Phase 1	DMR	TETRA TMO
Modulation	4-level FSK	4-level FSK	π/4-DQPSK
Outer deviation	±1800 Hz	±1944 Hz	— (phase)
Transmit pulse	RC × inverse-sinc	RRC α = 0.20	RRC α = 0.35
Access	FDMA	2-slot TDMA, 60 ms frame	4-slot TDMA
Downlink	continuous CC	repeater continuous, handheld bursty	continuous

Row one decides the demodulator: like P25, DMR’s dibit lives in an amplitude after the FM discriminator, so the receiver asks the absolute question and inherits everything the P25 opener catalogued — symbol AGC, an AFC because a tuner offset is a slicer bias, thresholds derived from a physical deviation (the demodulation primer has the theory).

Row five is what P25 Phase 1 never faced. A DMR repeater keys both timeslots continuously, so its carrier looks as steady as a P25 control channel; a DMR handheld in direct mode transmits one burst per frame — 27.5 ms on, 32.5 ms off. The level trackers were built for the first shape and are poisoned by the second, so the receiver carries a stage (carrierGate, Part 9) whose only job is to know which shape it is hearing. Two shapes of the same carrier, and a receiver that has to tell them apart.

The deviation ladder, DMR edition

DMR’s four levels sit at ±1944 Hz (outer, symbols ±3) and ±648 Hz (inner, symbols ±1) — the standard 3:1 ratio, so only the slicer scale differs from P25’s, and GopherTrunk calibrates it once:

// internal/radio/dmr/receiver/receiver.go (shape)
slicerScale := 1.0
if opts.DeviationHz > 0 {
    slicerScale = 2.0 * math.Pi * opts.DeviationHz / opts.SampleRateHz
}

At 1944 Hz and 48 kHz that is ≈ 0.254 rad/sample for an outer symbol — the “±0.25 rad/sample” the carrier gate’s documentation sets against the ±π of receiver noise, a comparison Part 9 turns into a squelch. The DeviationHz <= 0 fallback survives only for legacy pre-scaled fixtures.

The dibit map is P25’s, pinned by test:

// internal/radio/dmr/receiver/receiver.go (shape)
// +3 → 01, +1 → 00, -1 → 10, -3 → 11 (TIA-102.BAAA; ETSI TS 102 361-1 agrees)
func SymbolToDibit(sym int8) uint8 {
    switch sym {
    case 1:  return 0
    case 3:  return 1
    case -1: return 2
    case -3: return 3
    }
    return 0
}

The high bit is the sign, the low bit selects inner/outer — so negating every symbol, which is what a spectrum-inverted front end does, is exactly “add 2 mod 4” in dibit space. Part 2 leans on that.

The matched filter is where DMR parts from P25. The P25 series spent a section on the RRC model being wrong for C4FM — modelling the real raised-cosine-plus-inverse-sinc pulse as RRC left ISI on every capture (issue #275). DMR’s pulse is a plain root-raised-cosine at α = 0.20, so here the textbook filter is correct: demod.NewC4FM over filter.RootRaisedCosine(sps, span, alpha) taps, RolloffAlpha = 0.20, PulseSpanSymbols = 8 a side, where P25 goes through NewC4FMWithTaps(P25C4FMRxTaps(...)).

One carrier, two slots

DMR is two-slot TDMA. A 60 ms frame holds two 30 ms timeslots; each slot carries one burst of 264 bits — 132 dibits, dmr.BurstDibits — lasting 27.5 ms, with the remaining 2.5 ms as guard or, on a base-station outbound, the 24-bit CACH. Every burst has the skeleton Protocol Decoders Part 5 drew and Part 2 dissects: two payload halves around a central 48-bit field that is either a sync word or embedded signalling.

The arithmetic the whole series rests on follows. At 4800 dibits/s a 60 ms frame is 288 dibits. A repeater fills both slots, so consecutive bursts of one call — same slot, one frame apart — sit 288 dibits apart on a live outbound (132 + 12 CACH, twice) or 264 on a CACH-free stream. A direct-mode handheld transmits in one slot and leaves the other empty, so its bursts are also 288 apart — with noise where the repeater put the other slot. Same cadence, different filler; Part 3 is what happened when a decoder sliced those gaps as voice.

The tier family tree

ETSI TS 102 361 defines three tiers on one air interface; ParseProtocol (internal/trunking/site.go) maps them to three names:

Tier	What it is	protocol:	Sync words hunted	Grant source
I	licence-free direct mode	dmr-tier1	DM-Voice/Data TS1/TS2	Voice LC Header
II	conventional repeater / IPSC	dmr-tier2	all nine	Voice LC Header (+ late entry)
III	trunked control channel	dmr	all nine	CSBK grants

The Tier I, Tier II and Tier III reference pages carry the deployment context; here the point is how little changes below the state machine. newDMRTier1Pipeline builds a Tier II ConventionalChannel with the detector restricted to the four direct-mode words and the tag dmr-tier1; newDMRTier2Pipeline builds the same channel with all nine plus the operator’s colour-code filter; Tier III swaps in tier3.ControlChannel and an LCN resolver from dmr_band_plan (band-plan reference, Cookbook Part 2). All three construct the receiver identically:

// internal/scanner/ccdecoder/pipelines.go (shape)
rx := dmrrx.New(dmrrx.Options{
    SampleRateHz: opts.SampleRateHz,
    DeviationHz:  1944.0, // ETSI TS 102 361-1 §6.3 peak deviation
    ClockGain:    0.015,  // Tier I/II; Tier III uses 0.025
    DibitSink: func(dibits []uint8, baseIdx int) {
        opts.tapDibits(dibits, baseIdx)
        cc.Process(dibits, baseIdx)
    },
})

The one tier-dependent DSP constant is ClockGain, and it is measured: Tier II Voice LC Header bursts have a higher per-symbol transition magnitude than Tier III’s CSBK Aloha bursts (1.27 vs 0.90, TestDMRTier2VsTier3SymbolDensity) and the loop slips at 0.025 on them. Everything else is shared, and Parts 2, 4 and 5 walk it once for all three.

48 kHz and the receiver in one pass

The channel rate is chosen in one function:

// internal/scanner/ccdecoder/ddc.go (shape)
func ddcTargetForProtocol(p trunking.Protocol) float64 {
    switch p {
    case trunking.ProtocolTETRA, trunking.ProtocolTETRADMO:
        return tetraDDCTargetRateHz // 144_000
    case trunking.ProtocolMotorola:
        return motorolaDDCTargetRateHz // 18_000
    }
    return ddcTargetRateHz // 48_000 — DMR and the rest of the C4FM family
}

Ten samples per symbol: the AGC’s Rate: 1/256 is a ~53 ms window and the Mueller-Müller loop is sized for 10 sps. Receiver.Process composes the chain:

The DMR receiver: a P25-shaped C4FM chain with two DMR-specific placements — a carrier-presence gate ahead of the matched filter, and the coarse AFC moved behind the symbol clock.

Two stages the figure omits sit at the ends: before the discriminator, a one-shot coarse carrier acquirer (coarse_carrier.go) de-rotates grossly mistuned dongles; after the slicer, SymbolToDibit hands dibits to a dmr.DibitSink with the absolute baseIdx every framer downstream uses.

The carrier gate yields one presence flag per sample; on a continuous carrier every flag is true and the gated stages equal their ungated forms (TestReceiverCarrierGateIsNoOpOnContinuousCarrier). Then the DMR-specific placement: CoarseAFC runs on the recovered symbol stream, post-clock and pre-slicer, where P25 corrects before timing. The DC bias is identical in both domains, but the open-loop estimate wanders a few hertz chasing the data mean, and fed into the timing loop it destabilised symbol timing on a clean signal — verified to drive synthetic sync to zero. The symbol AGC normalises mean|x| to slicerScale·2/3 (C4FMAGCTarget): the unit-energy RRC has a DC gain near 3.1, and without it every inner symbol slices as outer while sync and slot type still pass — the “Tier III BPTC uncorrectable / Tier II instalock then nothing” field failure.

How the twin thread shaped the Go code

• One receiver, parameterised by evidence. dmrrx.Options has no tier field; tiers differ in the sync alphabet handed to dmr.NewSyncDetector and in a measured ClockGain.
• Gated variants are provably neutral. ProcessGated on the clock, AFC and AGC equal their ungated forms when every sample is present — the Two Pipelines lesson inside one receiver.
• Calibration is derived, never assumed. DeviationHz drives the slicer scale and C4FMAGCTarget derives the AGC target from it.
• The stream has an absolute clock. DibitSink(dibits, baseIdx) carries a monotonic index that Reset restarts at zero — the coordinate every cadence, late-entry and re-key rule in Parts 3–6 is expressed in.

Where this goes next

A dibit stream at 4800/s is a firehose with no punctuation. Part 2 adds the structure: the 132-dibit burst, the nine sync words and the uncomfortable fact that they are closed under a polarity flip, the Golay-protected slot type that routes each burst, and the moment a FEC-valid burst locks the stream’s polarity for good.

FAQ

Is DMR the same modulation as P25 Phase 1? Same family, different pulse and deviation. Both are 4800-baud four-level FSK in 12.5 kHz demodulated by an FM discriminator, and GopherTrunk uses the same SymbolToDibit map for both. DMR’s outer deviation is ±1944 Hz against P25’s ±1800, and DMR shapes with a root-raised-cosine where P25 does not.

Why does GopherTrunk decode DMR at 48 kHz? Because 48 kHz is exactly 10 samples per symbol at 4800 baud, the operating point every loop constant in the C4FM receivers was tuned at. ddcTargetForProtocol returns it for the whole 4800-baud family; TETRA gets 144 kHz and Motorola SmartNet 18 kHz from the same function.

What is the difference between DMR Tier I, II and III? Tier I is licence-free direct mode — handheld to handheld on one frequency. Tier II is licensed conventional: a repeater carrying two timeslots. Tier III adds a dedicated control channel and CSBK grants for trunking. In GopherTrunk they are dmr-tier1, dmr-tier2 and dmr, all built on one receiver.

Does a DMR repeater transmit continuously? Yes — a keyed base station fills both timeslots every 60 ms frame, with a CACH between bursts, so its carrier is as steady as a P25 control channel. A direct-mode handheld sends one 27.5 ms burst per frame and is silent for 32.5 ms, which is why the receiver carries a carrier-presence gate.

Why does DMR’s AFC run after the symbol clock when P25’s runs before? Because the open-loop coarse estimate wanders by a few hertz chasing the data mean, and on DMR feeding that bias into the Mueller-Müller loop destabilised timing on a clean signal — it drove synthetic decode sync to zero. Correcting the recovered symbols recentres the eye without touching the timing loop; the pre-clock coarse acquirer handles large offsets.

Series navigation

Part 1 of 14 · Next → Part 2: Bursts, Sync Words & Polarity