Also known as: CQPSK
CQPSK (compatible QPSK, also linear simulcast modulation, LSM) is the linear phase-modulation counterpart to C4FM used on P25. It produces the same symbol stream as C4FM so a single demodulator can receive either.1 Where C4FM is a constant-envelope FSK signal, CQPSK is an amplitude-and-phase-varying linear signal — yet by design they arrive at the receiver as the same four-level symbol sequence.
How it works
CQPSK maps the same 4800-baud dibit stream that C4FM carries onto carrier phase rather than frequency, using IQ modulation with root-raised-cosine pulse shaping. The clever part is that P25 chose the two schemes so that C4FM’s frequency trajectory and CQPSK’s phase trajectory are mathematically linked — frequency is the derivative of phase — with the result that a receiver’s symbol slicer sees the identical four levels either way. This is why a P25 radio never has to know in advance which modulation the far end used; it recovers symbols and the physical modulation is transparent above the slicer.
The price CQPSK pays for its phase-linear shaping is that it needs a linear power amplifier: the signal’s envelope dips between constellation points, and a saturated Class-C amplifier would clip those dips and regrow the spectrum. Subscriber portables, which prize battery efficiency, therefore transmit C4FM, while infrastructure transmitters that can afford a linear amplifier often use CQPSK/LSM.
Variants
CQPSK is closely related to the π/4-DQPSK family used elsewhere in land-mobile radio; the shared idea is a shaped QPSK whose trajectory avoids abrupt phase jumps. The reason CQPSK exists at all is simulcast: when several transmitters on the same frequency cover a wide area, their signals overlap at the receiver. A linear modulation superimposes those overlapping signals more gracefully than a constant-envelope FSK signal would, producing fewer distortion products in the combined waveform — hence the name linear simulcast modulation. Decoders often benefit from an LSM-aware equaliser or a slightly different symbol-timing strategy when a P25 system is running CQPSK simulcast.
Relevance to SDR
A P25 receiver can demodulate both C4FM and CQPSK, and on the constellation the recovered symbols look alike once locked. GopherTrunk decodes the P25 Phase 1 symbol stream regardless of which transmit path produced it, though heavily distorted simulcast CQPSK is one of the harder real-world cases — multipath and transmitter timing spread the constellation, and the GopherTrunk DSP notes treat such captures as front-end/channel-limited rather than a defect in the steady-state demodulator.
Sources
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Project 25 — Wikipedia, for the CQPSK/LSM linear path and its compatibility with C4FM on P25. ↩