Also known as: IQ modulation, I/Q modulation, quadrature modulation
IQ modulation impresses two independent baseband signals — the in-phase (I) and quadrature (Q) components — onto a single carrier by multiplying one with a cosine and the other with a sine of the same frequency and summing them.1 Because sine and cosine are orthogonal (90° apart), the two channels share the same band without interfering, and any amplitude-and-phase state of the carrier can be reached by choosing the pair (I, Q). This is the machinery behind essentially every modern digital modulation, and the reason SDRs work in I/Q data.
How it works
A carrier of arbitrary amplitude A and phase φ can be written A·cos(ωt + φ) = I·cos(ωt) − Q·sin(ωt), where I = A cos φ and Q = A sin φ. So instead of directly varying amplitude and phase — awkward to do at RF — a transmitter varies two ordinary baseband voltages, multiplies them by a cosine and a sine from the same local oscillator (a 90° hybrid supplies the quadrature pair), and adds the products. The composite carrier then sits at whatever amplitude and phase the (I, Q) pair encodes. Plotting I horizontally and Q vertically gives the constellation: a PSK scheme places points on a circle (constant amplitude, varying phase); QAM fills a grid (varying both). The receiver reverses the process — a quadrature demodulator mixes the incoming RF against the same cosine and sine and low-pass filters to recover I and Q.
Mathematically the (I, Q) pair is a complex number I + jQ, and the modulated RF is the real part of (I + jQ)·e^{jωt}. Treating baseband as complex is what makes the whole framework so powerful: a positive baseband frequency ends up above the carrier and a negative one below it, so I/Q can distinguish the two sides of the carrier that a single real signal cannot. That distinction is the entire reason the constellation is two-dimensional — the horizontal I axis and vertical Q axis are genuinely independent degrees of freedom, doubling the information a carrier can hold at a given instant compared with amplitude-only or phase-only schemes.
Relevance to SDR
IQ modulation is the reason software radio exists in the form it does. An SDR front end is essentially an IQ demodulator that hands the CPU a stream of complex samples, I + jQ, and almost every operation downstream — filtering, tuning, demodulation — is arithmetic on that complex baseband. GopherTrunk consumes I/Q from RTL-SDR, Airspy, and similar receivers and does all of its channelization and symbol recovery in the complex domain, so IQ modulation (and its inverse) is foundational to the whole decode chain. Practical IQ hardware is imperfect: gain or phase mismatch between the I and Q paths creates IQ imbalance, which raises an unwanted image of the signal that software must estimate and correct.
In practice
The great practical payoff is the image-reject property. Because I and Q are orthogonal, an IQ mixer can separate signal energy above the local oscillator from energy below it — something a single real mixer cannot do. That lets zero-IF and low-IF receivers place the LO in or near the band of interest without the mirror-image problem that forces classic superheterodyne designs to use bulky image filters.
The same orthogonality is what lets one carrier carry two data streams. Because the cosine and sine branches do not interfere, a modulator can send one bit stream on I and an independent one on Q — the definition of QPSK and the general principle behind every QAM constellation. It also means the receiver can, in software, rotate the whole constellation (multiply the complex samples by e^{jθ}) to correct a carrier phase offset, or spin it steadily to correct a frequency offset, using nothing but complex multiplication. These are the exact operations GopherTrunk’s carrier-recovery loops perform to lock onto a signal before slicing symbols.
Sources
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In-phase and quadrature components — Wikipedia, for the I/Q decomposition and quadrature-modulator description. ↩