I&Q procedure
The I&Q method ( in-phase & quadrature method ) is one way of obtaining the phase information when a high-frequency carrier signal is demodulated . So you can z. B. distinguish moving objects from non-moving objects with radar.
With simple demodulation, only the real part of a complex signal is determined, i.e. of a signal which has an amplitude variable and a phase position at the input of the demodulator, only the amplitude variable is present at the output of the demodulator circuit, the phase information has been lost.
The evaluation of the phase information is the prerequisite for an MTI circuit which detects a Doppler shift of the carrier frequency in the signal and can thus distinguish moving objects from immobile ones.
With simple demodulation it can even happen that the instantaneous value (real part) of the amplitude is equal to zero and the phase information (imaginary part) has its maximum value. In this case, no signal will be measurable at the output of the simple demodulator circuit. This has fatal consequences for radar devices that work according to the monopulse method, which means that only this one pulse is required to detect a target. So the whole signal has to be phase shifted by 90 ° in order to get a demodulated signal at all in this case.
However, since it is not known with which phase the signal is received, both ways of demodulation must be carried out:
The signal is divided into two ways, one way of the demodulation is carried out with the original phase position (English: in phase ) and produces the I data , the second way is carried out with a reference frequency shifted by 90 ° and produces the Q data (English: quadrature ). The size of the individual components I and Q can be calculated using an angle function:
A back calculation of the phase angle Φ can be made from this:
The I signal is an amplitude at the output of this circuit which describes the real part of the signal that is currently present. The Q signal is also an amplitude, but it represents the associated imaginary part. From both amplitudes, since they are at right angles to one another at the origin , the absolute size of the received echo signal can be calculated using the Pythagorean theorem .
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Approximate calculations
In practice, however, the technical implementation of a root calculation is complicated. In addition, at this stage of the signal processing, the radar data should, if possible, still be available in real time. Delays (internal runtimes due to calculation steps) should always be the same in order to be able to compensate for them later. This is why an approximation method is usually used here.
The length of the longer leg a plus half the length of the shorter leg b is approximately the length of the hypotenuse c . In contrast, this formula can be implemented very easily with an assembler program or even with extremely fast hardware wiring (for example in an FPGA ). The approximation is greater than or equal to the true value, with a maximum error of 12% at 26 °.
In addition to the approximation of Pythagoras, a much more precise calculation is also possible with the help of the CORDIC algorithm, which is often used in digital signal processing and in mobile communications and is also suitable for real-time applications. The CORDIC offers a resource-saving implementation for iterative rotation of pointers, i.e. it maps the trigonometric functions using simpler functions. When the CORDIC is actually used in the area of I&Q demodulation, the pointer of the input signal is rotated to match the unit pointer (CORDIC vector mode), from which the length (amplitude) and the phase angle result.