### Introduction Of I&Q Imbalance Correction

Imbalance introduces imaginary components of the spectrum in the output of the converter such that limits the demodulation performance. The imbalance in either the amplitude or phase of the I and Q-component signals create a shift from the normal I-Q graph.

Since the I and Q imbalance is frequency dependent, it makes the compensation of the imbalance more difficult in wideband direct-conversion receivers. Some I & Q imbalance correction algorithms are based on a single frequency signal. Thus, for wideband signals they are often failed.

In practice, some empirical algorithms may be used to partially improve imbalance compensation for wideband signals. The figure below shows collected human walking data by an X-band 9.8GHz Doppler radar. A person walks away from and, then, returns back to the radar during 8 seconds of time duration. Because of the I and Q imbalance, Figure (a) plots the I and Q imbalanced graph and (b) is the I and Q imbalanced micro-Doppler signature. Figure (c) and (d) show, after applying the empirical imbalance compensation algorithm, the I and Q graph and the micro-Doppler signature, respectively. It shows that the empirical algorithm works fine in this example, but it is not always like this.

(FIGUREI&Q Imbalance Correction) ### MAXIMUM RANGE COVERAGE

The maximum range coverage is the maximal unambiguous range that a radar signal can travel round trip before the radar transmits the next signal. The maximum range coverage is nothing to do with its frequency band and the radar range equation.

For an FMCW radar, its range resolution is determined by ΔR = c/(2B) and its velocity resolution is determined by Δvr = c/(2fcT), where c is the speed of the wave propagation, B is the bandwidth of frequency sweep, fc is the carrier frequency and T is the sweep time duration. The unambiguous velocity is vmax = ±c/(4T fc).

The maximum range coverage is determined by Rmax = fsT c/(4B) = Ns c/(4B), where Ns=fsT is the number of sample points within one sweep time. Thus, it is only proportional to the number of sample points in a sweep time and inversely proportional to the bandwidth B. It is nothing to do with the radar carrier frequency at fc, the transmitted power, and the RCS of the target.

For a given bandwidth B = 250 MHz and number of samples in a sweep Ns = 128, the maximum range coverage is Rmax = Ns c/(4B) = 38.4m. If a target at a range beyond the maximum range coverage, the target’s range cannot be measured unambiguously. To increase the maximum range coverage, a larger samples Ns, or reduced bandwidth B is needed. For more detailed maximum range coverages, please see the following figure:

(FIGURE Maximum Range Coverages) ### MAXIMUM DETECTION RANGE

The maximum detection range is the maximum distance at which a target with a given RCS can be detected with a given detection rate and a false alarm rate. Based on the radar equation, the maximum detection range for a target is determined by

wavelength of transmitting signal, λ; RCS of the target, σ; transmitting antenna gain, GT; receiving antenna gain, GR; transmitting power, PT; receiver noise bandwidth, Bn; receiver noise figure, Fn; required minimum SNR, (S/N)min, and system loss, L. For given target’s RCS, antenna gains, noise bandwidth, noise figure, required minimum SNR, and system loss, the maximum detection range is proportional to the square root of the wavelength, λ1/2, and the 4th roots of the transmitting power, (PT)1/4.

For a radar operating in C-band at 5.8GHz with wavelength λ = 0.0517m, the required SNR is 13dB for achieving a detection rate of Pd = 0.98 and a false alarm rate of Pfa = 10-4, the antenna gain is GT = GR = 20 dB, the noise bandwidth Bn is 1.0 MHz, the noise figure Fn is 2.2, the system loss L is 5, and the transmitting power PT = 0.1W ( or 20 dBm), the maximum detection range is:

• 52.5 m for detecting a bird with RCS = 0.01 sm;
• 198 m for detecting a human with RCS = 1 sm;
• 351 m for detecting a car with RCS = 10 sm.

For more detailed maximum detection ranges, please see the following Figure:

(FIGURE Maximum Detection Ranges) 