Introduction Receiver Design for Passive Millimeter Wave (PMMW) Imaging Millimeter Wave Systems, LLC Passive Millimeter Wave (PMMW) sensors are used for remote sensing and security applications. They rely on radiometric receivers to sense very small power differences. The performance of radiometric receivers should be characterized in different ways than communications and radar receivers. In communications we typically think in terms of carrier-to-noise ratio (CNR) or signal-to-noise ratio (SNR) relating a generated signal to noise floor. In a PMMW system, the signal sources are random white noise resulting from black body radiation from objects in a scene. The power emitted by an object is proportional to its temperature on a Kelvin scale (relative to absolute zero) and contrast is achieved in a PMMW image by spatial correlation of temperature differences within the scene. All objects radiate black body radiation and PMMW systems are sensitive enough to measure the minute noise power differences between objects. Objects in the scene will partially reflect the surroundings so the noise power perceived is a weighted average of the object s temperature and the surroundings. The weighting factor is known the object s emissivity, ε, and the observed temperature can be expressed as, = +(1 ) At millimeter wave frequencies, most clothing is relatively transparent while the human body is a good absorber (or emitter). Security sensors exploit both these attributes. Many concealed objects, even if they rise to body temperature, tend to reflect the temperature of the surroundings making them detectable. Contrast can be enhanced in these systems by lowering the temperature of the surroundings. For example, outdoor millimeter wave images will have contrasting bands at the tops of objects as a result of the reflection of the cold sky. These images are often shown in reverse contrast resulting in bright areas. The millimeter wave frequency band (30-300 GHz) is considered the most desirable band for personal security screening. Above the millimeter wave band clothing becomes less transparent and below, the resolution, which is limited by aperture (antenna/lens) diffraction, is insufficient or the size of the aperture becomes impractical. Other applications include all-weather imaging. PMMW cameras can see through environmental conditions that would obscure visual or IR cameras making it a desirable complimentary technology. Typical radiometer receiver block diagrams are shown below: (a) Direct Detection Receiver
(b) Heterodyne Receiver In both cases power is detected using a detector; typically a square-law detector diode. (a) is a direct detection receiver and (b) shows a heterodyne receiver. For the direct detection receiver, only gain is needed before the detector to overcome the detection limit (NEP) of the detector. The sensitivity of the detector is not critical, however lower NEP requires less RF gain and this is desirable. The heterodyne receiver does not require any gain on the RF end. Heterodyning makes higher frequency operation easier to achieve since mixers are more readily available than amplifiers above W-band. The LO frequency can be multiplied using diode multipliers or though harmonic mixing, or both. Heterodyning is somewhat less common, at least through W-band, with the availability of COTS low noise amplifier MMICs which are readily available and have significant bandwidth (10s of GHz). In both cases the post detection circuit is the same and the detected output is integrated over time to produce the radiometric output. The Noise Equivalent Delta-T (NEDT) is the temperature difference equivalent to the RMS noise level of the system and is given by the Radiometer Equation: where B is the pre-detection bandwidth, Tsys is the system noise temperature and τ is the integration time. It is interesting to note that one can increase B or τ to make an NEDT as small as desired. For imaging, at least a few times the NEDT level is needed to create contrast. The dwell time per pixel is usually limited; particularly if the application is at video rate. Achieving video rate, even for a modest number of pixels, requires a wide bandwidth and low noise temperature. Multi-element receiver arrays are used to overcome sensitivity and bandwidth limitations. Due to the cost and complexity of having a receiver for each pixel, these systems usually have some combination of multiple elements and scanning (e.g. a scanning mirror). Furthermore, practical limitations on minimum element spacing can be overcome with scanning to fill in between elements. In the radiometer equation T sys is the system noise temperature and includes the antenna temperature = +
Noise temperature is for the receiver is easily relatable to the noise figure by, or in db, ( )= ( 1) ( )= (10 1) Reception Bandwidth More precisely, the system bandwidth, B, in the radiometer equation is referred to as the radiometer Reception Bandwidth, and is defined as: () = () where G(f) is the gain of the system at frequency, f. Reception bandwidth is not the same as the -3dB bandwidth although it is often approximated that way. Over wide bandwidths the gain response versus frequency of the system can vary significantly and this can result in significant reduction in reception bandwidth (and therefore system performance). Integrator Integration of the output power over the integration time is performed by the integrator. The detector voltage is assumed to be proportional to power (square law): = () () The simplest integrator is an R-C low pass filter with an integration time constant, τ, approximately equal to R*C. R-C integrators have memory wherein some of the energy from one pixel position will bleed into the next pixel. This is typically mitigated by using a time constant that is much shorter than the dwell time per pixel and then summing multiple Nyquist-sampled measurements to form a single observable. = Other integrator schemes include using a V-to-F converter with a counter, and charging a capacitor through a current source proportional to the detector output. Receiver Budget Example Consider a 400 pixel single receiver system operating at 15 Hz. The maximum dwell time per pixel is 1/15*1/400 = 167 microseconds. With a reception bandwidth of 10 GHz, we have:
The result is an NEDT of 0.2 K (or C). Note that the noise power over that bandwidth is -74dBm. With 50dB of RF gain, we d have -24dBm into the detector which is more than adequate for a typical GaAs Schottky diode detector, yet is still in its linear (square law) range. Some MMIC LNAs can have an output compression point as low as -24dBm, so it is important to consider this. The P1dB of the receiver should be 10dB or more below the RMS noise level. A medium power amplifier could be used as a second stage, if needed, without substantively affecting the noise temperature which is set by the first MMIC. System Stability Bandwidth 10000 MHz Integration time (tau) 0.167 ms Tsys 300 K ktb -74.0 dbm RMS Out (dv/v) 0.000774 NEdT 0.2 K There are two main contributors to system instability: 1) Additive noise and 2) thermal drift. These effects can dominate over the radiometric uncertainty in milliseconds. Low frequency additive noise (ΔG/G) as a result of RF amplification (RF, IF and/or LO) typically has a characteristically 1/f dependence. The noise figure of a HEMT amplifier, for example, can have a 1dB noise figure at 1 GHz and over 15dB at 1 Hz due to 1/f noise. Most commercially available millimeter wave amplifiers are GaAs phemt and will exhibit significant 1/f. Bipolar transistors have comparatively better 1/f performance (Weinreb and Schleeh 2014). Thermal drift is typically dominated by the detector, but can also be caused by temperature induced gain fluctuations in the amplifiers. Comparison to a reference using a switch can be used to track out drift errors as in the example of a Dicke radiometer shown below: The NEDT of the Dicke radiometer is twice that of a total power radiometer: 2 Solid state switches at millimeter wave frequencies can significantly degrade the receiver noise temperature. Quasi-optical means (e.g. - chopper) can also be used to avoid switch loss. Dicke switching is not always necessary for imaging so long as the radiometer is relatively stable over the timescale of a video frame and the image is auto-scaled. The situation becomes significantly more complicated when
there are multiple pixels since each pixel can drift independently of each other and it may be necessary to perform two-point calibration to normalize their outputs. Stability Characterization The sources of instability are difficult to measure directly because they are small compared to the random fluctuations of the measurement over short periods of time. An excellent method for characterizing radiometer stability is Allan Variance (G. Rau et al 1984). This analysis method, named after David M. Allan, was originally used for characterizing time standards. The Allan variance of the radiometer output for a given integration time, τ 0, is ( )= ( ) 2( 1) for N samples, each with an integration time, τ 0. The Allan variance has the same value as the conventional variance for Gaussian noise. The Allan variance can be calculated for integration times that are a multiples of τ 0 by aggregating adjacent samples to effectively form samples of 2τ 0, 3τ 0,, using the same data set. When plotted on a log-log scale, the theoretical σ A is a straight line with a negative slope tracking the radiometer equation, whereas 1/f shows up as a positive slope. The ability of the Allan variance to make these distinctions makes it a powerful diagnostic tool. Other sources of drift can also be revealed using the Allan variance technique. Conclusions In general the PMMW receiver design needs to match the application. Stability factors can quickly dominate system performance and managing these factors in the design is at least as important as noise temperature. Dicke switching can be an effective way to mitigate drifts including 1/f over longer integration times. Generally Bipolar amplifiers (HBT) have better 1/f performance than FET amplifiers (HEMT). Maximizing the reception bandwidth is critical to achieving good system performance. Receiver and detector flatness are critical parameters in achieving wide reception bandwidth. Allan Variance is an excellent tool for analyzing the stability and sources of drift. Because it acts on the regular data output of system, and no additional measurement equipment is required.
References: S. Weinreb and J. Schleeh, Multiplicative and Additive Low-Frequency Noise in Microwave Transistors, IEEE Transactions on Microwave Theory and Techniques, VOL. 62, NO. 1, Jan. 2014 G. Rau, R. Schieder, B. Vohwinkel, Characterization and Measurement of Radiometer Stability, Proc. 14th European Microwave Conf., Sept. 10-13, 1984, pp248-253 About Millimeter Wave Systems, LLC Millimeter Wave Systems, LLC is a supplier of custom specialized millimeter wave hardware including sub-systems, modules and antennas. Our facilities are located in Amherst, Massachusetts. MWS is a U.S. small business.