# Static and Moving Target Imaging Using Harmonic Radar  
[PERSON]  
1U.S. Army Research Laboratory, Adelphi, MD 20783, USA; [EMAIL_ADDRESS] (K.A.G. ); [EMAIL_ADDRESS] (A.F.M. ); [EMAIL_ADDRESS] (K.D.S.) 1  
[PERSON]  
2 Department of Electrical Engineering, The Pennsylvania State University, University Park, PA 16802, USA 22  
[PERSON]  
3  
[PERSON]  
1U.S. Army Research Laboratory, Adelphi, MD 20783, USA; [EMAIL_ADDRESS] (K.A.G. ); [EMAIL_ADDRESS] (A.F.M. ); [EMAIL_ADDRESS] (K.D.S.) 1  
[PERSON]  
1U.S. Army Research Laboratory, Adelphi, MD 20783, USA; [EMAIL_ADDRESS] (K.A.G. ); [EMAIL_ADDRESS] (A.F.M. ); [EMAIL_ADDRESS] (K.D.S.) 1  
Circuit elements exhibit nonlinear properties either by design or by consequence. By design, P-N junctions, such as diodes, are inherently nonlinear. The nonlinear effects of diodes are especially important in the field of RF for their use in mixers, which are used to up- and down-convert signals from one frequency to another. The operation of mixing two signals together to create a new frequency is a nonlinear operation. Upconverting signals to higher frequencies allows for higher bandwidths, thus information can be transmitted faster [2]. By consequence, many RF and microwave circuit elements exhibit unintended nonlinear properties. The best example of this phenomenon is the amplifier. Amplifiers are generally expected to operate linearly, and boost the input signal without creating extraneous frequencies at the output. In practice, building an ideal linear amplifier is not possible. As a result of an amplifier's inherent nonlinear character, extra frequency content will be generated and possibly distort the desired signal. The unintended frequency content generated by the nonlinear properties of the amplifier can interfere with other radar and communication systems [3; 4; 5] as well as affect the sensitivity of the receiver. Much research has been done to linearize amplifiers [6; 7; 8; 9; 10]. Many nonlinear effects occur which are subtler and do not manifest themselves as often. Among these, the most prevalent is PIM, which is observed when high power signals interact with components that are weakly nonlinear. Weakly nonlinear components do not exhibit measurable nonlinear distortion under normal conditions. An early example of PIM in a RF system is the Luxembourg effect or cross-modulation, which was first observed in 1933 when a high-power radio transmitter caused interference to other radio stations by modifying the conductance of the ionosphere [11; 12]. A more recent example of PIM causing unintended nonlinearities occurs in mobile phone towers, which communicate with multiple users simultaneously. PIM distortion in mobile phone towers is generated by the antennas and connectors [13; 14; 15; 16; 17]. Lesser known observations of nonlinearities come from electrothermal coupling. As components heat and cool, they begin to exhibit nonlinear properties, which are generally very weak [18]. Starting in the 1970s, research began focusing on detecting, measuring, and exploiting nonlinear circuit elements at standoff distances. Most naturally occurring objects do not exhibit significant nonlinear characteristics [19; 20]. This permits detection of small nonlinear objects in the presence of larger linear clutter. Theoretical and experimental data have shown that different nonlinear junctions can be discriminated against at standoff distances [21; 22; 23; 24; 25; 26; 27; 28; 29; 30]. These systems traditionally operate at a single frequency and detect nonlinear devices connected to an antenna. A harmonic radar (a specialized form of nonlinear radar) transmits a frequency \(f_{t}\) and processes returns at a harmonic frequency \(nf_{t}\), where \(n=2,3,4,...\). Usually, the second harmonic, i.e., \(2f_{t}\), is used since it generally provides the strongest response from these types of targets. This radar approach effectively separates the harmonic target response from the clutter band, thereby making harmonic radar attractive for several applications.