Principles of Modern Radar - Volume 2 1891121537

11.2 Colored Space-Time Exploration 507Frequency (MHz)109876543210−80 −60 −40 −20 0Angle (°)Angle – Frequency−2.1−5.2100−8.350−11.4−14.5 0−17.6−20.7−50−23.8−100−26.9−30 −15020 40 60 80 −80 −60 −40 −20 0 20 40 60 80Angle – Range0−4−8−12−16−20−24−28−32−36FIGURE 11-10Circulating chirp.Formally, the code w nm is written:w nm = e iπ M (n+m)2 (11.3)Compared to standard DBF, such colored transmission schemes effectively provide angularseparation on transmit, at the price of an increased instantaneous frequency bandwidth:higher Doppler resolution is now possible, without clutter spreading in Doppler.Compared to the circulating pulse, the properties are similar, but all the availabletransmitters are now used simultaneously.More generally, any type of circulating code, with the general property: w nm =w n+m , can be designed. Their basic property is that different frequencies are transmittedin the different directions. This property can be demonstrated, for a regular linear array, byobserving that, for these codes, there is a time delay t between the signals transmitted byadjacent radiating elements; Consequently, since time delays translate as phase shifts in thefrequency domain, this property imposes, at each frequency f , a phase shift 2πft betweenadjacent sensors. This means that, at frequency f,the transmitted signals will be in phasefor a direction of observation θ such that, if d is the distance between adjacent sensors:2π f t = 2π d sin θ ⇒ sin θ = λ f t (11.4)λdThis means that there is a direct relation between the transmitted frequency and the transmissiondirection, as stated. The diagram at frequency f thus only depends on the array,not on the code itself – which can be a simple binary phase code, for instance: this opensthe way to low cost electronic scanning systems, as emphasized in [5]. Exercise 11.9.3illustrates some specificities of these circulating codes.11.2.2.5 Bidimensional frequency coding [15]Another example for fighter radars is illustrated in Figures 11-11 and 11-12, where abidimensional angular coding is implemented.The array is made of about 1000 elementary antennas (possibly grouped under subarraysarrangement), and the pattern of transmission shown in Figure 11-11 (3 columnstransmitting frequency f 1 at elevation θ 1 , 3 adjacent columns transmitting frequency f 2 atelevation θ 2 , and again 3 adjacent columns transmitting frequency f 3 at elevation θ 3 ),israpidly scanned horizontally through the array, thus realizing an azimuth coding througha circulating code technique similar to the ones described previously.