Principles of Modern Radar - Volume 2 1891121537

502 CHAPTER 11 Space-Time Coding for Active Antenna SystemsFIGURE 11-2Coloredtransmission(space-time coding).Subarray #1Subarray #2w 11 w 12 ... w 1M w 11 w 12 ... w 1Mw 21 w 22 ... w 2MT rw 21 w 22 ... w 2MSubarray #Nw N1 w N2 ... w NM w N1 w N2 ... w NM1 stDiagram2 ndDiagramM thDiagram11.2.2 Colored transmission, or space-time coding11.2.2.1 PrinciplesThe principle of colored transmission consists of simultaneously transmitting differentwaveforms in the different directions, thus achieving space-time coding 2 (Figure 11-2).In this figure, the coding is supposed to be a succession of M sub-pulses, coded in phaseor frequency, but any type of code can be used [3]. For instance, transmitting differentfrequencies through the different sub-arrays could also be a possibility. The directivity ontransmit is then recovered by signal processing on receive.For signal processing on receive, the transmitted waveforms should be orthogonal, sothat they can be separated from one another, on each receiving channel.It should be emphasized that the transmitted waveforms are still periodic in time,since that is a necessary condition for an efficient cancellation of long range clutter (e.g.mountains: use of non-periodic waveforms is generally a very bad solution, since the faraway returns from large structures, such as mountains or coasts, cannot be eliminated ifthey are not present in all the samples collected in the range gate – this is analyzed below,in Section 11.4).Another way of considering such concepts is to describe them as the transmission,during each subpulse # m, through successive diagrams, the mth diagram D m (θ)resultingfrom the illumination law w 1m ,w 2m ,...w Nm on the array, as illustrated in Figure 11-3 forthree different concepts, which will be analyzed in more details later: frequency coding(identical diagrams at different carrier frequencies), fast angular scanning, and pseudorandom orthogonal diagrams.If the antenna is made of N sub-arrays arranged on a line Ox, D m (θ) being thesuccessive diagrams, and x n the positions of the sub-arrays their analytical expression fora given coding sequence w nm is written:N−11 ∑D m (θ) =w∣nm e −2iπ x nsin θ λ(11.1)N∣n=02 This technique has been known as colored transmission, since the spatial distribution is then colored,as opposed to the white distribution corresponding to the wide beam. A more general denomination isspace-time coding, meaning that the transmitted signals are now bi-dimensional functions, both of timeand space.