Low sidelobe radar waveforms derived from orthogonal matrices

Diverse radar pulse-train with favourable autocorrelation and ambiguity functions

“…Note that the structure of the coding matrix is a sufficient condition for the rows to be a complementary set [4]. However, the opposite is not true -when the rows form a complementary set it does not necessarily imply that the columns are mutually orthogonal.…”

“…Using opposite direction cyclic shifts or the conjugate code results in rotating the diagonal ridge in 90º (extending from the central peak to the first Identical LFM pulse-train (no coding) 8x8 binary coding of identical LFM pulse-train 8x8 P4-based coding of identical LFM pulse-train and third quadrants instead of the second and fourth quadrant). Using generalized P4 [4] code, where the relatively prime integer to M is not ±1 (mod M), results in splitting the ridge to several smaller parallel ridges such that the ambiguity plot has a shape closer to that of the binary-coded LFM pulse-train.…”

“…Note that due to the construction method the code exhibits a random like nature. The second type of orthogonal code is based on the complementary set formed from all 8 cyclic shifts of a P4 sequence [4] [5]. Note that the second code is a quaternary code and that it is of regular nature since the P4 itself is of regular nature and the use of ordered cyclic shifts adds additional order to the code.…”

New Algorithms for Designing Unimodular Sequences With Good Correlation Properties

“…Indeed, in many cases, the maximum difference between the arrival times of the sequence of interest and of the interferences is (much) smaller than the duration of the emitted sequence (see, e.g., [16], [17], [21], and [23]). Consequently, in such cases, the interest lies in making small, for some , instead of trying to make all correlation sidelobes small; here the value of is selected based on a priori knowledge about the application at hand (for instance, in wireless communications, it is usually known that significant channel tap coefficients can occur up to a certain maximum delay, and so we can choose as the said delay).…”

Phase-coded interrupted continuous waves analysis, parameters design and processor design

“…As it will be shown as follows, column orthogonality of the complementary set matrix is one sufficient condition for our application. Some well known complementary sets possess column orthogonality, such as P4 (with the length of square number), Hadamard codes and etc [4], so they are adequate for our applications. What differs from inter-pulse coded waveforms [5] is that we toggle transmit and receive circularly to meet the required isolation between the transmitter and receiver since we aim at high power radars for long rang applications.…”