IEEE - Aerospace and Electronic Systems - April 2022 - 45

Wu et al.
Figure 2.
Illustration ofthe signal structure ofan FH-MIMO radar, where each radar pulse is divided into H hops, each hop randomly selects M (out of
K in total) subbands as hopping frequencies, one for each antenna. The conventional FH-MIMO waveform can have nonordered subbands
assigned over antennas in each hop, as seen from the waveform block shown on the left. A reordering process can be introduced to rearrange
the subbands in each hop in a deterministic order, such as from small to large in the figure.
At hop h, the mth antenna of the radar transmitter
transmits a single-tone signal, i.e.,
shmðiÞ¼ ej2pikhmD;i ¼ 0; 1; ... ;L 1
(3)
where i the sample index, L ¼bT=Tse is the number of
samples per hop, and Ts is the sampling interval. Here, be
rounds to the closest integer, and as in (2), D is a positive
integer. Since khm is also an integer, the real and imaginary
parts of shmðiÞð8h;mÞ consist of integer multiples
of cycles. Exemplary shmðiÞs are provided in Node A of
Figure 3. It is known that two sinusoidal signals are
orthogonal if they have integer multiples of cycles and different
frequencies. This can be readily validated by
PL1
i¼0 s
hmðiÞshm0 ðiÞ¼ 0, where ðÞ takes the complex
conjugate.
Before shmðiÞ is transmitted from radar antenna m,
Fhm is multiplied onto the signal to embed communication
information; if not required, we can simply take Fhm ¼ 1.
Propagating from the radar transmitter to the communication
receiver through the flat-fading SV channel illustrated
in the section " Channel Models Suitable for FH-MIMO
DFRC, " the M signals are scaled by the channel
where b is the channel vector given in (1), ðÞH denotes the
conjugate transpose, shðiÞ collected the information-modulated
radar signals transmitted byMantennas, andhðiÞ is an
AWGN. Note that the above signal model is obtained based
on a perfect timing, which may be challenging to realize in
practice, as will be discussed in the section " Information
Demodulation. " Differentiated by Fhm, we have different
signaling schemes/strategies which are illustrated next.
coefficients which are the elements of the vector b given
in (1). The scaling is illustrated in Figure 3 through the
second column of multipliers before Node B. The signal
received by the single-antenna communication receiver is
the sum of the scaled signals plus an AWGN (inherent in
any receiver). An AWGN is also exemplified in Figure 3.
Based on the above description, the baseband signal at the
communication receiver, i.e., the signal arriving at Node
B, is given by
yhðiÞ¼ bHshðiÞþhðiÞ
s:t: shðiÞ¼½sh0ðiÞFh0ðiÞ; .. . ;shðM1ÞðiÞFhðM1ÞðiÞT
(4)
Figure 3.
Illustration of the signal flow in FH-MIMO DFRC. For ease of illustration yet without loss of generality, four antennas, i.e., M ¼ 4 are considered.
At hop h (whose value does not affect the signal flow and hence is not specified), the subbands 1; 2; 4; and 5 are selected for antennas
0; 1; 2; and 3, respectively, which leads to kh0 ¼ 1, kh1 ¼ 2, kh2 ¼ 4 and kh3 ¼ 5. Here khm ðm ¼ 0; 1; 2; 3Þ is the subband index illustrated
in Figure 2. Nodes A, B, C, D, and E illustrate the signals given in (3), (4), (5), (6), and (7), respectively. The detailed descriptions between
the nodes and equations are presented in the respective contexts of the equations.
APRIL 2022
IEEE A&E SYSTEMS MAGAZINE
45

IEEE - Aerospace and Electronic Systems - April 2022

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