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abs denotes absolute operation.
The used chaotic system includes signum functions, maximum function and absolute operation term.
The phase rotations of all correlations are the same at all sampling points, which can be eliminated by the absolute operation.
We define an absolute operation | · | on a matrix A with elements a ij denoted by |A| whose ij th element is |a ij |.
So the approximation will not be significantly affected by the mean values, but will become less accurate with large covariance and increased number of bits because of the absolute operation in (7).
The block of only first source active is detected as block (q_1) as follows: begin{aligned} {q_1}=arg max _{q} |{Psi }({bar{mathbf {R}}} omega,q -{Psi }({bar{mathbf {R}}}(omega ))| end{aligned} (21)here (|cdot |) is the absolute operation.
Similar(54)
where |·| indicates an element-wise absolute value operation.
Taking into account that the peak detection is performed after absolute value operation, the probability density function of can be written as.
Because of the ambiguity of target vertical orientation as represented by the absolute value operation in (13), we divide the problem into two cases, i.e., when the target ascends or when it descends.
We will reserve ⊗ for Kronecker product, ⌈·⌉ for round up to an integer, (left |cdot right |) for absolute value operation, and (mathbb {N}) for the set of natural numbers without including zero; and (text {mod}left {a,bright }) denotes a modulo b, tr tracing operation, E averaging operation, round rounding operation, max maximum value operation, and diag diagonalization.
Therefore, to complete a TFC identification process, about 3N s D a real additions, N s D a real comparisons, N s D a taking absolute value operations (ABS), and N s D a XNOR gate operations are consumed by the SD, and about 4 × 8 × 0.45N s D a real additions, 4 × 0.45N s D a integer comparison, and 4 × 128 × 0.45N s D a XNOR gate operations are consumed by the TTD.
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