50 research outputs found
Almost Linear Complexity Methods for Delay-Doppler Channel Estimation
A fundamental task in wireless communication is channel estimation: Compute
the channel parameters a signal undergoes while traveling from a transmitter to
a receiver. In the case of delay-Doppler channel, i.e., a signal undergoes only
delay and Doppler shifts, a widely used method to compute delay-Doppler
parameters is the pseudo-random method. It uses a pseudo-random sequence of
length N; and, in case of non-trivial relative velocity between transmitter and
receiver, its computational complexity is O(N^2logN) arithmetic operations. In
[1] the flag method was introduced to provide a faster algorithm for
delay-Doppler channel estimation. It uses specially designed flag sequences and
its complexity is O(rNlogN) for channels of sparsity r. In these notes, we
introduce the incidence and cross methods for channel estimation. They use
triple-chirp and double-chirp sequences of length N, correspondingly. These
sequences are closely related to chirp sequences widely used in radar systems.
The arithmetic complexity of the incidence and cross methods is O(NlogN + r^3),
and O(NlogN + r^2), respectively.Comment: 4 double column pages. arXiv admin note: substantial text overlap
with arXiv:1309.372
On the diagonalization of the discrete Fourier transform
The discrete Fourier transform (DFT) is an important operator which acts on
the Hilbert space of complex valued functions on the ring Z/NZ. In the case
where N=p is an odd prime number, we exhibit a canonical basis of eigenvectors
for the DFT. The transition matrix from the standard basis to the canonical
basis defines a novel transform which we call the discrete oscillator transform
(DOT for short). Finally, we describe a fast algorithm for computing the
discrete oscillator transform in certain cases.Comment: Accepted for publication in the journal "Applied and Computational
Harmonic Analysis": Appl. Comput. Harmon. Anal. (2009),
doi:10.1016/j.acha.2008.11.003. Key words: Discrete Fourier Transform, Weil
Representation, Canonical Eigenvectors, Oscillator Transform, Fast Oscillator
Transfor
Performance Estimates of the Pseudo-Random Method for Radar Detection
A performance of the pseudo-random method for the radar detection is
analyzed. The radar sends a pseudo-random sequence of length , and receives
echo from targets. We assume the natural assumptions of uniformity on the
channel and of the square root cancellation on the noise. Then for , where , the following holds: (i) the probability of
detection goes to one, and (ii) the expected number of false targets goes to
zero, as goes to infinity.Comment: 5 pages, two figures, to appear in Proceedings of ISIT 2014 - IEEE
International Symposium on Information Theory, Honolul