Blind Estimation of Direct Sequence Spread Spectrum Signals(2)
时间:2025-07-11
时间:2025-07-11
Abstract—Self-recovering receivers for direct-sequence spreadspectrum signals with unknown spreading codes are discussed in this paper. Applications include signal interception, jamming, and low probability of intercept (LPI) communications. A multirate/m
1242IEEE TRANSACTIONS ON SIGNAL PROCESSING,VOL.45,NO.5,MAY
1997
Fig.1.Direct-sequence spread-spectrum
modulation.
Fig.2.Direct-sequence spreading operation.
whereas issues related to timing and bit rate estimation are discussed in Section VI.Finally,some illustrative simulation results and conclusions are presented in Sections VII and VIII,respectively.
II.DS/SS S IGNAL M ODEL
In most studies of DS/SS systems,the continuous-time transmitted signal
1is modeled as a product of two waveforms (see Fig.
1)
(1)
where is the information bearing signal before spreading,whereas is the (periodically extended)spreading code waveform that is typically of much larger bandwidth
than
.
Despite its simplicity,this formulation does not reveal the multirate nature of the spreading operation and does not lend itself to the derivation of convenient discrete-time models.Since the spreading procedure is typically performed in discrete time,it will be useful in the sequel to describe it as a multirate convolution.A.Multirate Framework
Let
be a spreading code
chip sequence of
length
chips per
information symbol.Then,the transmitted discrete-time signal at the chip rate
is
and filtered
by
.
In some DS/SS systems,a spreading code that is longer than the bit period is used.In this case,consecutive information
1Subscript
c is use
d to denot
e continuous time signals,and index t denotes
continuous time.
symbols modulate different consecutive portions of the spread-ing code in a circular fashion.Equation (2)can be extended to cover this case,as we explain next.
Let be a code sequence of
length .
Let
be a family of sequences defined
as
and,
if
mod
,.Then,the transmitted
discrete-time signal can be expressed
as
is transmitted through a possibly dispersive
channel at a chip
rate denote the complex baseband representation of the overall impulse response of the channel,including multipath effects and the transmitter and receiver spectral shaping filters.Then,the received signal at the receiver
is
(4)
where
is additive Gauss-ian noise.
Substituting
from (2)to (4),we
obtain
is the combined impulse response of the channel
and the spreading code.The summation limits in (6)come from the nonzero support
of
over
(7)
where
is the sampled impulse response,
and .In addition,from (6),the overall impulse
response
is
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