Blind Estimation of Direct Sequence Spread Spectrum Signals(5)

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

TSATSANIS AND GIANNAKIS:BLIND ESTIMATION OF DIRECT SEQUENCE SPREAD SPECTRUM SIGNALS IN MULTIPATH 1245

set the sampling rate equal

to

in this way resulting in a problem of smaller

dimensionality.

2)The proposed method can estimate the convolution of the spreading code with the multipath channel and is useful when the code is unknown.It is still applicable,however,if the

code is known,and we are interested in the estimation of the multipath

parameters .In

this case,the

relationship

can be written in the time domain

as

after a permutation of its elements.Hence,after substi-

tuting

],the former can be solved with

respect to the

parameters

(i.e.,

is large.

Due to the inherent difficulty of the problem,it is common practice when dealing with long spread-spectrum codes to focus on identifying the parameters of the code-generating mechanism (e.g.,code-generating polynomial)rather than in estimating the entire code sequence [26].In this approach,the parameter space is systematically searched,and each generating polynomial candidate is tested against the given data.Although in the presence of multipath and bit modulation the method of [26]is not applicable,the idea of testing each candidate code can still be applied.In this framework,(24)

2We

wish to thank the anonymous reviewer who pointed out this direction.

can be extended to

describe

,

contains the elements

of

.If the candidate se-quence coincides with the true one,there exists a non-trivial solution of (29).Hence,the smallest eigenvalue

of

should be zero,and the

solution is given by the corresponding eigenvector.Thus,a test on the smallest singular value (against zero)provides a means of determining the validity of a candidate code sequence.This test should be used in connection with a systematic search of the parameter space of the generating polynomial.Uniqueness questions regarding the solution of (29),as well as identifiability conditions for this case,however,will not pursued here any further.

IV.R ECEIVER D ESIGN

The estimated signal

parameters

from the received

data .

It is well known that in a multipath environment,the maximum likelihood receiver can be implemented using the Viterbi algorithm (e.g.,[15]).Due to its computational com-plexity,however,considerable interest exists for simpler,linear solutions.In this section,we are interested in developing linear

receivers

in some

sense.Although simpler solutions may be possible if more than one sample per chip is available (e.g.,RAKE receivers),we will not pursue this direction here.

In the special case where no multipath is present,the matched filter followed by a hard limiter is known to be the optimal way to process and decode the received data (e.g.,[15]).Hence,in this

case,

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

1246IEEE TRANSACTIONS ON SIGNAL PROCESSING,VOL.45,NO.5,MAY 1997

This approach may provide satisfactory performance even when mild ISI is present,but different techniques should be applied when the ISI is severe.A.Zero-Forcing Receivers

A simple linear design that can completely eliminate ISI is the ZF receiver [9],[18].In this approach,the

receiver

in (30)is

identical

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