Blind Estimation of Direct Sequence Spread Spectrum Signals

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

IEEE TRANSACTIONS ON SIGNAL PROCESSING,VOL.45,NO.5,MAY19971241 Blind Estimation of Direct Sequence

Spread Spectrum Signals in Multipath

Michail K.Tsatsanis,Member,IEEE,and Georgios B.Giannakis,Fellow,IEEE

Abstract—Self-recovering receivers for direct-sequence spread-spectrum signals with unknown spreading codes are discussed in this paper.Applications include signal interception,jamming, and low probability of intercept(LPI)communications.A mul-tirate/multichannel,discrete-time model of the spread spectrum signal is introduced,which establishes links with array processing techniques.Borrowing blind channel estimation ideas,which were originally developed in the context of fractionally spaced equalizers or receivers with multiple antennas,linear solutions are obtained that are independent of the input distribution.The signal interception problem is further studied,and a zero-forcing (ZF)receiver/equalizer is proposed to recover the transmitted data.Its performance is analyzed,and some illustrative simula-tions are presented.

I.I NTRODUCTION

S PREAD-SPECTRUM(SS)signals have been used for secure communications,command,and control for sev-eral decades[17].For certain applications,their antijamming capabilities and low probability of intercept justify the price to be paid in increased bandwidth.In direct-sequence spread-spectrum(DS-SS)systems,the information signal is modu-lated by a pseudo-noise(PN)sequence prior to transmission resulting in a wideband signal resistant to narrowband jam-ming or multipath.

In multiuser CDMA systems,the PN spreading sequence is typically known to the receiver,where it is used to perform the matchedfiltering(or“despreading”)operation and recover the transmitted data(e.g.,[14]).In single-user systems,however, there are cases where the receiver may have no knowledge of the transmitter’s PN sequence(e.g.,when intercepting an unfriendly transmission in LPI communications).Then,all the related issues of synchronization,multipath equalization,and data detection become more challenging.

There is an abundance of references in the literature on the problem of synchronization or“code-delay acquisition”under various interference and multipath environments,when the PN sequence is known to the receiver[1]–[3].However,

Manuscript received July5,1995;revised December27,1996.This work was supported by the National Science Foundation under Grant NSF-MIP 9424305.The associate editor coordinating the review of this paper and approving it for publication was Prof.Michael D.Zoltowski.

M.K.Tsatsanis is with the Electrical and Computer Engineering Depart-ment,Stevens Institute of Technology,Hoboken,NJ07030USA(e-mail: mtsatsan@stevens-tech.edu).

G.B.Giannakis is with the Department of Electrical Engineering,Uni-versity of Virginia,Charlottesville,V A22903-2442USA(e-mail:geor-gios@virginia.edu).

Publisher Item Identifier S1053-587X(97)03343-6.the literature is not equally rich for the case where the PN sequence is unknown.

In[11]and[26],the problem of identifying the code-generating mechanism(i.e.,the primitive generating poly-nomial)from a subset of noiseless or noisy chip sequence observations has been studied.However,these methods as-sume perfect chip synchronization and absence of multipath and data modulation,thereby limiting their applicability. Contrary to these approaches,the combined effects of the unknown spreading code and multipath channel are estimated in this work without assuming a specific structure for the code generating mechanism.In particular,novel blind algo-rithms are developed for estimating the time-delay,multipath parameters,and spreading code of the received signal.The multirate nature of the spreading and despreading operations is exploited,and a multirate/multichannel discrete-time model of the DS-SS system is introduced.This model links the spread-spectrum signal estimation problem to recently developed methods for the estimation of multiple FIR channels[13],[18], [21],[28].Multichannel methods obviate the use of higher order statistics and provide subspace-based algorithms with considerably improved performance.

The introduction of multirate/multichannel models for frac-tionally spaced equalizers has facilitated the development of fast blind algorithms for channel equalization applications [21].Multirate models of CDMA systems have also been studied in order to improve interference suppression schemes [23],[24].In this paper,the multirate spread-spectrum model is exploited to derive second-order-statistics-based,linear blind signal estimation methods.The signal parameters may be useful for purposes of intercepting or jamming the received spread-spectrum signal.

The focus of the present paper is on the interception/user acquisition problem,that is,on the recovery of the trans-mitted information data stream.Zero-forcing(ZF)linear re-ceivers/equalizers are proposed based on the estimated signal parameters.Their performance is analyzed and compared with matchedfilter-based solutions.Optimal mean-square-error ZF receivers are also derived,and their performance is studied. The rest of the paper is organized as follows.In the next section,the spread-spectrum signal estimation problem is stated in a discrete-time framework,whereas in Section III,the proposed algorithms are delineated,and identifiabil-ity issues are addressed.In Section IV,the receiver design problem is studied,and some linear solutions are proposed. The performance of these methods is evaluated in Section V,

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