Blind Estimation of Direct Sequence Spread Spectrum Signals(2)

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