Analysis of non-coherent correlation in DS/BPSK spread spectrum acquisition

Abstract

coherent detectors for initial code synchronization (acquisition) of BPSK direct sequence spread spectrum signals on an AWGN channel are analyzed. In addition to the thermal noise, in many applications such detectors are faced with the \self-noise", due to the partial period correlations. Under the random code sequences assumption, in this paper an exact analysis of the non-coherent correlator's detection performance is carried out by using the theory of circularly symmetric random variables. The exact analysis shows that the familiar Gaussian approximation to the distribution function of the code self-noise is justi ed for all cases of practical interest. Furthermore, the overall detection performance was found to be determined asymptotically by the sum of the thermal and correlator's self-noise. In most cases of practical interest, this asymptotic result provides a very good approximation to the actual detection performance of a non-coherent correlator, improving the approximations devised previously.

Direct-Sequence Communication Systems

“…The number of cells that are actually tested in a sweep of the timing uncertainty region becomes q(1 + δT 11 /∆) −1 . Since incorrect cells predominate, the substitution of the latter quantity in place of q in (7-24) and (7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20)(21)(22)(23)(24)(25) gives approximate asymptotic expressions forT a and σ 2 a when the Doppler shift is significant.…”

“…Under these conditions, V 1 is a constant, and V has a Gaussian distribution. Equations (3)(4)(5)(6)(7)(8)(9)(10) and (3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20)(21) imply that the conditional expected value of V is…”

“…Substituting (2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17) and then a i = s m (i) into (2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19), we obtain a i = a i−m ⊕ linear m-stage feedback shift register has exactly 2 m − 1 nonzero states, the period of its output sequence cannot exceed 2 m − 1. A sequence of period 2 m − 1 generated by a linear feedback shift register is called a maximal or maximal-length sequence.…”

“…The tone interference has the form i (t) = √ 2I cos (2πf c t + φ) (3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18) where I is the average power and φ is the phase relative to the desired signal. Assuming that f c >> 1/T c , (3)(4)(5)(6)(7)(8), (3)(4)(5)(6)(7)(8)(9)(10)(11), (3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18) and a change of variables give…”

“…Thus, the balanced QPSK system, for which d 1 (t) = d 2 (t), provides a lower symbol error probability against tone interference than the dual quaternary or QPSK system for which Figure 20 illustrates the performance advantage of the balanced QPSK system of Figure 19 against tone interference when f d < 1/T s . Equations (4-9) to (4-13) and (4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16) to (4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18) are used for the dual quaternary and the balanced QPSK systems, respectively, and G = 17 dB, E s /N 0 = 14 dB, and GS/I = 10 dB. The normalized frequency offset is f d T c .…”