## 1. Introduction

[2] Phase coding techniques include biphase and polyphase coding. They use digital methods to develop a compressed pulse having low sidelobes and permit to reduce the peak transmitting power of the ionospheric sounders and radar systems [*Bibl and Reinisch*, 1978; *Reinisch*, 1986; *Huang and MacDougall*, 2005]. Compared with biphase coding, polyphase coding produces lower sidelobe levels, but it is more sensitive to Doppler and its coding and decoding systems are more complex [*Golomb and Scholtz*, 1965; *Somaini and Ackroyd*, 1974]. Therefore, the practical biphase coding has been widely applied to radio systems.

[3] In binary phase coding, the phase of any pulse has one of two possible values. The values 0 and *π* are popular choices that have the widest possible separation (since phase is modulo 2*π*) and generally lead to the best performance. In order to get a unique echo after pulse compression, one requires the phase coding sequence having three perfect randomness properties, including perfect balance property, run property and autocorrelation property [*Golomb*, 1982], thereinto, the autocorrelation property is the most important and determines the sequence performance. The poor autocorrelation property would produce the sidelobes, which raise the noise level and induce the false echoes.

[4] The binary pseudorandom sequences with zero out-of-phase autocorrelation coefficients are perfectly suited for phase coding radio system and we call them perfect sequences [*Golomb*, 1992; *Freedman et al.*, 1995; *Jungnickel and Pott*, 1999]. The detection signals coded by perfect sequences have no extended range sidelobes theoretically. A perfect sequence of period *n*, written as a row vector *B* = [*b*_{0}, *b*_{1}, …*b*_{i} …, *b*_{n−1}], *b*_{i} ∈(− 1, + 1), has the autocorrelation function shown as follows:

In this expression, *E* denotes the energy of vector *B* and *b*_{i+τ} is the shifted vector of *b*_{i}. However, in the case of (−1, +1) sequences of period *n*, it has been proven that there is no perfect sequence with period 4 < *n* ⩽ 12100 [*Baumert*, 1971]. However, detection without range sidelobes by binary coding is still possible and the complementary code is a very good solution [*Golay*, 1961].

[5] In this paper we describe another biphase coding technique (almost perfect sequence) to eliminate range sidelobes. Almost perfect sequence exhibiting zero out-of-phase autocorrelation except one value in the middle could replace perfect sequence to sound without sidelobes and so the problem that the superposed sidelobes submerge the mainlobes of the weak echoes in ionospheric oblique backscattering detection can be solved. We give an algebraic explanation of almost perfect sequences and then compare them with perfect sequence and *m* sequences by ambiguity function and real detection. The Wuhan ionospheric oblique backscattering sounding system (WIOBSS) developed by Ionospheric Laboratory is used to test the sequences [*Chen et al.*, 2007, 2009].