## 1 Introduction

[2] Incoherent scatter radars are high-power large-aperture radars that are used for detecting the weak radio wave scattering from thermal fluctuations in the ionospheric plasma. Pulse compression by means of binary phase coding is routinely applied in incoherent scatter measurements, often in the form of Barker codes [*Barker*, 1953] or alternating codes [*Lehtinen and Häggström*, 1987; *Sulzer*, 1993].

[3] Barker codes are mainly used in the ionospheric D-region, because coherence requirements set by the Barker code decoding can typically only be met there. At higher altitudes, the Barker codes can be used for subcoding individual bits of other modulations. Binary Barker codes are only known for code lengths of 2, 3, 4, 5, 7, 11, and 13 bits.

[4] Barker codes are conventionally decoded by means of matched filtering, which causes range sidelobes to the decoded signal. The definition of Barker codes requires that the amplitude of a range sidelobe of an *N*_{b}-bit code is at most a fraction 1/*N*_{b} of the mainlobe amplitude. Alternatively, the sidelobes can be suppressed by means of inverse filtering [*Ruprecht*, 1989; *Lehtinen et al.*, 2004]. Because inverse filtering is applicable to almost any modulation, an extensive search for optimal binary codes for *N*_{b}=3,…,25 has been performed by *Lehtinen et al.* [2004]. Codes providing signal-to-noise ratio within 25% from optimal in inverse filter decoding were found for most of these code lengths.

[5] Alternating codes are designed for spectrally overspread targets, which makes them suitable for incoherent scatter measurements from the ionospheric E- and F-regions. Alternating codes consist of code cycles of *N*_{c} codes with *N*_{b} bits in each code. For the type 1 alternating codes of *Lehtinen and Häggström* [1987], *N*_{b}=2^{m}, where *m* is a positive integer and *N*_{c}=*N*_{b} for “weak” codes and *N*_{c}=2*N*_{b} for “strong” codes. Strong codes are typically used, because they allow uncoded bits to be transmitted without intervening gaps.

[6] Codes of an *N*_{b}-bit alternating code cycle can be truncated to any length shorter than *N*_{b}, but the length of the code cycle will still be *N*_{c}=2*N*_{b} for strong codes and *N*_{c}=*N*_{b} for weak codes. Type 2 [*Sulzer*, 1993] alternating codes provide code and code cycle lengths that are not restricted to powers of two, but these codes are only known for the lengths of 8, 9, 10, 11, 12 and 14 bits [*Sulzer*, 1993; *Markkanen et al.*, 2008].

[7] An obvious possibility for finding more and better phase codes is to use more than two phases. A polyphase generalization of Barker codes was published already by *Golomb and Scholtz* [1965], and new code lengths up to 77 bits have been published by several authors [*Bömer and Antweiler*, 1989; *Friese*, 1996; *Brenner*, 1998; *Nunn and Coxson*, 2009]. Similar generalizations are possible for type 1 alternating codes, [*Markkanen et al.*, 2008] and for the codes optimized for inverse filtering [*Damtie et al.*, 2008].

[8] *Damtie et al.* [2008] have evaluated individual phase codes in terms of the signal-to-noise ratio after inverse filter decoding, and performed an exhaustive search for optimal quadriphase codes for code lengths of *N*_{b}=2,…,22. The quadriphase coding provided codes with higher signal-to-noise ratio in inverse filter decoding than the binary coding in [*Lehtinen et al.*, 2004] at several code lengths.

[9] The polyphase alternating codes of *Markkanen et al.* [2008] have code lengths of *N*_{b}=*p*^{m} or *N*_{b}=*p*−1 bits, where *p* is a prime and *m* is a positive integer. As the cycle length of strong codes is still *N*_{c}=2*N*_{b}, the polyphase generalization obviously provides a larger number of code cycle lengths when compared with the binary alternating codes.

[10] As an arbitrary waveform generator has recently been installed at the Millstone Hill incoherent scatter radar, part of the National Science Foundation (NSF) Geospace Facility operated by the Massachusetts Institute of Technology (MIT) Haystack Observatory, a possibility for testing the polyphase modulations in incoherent scatter measurements has now become available. We have performed a set of experiments in which both polyphase codes and closely similar binary codes were transmitted. We can thus investigate both the absolute performance of the modulations as well as compare the performance of polyphase codes with the traditional binary ones.