## 1. Background and Introduction

[2] The incoherent scatter technique has been successfully used to study the Earth's ionosphere for almost 50 years, and has demonstrated its usefulness under widely varying conditions. As the technique has been applied to more demanding conditions, huge advances in instrumentation and techniques has improved the precision of the measurements and the speed at which they can be made by orders of magnitude.

[3] While there are some special cases where measurement of back-scattered power is enough to be of interest, the more usual case is that the experimenter is interested in the physics embodied in the thermal or excited fluctuation spectrum of the ionospheric plasma, and then the spectral properties of the scattered signal must be measured. It is possible to estimate this spectrum directly, e.g., through a filter-bank technique [*Farley*, 1969], but this requires a prohibitively long pulse to be used, and the more common approach is to admit a band-limited signal into the radar receiver, and then estimate its spectrum by one of a multitude of techniques, depending on the operating parameters of the radar and the properties of the plasma under observation.

[4] When the correlation time of the plasma is much longer than the pulse round-trip time to the observed volume, pulse-to-pulse correlation techniques are used. (low radar frequencies; mesopause and below; not explained or discussed further here).

[5] Otherwise, the correlation time of the plasma is short enough that no correlations will remain between independently transmitted and received pulses. In this case, the spectrum must be estimated from the scattering from every transmitted pulse or pulse group. While it is possible to use Fourier transform-based techniques on the received signal, it is more common to estimate the spectrum by way of the signal's autocorrelation function (ACF), whose Fourier transform is an estimate of the scattered power spectral density, or power spectrum [e.g., *Peebles*, 1993]. For the scattered spectrum to be accurately measured, the pulse must be longer than 3.5 times the correlation time of the plasma [*Vallinkoski*, 1988]. At the same time, the pulse must be short enough that it does not average over volumes with too different physical parameters (e.g., it must be shorter than a typical ionospheric scale height), and it must also be short enough that it can be transmitted before the first signal of interest begins to arrive at the receiver. When these requirements can all be met simultaneously, a long, uncoded pulse can be used [e.g., *Farley*, 1969].

[6] In many interesting situations, however, these requirements cannot be satisfied simultaneously, and some sort of subpulse technique is necessary. The simplest of these, and the easiest to understand, is the double-pulse technique [*Farley*, 1969]. To estimate the ACF from range *h* at lag *τ* with a range resolution of *δh*, two pulses, each of length *δt* = 2*δh*/*c* are transmitted with an interval of *τ* between the start of the two pulses. The receiver is then opened, and (complex baseband) samples *v*_{0} and *v*_{1} are taken at times 2*h*/*c* and 2*h*/*c* + *τ*. The experiment is repeated a number of times, and the quantity 〈*v*_{0}*v**_{1}〉, where 〈〉 signifies average and *v** is the complex conjugate of *v*, is our estimate of the desired correlation at this lag. The setup is illustrated in Figure 1. In Figure 1, range increases along the vertical axis and time along the horizontal axis. This type of diagram is called a range-time diagram, or a Farley diagram. The diagonal lines rising with increasing time (to the right) indicate how the bauds of the transmitted pulse propagate outward with time, while the diagonals which descend with increasing time indicate what regions of range and time could potentially influence a measurement taken at a particular time, i.e., the time when these lines reach the horizontal axis.

[7] Every sample contains scattered signal from both elementary pulses, but the signal contributions from the nonoverlapping regions in Figure 1 do not correlate, and will instead contribute to an increased noise floor in the measurement. This noncorrelating signal we call self-clutter. Even in the absence of noise the standard deviation of an autocorrelation functions estimate is greater than the expected value for single measurements. The variance for correlated products is reduced to tolerable levels through incoherent integration, usually over a few hundred to several thousand realizations (radar pulses). In practice, a number of samples are taken to cover all ranges of interest with every pulse, while the spacing *τ* is varied to obtain a sufficiently densely sampled ACF such that the scattered spectrum can be estimated. If 1000 incoherent integrations are required, and the time between transmitted pulse pairs (the interpulse period, or IPP) is 10 ms, it will take 10 s to estimate a single lag of the ACF. Typical time to complete a spectral measurement is then 2–5 min.

[8] An interesting variation of the double-pulse technique is to transmit the two elementary pulses with orthogonal polarizations, and to sample both polarizations simultaneously in independent receivers. In this case, every polarized sample contains signal from only the transmitted pulse with that polarization [*Farley*, 1969], and the variance of the lagged product is reduced by a factor of 4, as explained below.

[9] By using several short pulses with nonredundant spacing (i.e., the spacing between any pair of short pulses in the sequence appears only once) it is possible to measure several lags with every set of pulses [*Farley*, 1972]. This dramatically reduces the time necessary to obtain the spectral measurement, at the price of an increase in self-clutter. For an multipulse code with *N* short pulses, the variance of each lagged product is proportional to *N*^{2}.

[10] The double pulse and multipulse measurements share the drawback that the transmitter is used only for a small proportion of the time theoretically available for transmission. One improvement possible, if the transmitter has sufficient fidelity, is to interleave several multiple-pulse patterns at different frequencies. The EISCAT radars were designed to have such capability from the outset, and used this approach for many years [*Turunen and Silén*, 1984].

[11] While this approach keeps the transmitter fully occupied, it is only possible to form correlations between the signal from the elementary pulses at a single frequency. A multiple-pulse sequence can only have a single estimate of each lag at every range, and for *N* > 4 there will always be lags that are missing in the lag sequence.

[12] Ideally, one would want to keep the transmitter at the same frequency and transmit the elementary pulses with no spacing between them, as long as the signal from the elementary pulses can be distinguished on the receive side. (When phase coding is used, we will refer to the shortest constant-phase element of a transmitted pulse as a baud.) It is a remarkable fact that this is actually possible: not in a single pulse measurement, but through a phase coding which is varied from one pulse to the next. The working of this alternating code approach [*Sulzer*, 1986; *Lehtinen*, 1986; *Lehtinen and Häggström*, 1987] is repeated more fully in the next section. Then in the following section we show the benefits of transmitting consecutive bits of the code in orthogonal polarization.