The wideband HF (WBHF) channel impulse response measurements presented here were taken over a high-latitude auroral path using the MITRE experimental WBHF test facility. A nominal instantaneous bandwidth of 1 MHz was used for the majority of the tests. These tests took place from 14 March through 1 April 1992 over a path from Sondrestrom AFB, Greenland, to Bedford, Massachusetts, a distance of approximately 3,100 km. The measurements were made using a direct-sequence pseudo-noise (DSPN) channel probe with a (±180°) chip modulation and chip rate of 1024 kchips/second. Complex channel impulse response values at increments of 500 nanoseconds in delay were derived by correlating the received signal with a set of local DSPN references uniformly spaced in delay over a delay range of 2 ms. Each of these channel impulse response values was sampled in time at a rate of up to 62.5 samples per second, resulting in the ability to observe (one-sided) Doppler spectra and shifts of up to 31.25 Hz. From these measurements, the channel scattering function, rms (2σ) Doppler spread, rms (2σ) Delay spread, Doppler shift, and rms (2σ) spread factor were calculated. In addition, for the first time, the impulse response correlation along the delay axis was calculated. These latter measurements support the use of an uncorrelated scattering hypothesis in modeling the disturbed WBHF channel.
 The scattering function is a concept that arises in modeling of random time-variant scatter-type channels. Strictly speaking, it is associated with the idealized wide-sense-stationary uncorrelated-scattering (WSSUS) channel model [Bello, 1963]. In this model, the channel is represented by a continuum of uncorrelated statistically stationary fluctuating scatterers. The scattering function is proportional to the power density spectrum of these scatterers as a function of path delay.
 An important question explored in this paper, for the first time, is the validity of the uncorrelated-scattering (US) property for the WBHF channel. The measured impulse response is the convolution of the WBHF channel impulse response with the impulse response of a composite terminal equipment filter. This equipment filter is composed of the cascade of any filters in the transmitter and receiver with a filter representing the DSPN chip pulse. Due to the smearing operation of the equipment filter, the measured impulse response will no longer be US even if the WBHF channel were WSSUS. However, one may show that if the channel were WSSUS, the correlation between impulse response fluctuations at two different delay values separated by Δ μs is proportional to the autocorrelation function of the equipment filter at the lag Δ μs. Thus, it is still possible to explore the US property to within the resolution of the equipment filter.
2. Data Collection and Processing
 The channel was probed by a 500-watt filtered DSP channel probe with a (±180°) chip modulation and chip rate of 1024 kchips/sec. A transmitter filter with a nominal bandwidth of 1 MHz was used. At the receiver, digital filtering occurred with a sampling rate of 8,192 ksamples/sec. This was followed by down sampling to 2048 complex ksamples/second. The resulting equivalent IF passband was flat to 0.1 dB over 1 MHz, but had negligible transmission outside a 2 MHz band. Thus, the composite equipment filter was essentially the same as the 1 MHz bandlimiting filter at the transmitter.
 The sampled waveform was next processed by a narrowband interference excisor, and correlated with the reference DSPN signal over 4096 taps, each spaced approximately 500 nanoseconds apart. This resulted in a total delay window of approximately 2 ms. Each correlator includes an integrate and dump (I&D) circuit, the outputs of which are used to produce estimates of the channel impulse response. For these experiments, a channel measurement consisted of a series of 512 impulse response measurements taken at sampling rates of 62.5, 31.25, or 15.625 samples/second, resulting in channel measurement durations of 8.192, 16,384, or 30.768 seconds, respectively. The selection of sampling rate was guided by the extent to which the channel appeared disturbed as evidenced by the prior chirp sounder results. The more disturbed the channel the higher the sampling rate used. At the very beginning of the probe experiment, before data collection began, the delay of the DSPN sequence was adjusted such that substantially all of the impulse response was positioned in the correlator window. The resulting channel probe data was processed off-line after completion of the testing. An approximation of the scattering function was calculated from the family of 512 impulse response measurements by averaging the squared magnitude of four successive 128-point discrete Fourier transforms of the impulse response at each value of delay and smoothing in both the delay and Doppler dimensions by use of windows. A 25-point Kaiser-Bessel window was used in the Doppler domain and a 45-point Kaiser-Bessel window was used in the delay domain. The resulting calculation is referred to here as the scattering function estimate.
 The above procedure was used to estimate the scattering function for each of the channel measurements recorded during the tests. The rms (2σ) Doppler spread, rms (2σ) Delay spread, and Doppler shift values were then compiled to form a database of measured channel conditions during the testing interval.
Figure 1a is an example scattering function and Figure 1b, the associated contour plot for the channel measurement taken on 1 April 1992 at 0734 UTC at a center frequency of 15.5 MHz. Here, the contour plot is shown to illustrate the fine details regarding the location of the major propagation modes in terms of delay and Doppler axis values. The levels of the contour were chosen to subdivide the power axis into 20 equal divisions. The rms Doppler spread for this example is 7.5 Hz, the rms multipath spread is around 100 μs, and the mean Doppler shift is 6.6 Hz.
Figure 2 shows a standard oblique-incidence ionogram using a chirp sounder. The ticks on the vertical scale are separated by a ms. This ionospheric snapshot was taken just after the WBHF channel measurement shown in Figure 1. As noted, the rms multipath spread of the measurement in Figure 1 is 100 μs. This is consistent with the energy spread in delay over 300 to 400 microseconds evident on the oblique ionogram at the center frequency of 15.5 MHz.
Figures 3a through 3d present plots of the cumulative distribution functions of the rms Doppler spread, Doppler shift magnitude, rms delay spread, and rms spread factor (product of multipath spread and Doppler spread) values for the entire WBHF channel probe database obtained during the tests. Because the study was focused on the parameters for individual propagation modes, impulse response measurements that had significant signal contributions from more than one propagation mode were removed. There were approximately 100 channel probe measurements left in the database.
Figure 3a shows that the median value of rms Doppler spread observed during the tests was 5 Hz, with 10th and 90th percentile values of 1.75 and 13 Hz, respectively. The largest value observed was 17 Hz. Extensive use was made of geophysical and solar-terrestrial conditions as reported by the Space Environment Services Laboratory (SESL) during the tests. There was a noticeable correlation between large solar flares on 15 March and 1 April and the measured wideband channel conditions. The largest value of rms Doppler spread was measured on 15 March and it is believed that this disturbance is directly attributable to the major M-class solar flare observed on that day. Although the test period could be characterized as relatively “quiet” to “unsettled” except for the events around 14 and 15 March and 1 April, there was an overall “floor,” or average value during periods of quiet geomagnetic activity, of roughly 2 Hz rms Doppler spread. Even this value represents mildly disturbed conditions relative to the nominal Doppler spread of less than 0.4 Hz recorded on midlatitude paths [Clune et al., 1991].
 The Doppler shifts of the main propagation modes recorded by the channel probes were generally small. Figure 3b shows the cumulative distribution of the Doppler shift magnitude for the database. Here the median value is seen to be roughly 0.5 Hz; the 10th percentile indicated no shift, and the 90th percentile shift is just below 3 Hz. Increased shift values were noted on 1 April, the date of the disturbed magnetic conditions, when there were several consecutive positive Doppler shifts of relatively large magnitude, implying a pronounced “drift” velocity of the ionosphere.
Figure 3c is a plot of the cumulative distribution of the rms delay spread. The median value is seen to be roughly 100 microseconds; the 10th percentile point was found to be 17 microseconds; the 90th percentile point is slightly larger than 400 microseconds. Values of delay spread were moderately large during unsettled to active periods of geomagnetic disturbances. Large delay spread values are indicative of disturbed channels commonly described as “spread F” or “auroral F. The latter terminology arises from the large spread easily identified on the F-layer traces of a standard oblique ionogram. It was again noted that the largest values of delay spread were recorded on 1 April.
Figure 4 shows a scatterplot of the Doppler and delay spread for each experiment. The product of rms delay spread and rms Doppler spread we call the rms spread factor. Kailath  showed that a random time-varying channel becomes nonmeasurable when the spread factor exceeds 1, where he defined spread factor as the product of total Doppler spread by total delay spread. Bello  sharpened this criterion by showing that the channel becomes nonmeasurable when the area spread factor is greater than 1, where the area spread factor is the area occupied by the scattering function over the delay-Doppler plane. The ambiguity associated with the term “spread factor” is analogous to the ambiguity of the term “bandwidth”. We have chosen to measure rms-spread factor to simplify the processing.
 An important reason for measuring spread factor is the fact that the maximum output SNR of the channel impulse response or transfer function measurement (by any means) is equal to the input SNR to the receiver divided by the area spread factor. In many advanced communication and radar techniques involving adaptive processing of multipath-distorted radio signals, real-time measurements of impulse response or transfer function are used. Knowing the spread factor statistics of a channel allows one to determine whether the desired level of processing gain can be achieved.
 The rms spread factor has been calculated for each of the channel measurements in the database. The cumulative distribution of the values is shown in Figure 3d. Because this figure was plotted to show the common range of values, the absolute minimum value of 7.4 × 10−6 cannot be read. The absolute largest value was 7.5 × 10−3; the median was 5.3 × 10−4; the 10th percentile was less than 10−4; and the 90th percentile was 6 × 10−3. Thus minimum processing gains in channel measurement of around 21 dB should be achievable with the disturbed WBHF channels measured in the experiments reported herein. The values of delay spread, Doppler spread, and spread factor are comparable to those obtained by Wagner  for a near vertical incidence Auroral HF channel, although our Doppler spreads and spread factors are somewhat larger.
4. Correlation Coefficient of Channel Measurements
 The normalized correlation between impulse response samples, ρ(m, p), is estimated from the ensemble of measured impulse responses, as follows:
where h(kT, mΔ) is the N-sample complex channel impulse response measured at t = kT seconds. The spacing between samples is Δ seconds and mΔ is the mth impulse response sample. μm is the sample mean of the impulse response at the delay mΔ. We are interested in the way that decreases with the time delay pΔ. For the experiment the tap spacing, Δ, was 0.488 μs and T was 0.032 seconds.
 The correlation coefficients were calculated for the channel impulse response measurement examined above in the discussion of the channel scattering function. The impulse response has significant magnitude between samples 200 and 400. ρ(m, p) was then calculated using samples 200 through 399 resulting in the 200 × 200 correlation coefficient matrix. Figure 5 presents the estimated magnitude of the normalized correlation between impulse response samples as a function of the delay separation in microseconds. We obtained this estimate from the correlation matrix by averaging all the correlation values corresponding to a fixed delay separation between taps. The correlation between taps is seen to drop to small values within a few microseconds. The results presented using this example are representative of several such correlation analyses that were performed.
 High-latitude HF-channel 1 MHz bandwidth impulse responses were measured at several frequencies over a 3,100-km path from Sondrestrom AFB, Greenland, to Bedford, Massachusetts, from 14 March through 1 April 1992. From these measurements, computations were made of delay-Doppler scattering functions, rms (2σ) Doppler spreads, Doppler shifts, rms (2σ) delay spreads, rms (2σ) spread factors, and impulse response correlations versus path delay. The largest value, 90th percentile, and 10th percentile of the rms Doppler spread, Doppler shift, rms delay spread and rms spread factor were (16.8 Hz, 13.0 Hz, 1.75 Hz, respectively), (7.0 Hz, 3 Hz, ≪ 1 Hz, respectively), (780 μs, 400 μs,17 μs, respectively), and (7.5 × 10−3, 6 × 10−3, <10−4, respectively). The ionosphere was mildly disturbed, except for major solar flares on 14 and 15 March and 1 April. Larger Doppler spreads and shifts can be correlated to these events. Impulse response correlations versus path delay drop to small values for delay changes of the order of the equipment filter impulse response autocorrelation function, supporting the hypothesis of an uncorrelated scattering channel model.
 The authors would like to extend thanks to all the people that participated in the experiment preparation and execution. We would especially like to thank the equipment operators including Paul Fine, Marc Richard, Marcel Jussaume, and Joel Freedman for the long hours and dedication they displayed. We would also like to thank Ed Piekielek for the uploading and copying of the data tapes.