A new method for decoding phase codes - Sodankylä Geophysical ...

A **new** **method** **for** **decoding**

**phase** **codes**

Ilkka. I. Virtanen 1 M. S. Lehtinen 2 T. Nygrén 1

M. Orispää 2 J. Vierinen 2

1 Department of Physical Sciences

University of Oulu, Finland

2 **Sodankylä** **Geophysical** Observatory

Finland

Outline

◮ Recording the amplitude data

◮ Short introduction to lag profile inversion

◮ Comparison to alternating code **decoding**

◮ First results of a code pair experiment

Data recording

◮ The attenuated transmitter signals and ionospheric echoes are

recorded in amplitude domain

◮ The digitizer is connected to the second IF stage of the radars

◮ Sampling frequency usually 1 MHz

◮ Raw samples saved in hard disk **for** later analysis

Lagged products and range

ambiguity functions

◮ Transmission envelopes env(t) and the echoes z(t) in the

same data stream

◮ A data vector contains one integration period of data

◮ Lagged products of the data vector and its complex conjugate

◮ Ambiguous lagged products from the echo part

m τ (t) = z(t)z(t − τ)

◮

Range ambiguity functions from the transmission part

W τ (t, S) = env(t − S)env(t − τ − S)

c(0, Re(z[(k 0) + 1):5000] * Conj(z[1:(5000 Re(env[1:(5000 − k)])) − k)]) Re(env[(k + 1):5000])

z(t)

env(t)

z(t')*

env(t')*

m(t,t')

W(t,S)

t

t

t

t

Lag profile inversion

◮ The radar beam is divided into range gates

◮ x k τ

is the unknown lag value in gate k

◮ Each m τ (t) is a weighted sum of the unknowns xτ

k

N∑

m τ (t) = aτ k (t)xτ k + ε τ (t),

k=1

◮ Coefficient a k τ (t) is the integral of W τ (t, S) over range gate k

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a 11 a 10 a 9 a 8 a 7 a 6 a 5 a 4 a 3 a 2 a 1

m = a 1 x 1 + a 2 x 2 + . . . + a N x N

◮ All lagged products from one integration period are collected

in a large set of linear equations

m τ = A τ x τ + ε τ

◮ The most probable lag profile and its variance can be solved

with FLIPS

◮ The same procedure **for** all lag profiles ⇒ ACF

◮ Parameter fit to the ACF using iterative **method**s

MANDA, Nov. 25th 2006, 22:05 UT, 6s integration time, real part

range / km

100 150 200 250

0.003 ms

0.048 ms

0.093 ms

0.138 ms

−1.0 0.0 1.0

−1.0 0.0 1.0

−1.0 0.0 1.0

−1.0 0.0 1.0

MANDA, Nov. 25th 2006, 22:05 UT, 6s integration time,

imaginary part

range / km

100 150 200 250

0.003 ms

0.048 ms

0.093 ms

0.138 ms

−1.0 0.0 1.0

−1.0 0.0 1.0

−1.0 0.0 1.0

−1.0 0.0 1.0

MANDA, Nov. 25th 2006, 22:05 UT, 1 min integration time

Range [km]

100 150 200 250

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Range [km]

100 150 200 250

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10.0 10.5 11.0 11.5 12.0 −200 −100 0 100 200

Log(N e

) [m −3 ]

vi [ms −1 ]

Range [km]

100 150 200 250

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Range [km]

100 150 200 250

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0 500 1000 1500 2000

Ti [K]

0 500 1000 1500 2000

Te [K]

Binary code pair experiment

◮ Nov. 26th 2006

◮ 21-bit binary code pair

◮ Bit length 10 µs

◮ In this example:

◮ Full lags 1,2,...,17,18

◮ In each full lag ± 2 µs fractional lags included

◮ Time resolution 10 seconds

◮ Range resolution 2 km

Log(N e ) [m −3 ]

range [km]

range [km]

range [km]

range [km]

180

160

140

120

100

180

160

140

120

100

180

160

140

120

100

180

160

140

120

100

21:00 21:15 21:30 21:45 22:00 22:15 22:30 22:45

UT

Ion Temperature [K]

21:00 21:15 21:30 21:45 22:00 22:15 22:30 22:45

UT

Electron Temperature [K]

21:00 21:15 21:30 21:45 22:00 22:15 22:30 22:45

UT

Ion velocity [ms −1 ]

21:00 21:15 21:30 21:45 22:00 22:15 22:30 22:45

UT

0

12.0

11.5

11.0

10.5

10.0

2000

1500

1000

500

3000

2500

2000

1500

1000

500

0

200

150

100

50

0

−50

−100

−150

−200

Summary

◮ Lag profile inversion was introduced as an analysis **method** **for**

any **phase** and / or amplitude modulated ISR experiment

◮ Lag profile inversion was successfully used **for** analysing

alternating code experiment

◮ A **new** experiment with a **phase** code pair was designed

◮ Amplitude data from the **new** experiment was successfully

analysed with lag profile inversion