(ATBD) SMAP Level 1 Radar Data Products - NASA

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where P n is the internal thermal noise power. Ground processing will estimate the
internal noise power using noise only measurements and subtract this from the raw
signal+noise measurements. The resulting estimate of P s is subject to statistical
error from both P sn and P n which is given by [10]
K 2 pc = 1
Nτ p B (1 + 2
SNR + 1
SNR 2 ) (40)
where N is the number of pulses averaged together, τ p is the pulse width, and B is
the measurement bandwidth.
Both K pc and N vary as a function of scan position or cross-track position. K pc
also varies as a function of SNR which depends on the scene being observed. The
requirements are generally applied for the worst case position which is the inner
edge of the usable swath for K pc , and assuming the average scene backscatter level
matches the designated minimum σ 0 level of -25 dB. Figures 15 and 16 show the
variation of looks (N) and K pc as functions of cross track distance. The inner edge
of the usable swath occurs at 150 km cross track distance, while the outer edge lies
at 500 km cross track distance. Additional details on these performance parameters
and how they relate to requirements are available in a preliminary calibration report
[7].
9.4 Radar Equation and Error Budget
The normalized backscattering cross-section σ 0 is related to the received power by
the radar equation (Sec. 7.16, [8]),
P s (t) =
λ2 P t (t −
(4π)
∫A
2R)u c rw(t)G 2 σ 0
dA (41)
3 R 4
where P s (t) is the received signal power referenced at the antenna port at time t, λ is
the transmitted wavelength, A is the area on the surface illuminated by the antenna
main lobe, P t (t) is the radiated transmit power pulse train, urw(t) is the receive
window filter, G is the antenna gain (neglecting transmit receive differences due to
spacecraft motion during the round trip time), σ 0 is the normalized backscattering
cross-section, and R is the range to the surface. The receive window filter is defined
by
{
1 for τrwd < t < τ
urw(t) =
rwd + τrw
(42)
0 otherwise
where τ rwd is the delay from the start of a transmitted pulse train to the time the
receive window is opened and the receiver begins digitizing echo power, and τrw is
the duration of the echo buffer.