Phase II Final Report - NASA's Institute for Advanced Concepts

Planetary Exploration Using Biomimetics
An Entomopter for Flight on Mars
⎛ E
BER = Q⎜
0.5*
⎝ N
b
o
⎞
⎟
⎠
Equation 4-8
where Q(x) is the complementary error function defined as
∞
∫
x
1
2
Q ( x)
= exp( −u
/ 2)
du
2π
Equation 4-9
Thus, the required peak power can be related to desired BER. The average power, on the other
hand, depends on the data rate R b . The data rate for OOK can be expressed as one transmitted
pulse, or bit, per interpulse period T, or
1
R b
= bits/second.
T
Equation 4-10
It follows that the duty cycle dt can be expressed as
T
dt =
T
w
Equation 4-11
and the average transmitter power can be expressed as
P
avg
= dt P T
Equation 4-12
or in terms of data rate as
P = T
avg
w
R
b
P
T
Equation 4-13
4.3.5.2 Radar Analysis
Unlike communications, when using a MGW for radar, the required peak transmitting power is
dependent on the waveform [291] and can be expressed as
P
T
4 4 2
SNR Lo
k
BT
4 π r c Tmgw
=
2 2
σ G λ T 3
3
o
2
T
w
Equation 4-14
In this equation, Tmgw is a time scale parameter, c is the speed of light, σ is the effective radar
cross-section of the target, and f m is a factor introduced by the modulation of the waveform
around a carrier frequency f o .
2
⎡ w1
− ⎤
2
3⎢1
+ e ⎥
Equation 4-15
⎢ ⎥
f =
⎣ ⎦
m
1+
w
2
1
+ e
2
w1
−
2
where w 1 =ω o Tmgw and ω o = 2 π f o.
2
f
m
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Phase II Final Report