Information Technology Reference
In-Depth Information
The wireless channel is modeled using the Nakagami fading [10]. This distribution spans,
via the fading parameter
m,
the widest range of multipath distributions. When
→
m
,
it
converges to the AWGN channel and for
m=1
is the Rayleigh fading. Using
m<1
or
m>1
fading intensities more and less severe than Rayleigh are obtained, respectively. The
Nakagami probability density function is given by:
∞
m
m
γ
m
−
1
⎛
−
γ
⎞
⎜
⎝
⎟
⎠
f
(
γ
)
=
exp
,
for
γ
≥
0
()
m
Γ
m
γ
γ
where
γ
is the average received SNR. It is assumed that the propagation conditions between
the transmitter and the receiver are the same in both directions.
The access code and header of 2-DH packet still use the GFSK modulation mode, but the
payload of 2-DH packet uses π/4-DQPSK modulation mode. The bit error probability for the
access code and header of the forward and reverse packets are computed by the method
previously presented. The bit error probability for the payload of the forward packet is
computed according to the bit error probability in π/4-DQPSK modulation mode [15].
Compared to GFSK modulation, π/4-DQPSK modulation has higher frequency band
utilization ratio. The π/4-DQPSK demodulation of the Bluetooth system can employ the non-
coherent demodulation or frequency-discriminating demodulation, thus the hardware is
relatively simple to realize, and the system has good ability for decreasing the interference
caused by random frequency modulation of fading channel. The theoretical, closed-form
representation of bit error probability of the π/4-DQPSK modulation is [10]:
[
]
1
(
) (
)
p
(
γ
)
=
1
−
Q
γ
b
,
γ
a
+
Q
γ
b
,
γ
a
where
a
=
2 −
2
b
=
2 +
2
and
.
This expression is also closely estimated as
(
γ
∞
1
p
(
γ
)
=
Q
1
.
1716
,
where
.
2
∫
−
t
/
2
Q
(
x
)
=
e
dt
2
π
x
Similar to the 2-DH packet, the access code and header of 3-DH packet still use the
GFSK modulation mode, but the payload of 3-DH packet uses 8DQPSK modulation mode.
The bit error probability for the access code and header of the forward and reverse packets are
computed by way of GFSK. The bit error probability for the payload of the forward packet is
analyzed according to the bit error probability in 8DQPSK modulation mode. It's difficult to
calculate the exact bit error probability expression of the 8DPSK. However the noise variance
of DPSK is 200% more than that of 8DPSK [15]. As a result, PSK is 3dB superior to DPSK
[10]. According to the definition in [10], let
k
=log2
M
:
1
π
⎛
⎞
p
(
γ
)
≈
2
Q
2
k
(
γ
−
3
sin
⎝
⎠
k
M
where
M
=8, and
k
will be 3. By substituting
M
and
k
,
