Bluetooth low energy frequency offset and modulation index estimation
View Patent ↗A Bluetooth Low Energy (BLE) device, having a demodulator configured to translate in-phase and quadrature components of a received BLE signal into a differential phase signal; an estimator configured to estimate a frequency offset of the differential phase signal; and a detector configured to detect information in the differential phase signal corrected by the estimated frequency offset.
1. A Bluetooth Low Energy (BLE) device, comprising:
a demodulator configured to translate in-phase and quadrature components of a received BLE signal into a differential phase signal;
an estimator configured to estimate a frequency offset of the differential phase signal, and configured to estimate a modulation index of the differential phase signal; and
a detector configured to detect information in the differential phase signal corrected by the estimated frequency offset using the estimated modulation index,
wherein
the differential phase signal is represented as
d
Θ
k
=
2
f
off
·
dt
+
η
·
∑
l
=
k
-
19
l
=
k
+
19
b
l
·
g
(
t
-
1
·
dt
)
+
w
k
,
where dΘ k is the differential phase signal, f off is the frequency offset, η is the modulation index, b l is the data sequence, g(t) is the Gaussian pulse, k is an index, and w k is the noise, and
the estimating the frequency offset comprises:
calculating coefficients C k in accordance with the following equation:
C
k
=
∑
l
=
k
-
19
l
=
k
+
19
b
l
·
g
(
t
-
1
·
dt
)
,
where dΘ k =2f off ·dt+C k ·η,
summing differential phase signals which have data sequences b k positively aligned, and summing differential phase signals that have data sequences b k negatively aligned, to obtain the following positive and negative equations, respectively:
ɛ
M
=
∑
m
=
1
M
d
Θ
m
=
M
·
2
π
f
off
·
dt
+
∑
m
=
1
M
C
m
·
η
,
where b m =1,m=1 . . . M, and
ɛ
N
=
∑
n
=
1
N
d
Θ
n
=
N
·
2
π
f
off
·
dt
+
∑
n
=
1
N
C
n
·
η
,
where b n =1,n=1 . . . N,
calculating α in accordance with the following equation:
α
=
∑
m
=
1
M
C
m
∑
n
=
1
N
C
n
,
and
calculating the frequency offset in accordance with the following equation:
f
^
off
=
ɛ
M
+
α
·
ɛ
N
2
·
dt
·
(
M
+
α
·
N
)
.
2. The BLE device of claim 1 , wherein the demodulator comprises:
a COrdinate Rotation Digital Computer (CORDIC) configured to obtain from the in-phase and quadrature components of the received BLE signal a phase signal; and
a differentiator configured to generate from the phase signal the differential phase signal.
3. The BLE device of claim 1 , wherein the detector is a Maximum Likelihood Sequence Detector (MLSD).
4. A Bluetooth Low Energy (BLE) system, comprising:
a first BLE device, which is the BLE device of claim 1 ; and
a second BLE device communicating with the first BLE device.
5. The BLE device of claim 1 ,
wherein estimating a modulation index of the differential phase signal comprises calculating the modulation index in accordance with the following equation:
η
^
=
ɛ
M
+
ɛ
N
-
(
M
+
N
)
·
2
f
^
off
·
d
t
∑
m
=
1
M
C
m
-
∑
n
=
1
N
C
n
.
6. A Bluetooth Low Energy (BLE) method, comprising:
translating, by a demodulator, in-phase and quadrature components of a received BLE signal into a differential phase signal;
estimating, by an estimator, a frequency offset of the differential phase signal;
estimating, by the estimator, a modulation index of the differential phase signal; and
detecting, by a detector, information in the differential phase signal corrected by the estimated frequency offset using the estimated modulation index,
wherein
the differential phase signal is represented as
d
Θ
k
=
2
f
off
·
dt
+
η
·
∑
l
=
k
-
19
l
=
k
+
19
b
l
·
g
(
t
-
1
·
dt
)
+
w
k
,
where dΘ k is the differential phase signal, f off is the frequency offset, η is the modulation index, b l is the data sequence, g(t) is the Gaussian pulse, k is an index, and w k is the noise, and
the estimating the frequency offset comprises:
calculating coefficients C k in accordance with the following equation:
C
k
=
∑
l
=
k
-
19
l
=
k
+
19
b
l
·
g
(
t
-
1
·
dt
)
,
where dΘ k =2f off ·dt+C k ·η,
summing differential phase signals which have data sequences b k positively aligned, and summing differential phase signals that have data sequences b k negatively aligned, to obtain the following positive and negative equations, respectively:
ɛ
M
=
∑
m
=
1
M
d
Θ
m
=
M
·
2
π
f
off
·
dt
+
∑
m
=
1
M
C
m
·
η
,
where b m =1,m=1 . . . M, and
ɛ
N
=
∑
n
=
1
N
d
Θ
n
=
N
·
2
π
f
off
·
dt
+
∑
n
=
1
N
C
n
·
η
,
where b n =1,n=1 . . . N,
calculating α in accordance with the following equation:
α
=
∑
m
=
1
M
C
m
∑
n
=
1
N
C
n
,
and
calculating the frequency offset in accordance with the following equation:
f
^
off
=
ɛ
M
+
α
·
ɛ
N
2
·
d
t
·
(
M
+
α
·
N
)
.
7. The BLE method of claim 6 , further comprising buffering the differential phase signal until synchronization is found.
8. The BLE method of claim 6 ,
wherein estimating a modulation index of the differential phase signal comprises calculating the modulation index in accordance with the following equation:
η
^
=
ɛ
M
+
ɛ
N
-
(
M
+
N
)
·
2
f
^
off
·
d
t
∑
m
=
1
M
C
m
-
∑
n
=
1
N
C
n
,
and
further comprising detecting, by the detector, the information in the differential phase signal using the estimated modulation index.
9. A computer program product embodied on a non-transitory computer-readable medium comprising program instructions configured such that when executed by processing circuitry cause the processing circuitry to implement the method of claim 6 .