Demodulation of a frequency-modulated received signal by means of a Viterbi algorithm
View Patent ↗Apparatus for demodulation of a signal which is frequency-modulated with a data symbol sequence {d k }, having a zero crossing detector ( 1 ), a generator ( 2 ) for production of a sequence {z i }, with z i being calculated from zero crossings t i and t i+1 , and having a unit ( 3 ) for reconstruction of the data symbol sequence {d k }, which is characterized by a minimum Euclidean distance between the sequence {z i } and an auxiliary sequence, with each sequence element in the auxiliary sequence being formed from convolution of the data symbol sequence {d k } with a sequence {h i,k } relating to the index k, and with the sequences {h i,k } being functions of the times t i and t i+1 .
1. An apparatus for demodulation of an analog received signal which is frequency-modulated at the transmitter end with a data symbol sequence {d k }, said apparatus comprising:
a detector for zero crossings of the received signal,
a sequence generator for production of a sequence {z i }, with a sequence element z i being a function of the difference between the times t i and t i+1 associated with two successive zero crossings, and
a calculation unit for reconstruction of the data symbol sequence {d k }, with that data symbol sequence being chosen from the possible data symbol sequences as the sought data symbol sequence {d k } for which the Euclidean distance between the sequence {z i } and a sequence which is calculated at the receiver end is a minimum, with each sequence element in the calculated sequence being formed from a convolution of the data symbol sequence {d k } with a coefficient sequence {h i,k } for the index k, wherein the coefficient sequences {h i,k } are obtained from the times t i and t i+1 , wherein the sequence elements h i,k in the coefficient sequences {h i,k } are defined in such a way that
z
i
=
∑
k
=
-
∞
∞
d
k
·
h
i
,
k
wherein the sequence elements z i are given by the function
z
i
=
1
-
2
ω
0
π
·
(
t
i
+
1
-
t
i
)
where ω 0 is the carrier frequency of the unmodulated signal,
in that the coefficients h i,k are given by the function h i,k =2η·[q(t i+1 −k·T)−q(t i −k·T)] where η is the modulation index, T is the symbol time duration and q(t) is the integral over the elementary pulse shape g(t), and
the modulation index ii is given by
η
=
Δω
·
T
π
and the integral q(t) over the elementary pulse shape g(t) is given by
q
(
t
)
=
1
T
∫
-
∞
t
g
(
τ
)
ⅆ
τ
,
where Δω is the modulation shift.
2. An apparatus according to claim 1 , wherein the apparatus and the transmitter which transmits the frequency-modulated signal are synchronized and, in particular, have units for symbol synchronization.
3. An apparatus according to claim 1 , wherein the frequency-modulated received signal is a CPFSK signal.
4. A cordless digital communications system based on the BLUETOOTH™ wireless technology Standard, the DECT Standard or the WDCT Standard, having an apparatus according to claim 1 .
5. An apparatus for demodulation of an analog received signal which is frequency-modulated at the transmitter end with a data symbol sequence {d k }, said apparatus comprising:
a detector for zero crossings of the received signal,
a sequence generator for production of a sequence {z i }, with a sequence element z i being a function of the difference between the times t i and t i+1 associated with two successive zero crossings, and
a calculation unit for reconstruction of the data symbol sequence {d k }, with that data symbol sequence being chosen from the possible data symbol sequences as the sought data symbol sequence {d k } for which the Euclidean distance between the sequence {z i } and a sequence which is calculated at the receiver end is a minimum, with each sequence element in the calculated sequence being formed from a convolution of the data symbol sequence {d k } with a coefficient sequence {h i,k } for the index k, wherein the coefficient sequences {h i,k } are obtained from the times t 1 and t i+1 , wherein a Viterbi algorithm is implemented in the calculation unit, wherein the frequency modulation of the analog received signal with the data symbol sequence {d k } is understood as the data symbol sequence {d k } being fed into a filter in which the coefficients h i,k are present, and which generates an equivalent sequence to the sequence {z i } on the output side by convolutions of the data symbol sequence {d k } with the coefficient sequences {h i,k }, wherein the calculation unit includes a trellis diagram whose nodes represent the filter states, with nodes located vertically one above the other in the trellis diagram relating to a same symbol clock cycle boundary,
the calculation unit calculates transmission metric values, and carries out ADD operations but no COMPARE or SELECT operations for the time t i+1 when the times t i and t i+1 are in the same symbol clock cycle, and
the calculation unit calculates transmission metric values and carries out ADD, COMPARE and SELECT operations at the time t i+1 when a symbol clock cycle boundary is crossed between the time t i and the time t i+1 .
6. A method for demodulation of an analog received signal which is frequency-modulated at the transmitter end with a data symbol sequence {d k }, said method comprising:
(a) detection of zero crossings in the received signal;
(b) generation of a sequence {z i }, with a sequence element z i being a function of the difference between the times t i and t i+1 associated with two successive zero crossings, and
(c) reconstruction of the data symbol sequence {d k } with a Viterbi algorithm, with that data symbol sequence being chosen from the possible data symbol sequences as the sought data symbol sequence {d k } for which the Euclidean distance between the sequence {z i } and a sequence which is calculated at the receiver end is a minimum, with each sequence element in the calculated sequence being formed from a convolution of the data symbol sequence {d k } with a coefficient sequence {h i,k } for the index k, wherein the coefficient sequences {h i,k } are obtained from the times t i and t i+1 , wherein the frequency modulation of the analog received signal with the data symbol sequence {d k } is understood as the data symbol sequence {d k } being fed into a filter in which the coefficients h i,k are present, and which generates an equivalent sequence to the sequence {z i } on the output side by convolutions of the data symbol sequence {d k } with the coefficient sequences {h i,k }, wherein a trellis diagram whose nodes represent the filter states is used for reconstruction of the data symbol sequence {d k }, said nodes located vertically one above the other in the trellis diagram relating to a same symbol clock cycle boundary,
branch metric values are calculated and ADD operations are carried out, but not COMPARE or SELECT operations, for the time t i+1 when the times t i and t i+1 are in the same symbol clock cycle, and
branch metric values are calculated and ADD, COMPARE and SELECT operations are carried out for the time t i+1 when a symbol clock cycle boundary is crossed between the time t i and the time t i+1 .
7. A method according to claim 6 , wherein before carrying out the method steps (a) to (c), the transmitter which is transmitting the frequency-modulated signal and the receiver which is receiving the frequency-modulated signal are synchronized.
8. A method according to claim 6 , wherein the frequency-modulated received signal is a CPFSK signal.
9. A method for demodulation of an analog received signal which is frequency-modulated at the transmitter end with a data symbol sequence {d k }, said method comprising:
(a) detection of zero crossings in the received signal;
(b) generation of a sequence {z i }, with a sequence element z i being a function of the difference between the times t i and t i+1 associated with two successive zero crossings, and
(c) reconstruction of the data symbol sequence {d k }, with that data symbol sequence being chosen from the possible data symbol sequences as the sought data symbol sequence {d k } for which the Euclidean distance between the sequence {z i } and a sequence which is calculated at the receiver end is a minimum, with each sequence element in the calculated sequence being formed from a convolution of the data symbol sequence {d k } with a coefficient sequence {h i,k } for the index k, wherein the coefficient sequences {h i,k } are obtained from the times t i and t i+1 , wherein the sequence elements h i,k in the coefficient sequences {h i,k } are defined in such a way that
z
i
=
∑
k
=
-
∞
∞
d
k
·
h
i
,
k
,
wherein the sequence elements z i are given by the function
z
i
=
1
-
2
ω
0
π
·
(
t
i
+
1
-
t
i
)
where ω 0 the carrier frequency of the unmodulated signal,
the coefficients h i,k are given by the function h i,k =2η·[q(t i+1 −k·T)−q(t i −k·T)] where η is the modulation index, T is the symbol time duration, q(t) is the integral over the elementary pulse shape g(t), and
the modulation index η is given by
η
=
Δω
·
T
π
,
the integral q(t) over the elementary pulse shape g(t) is given by
Q
(
t
)
=
1
T
∫
-
∞
t
g
(
τ
)
ⅆ
τ
,
wherein Δω is the modulation shift.