Demodulation of a frequency-modulated received signal by means of a Viterbi algorithm

An apparatus for demodulation of an analog received signal which is frequency-modulated at the transmitter end with a data symbol sequence {dk}, said apparatus comprising:

• a detector for zero crossings of the received signal,
• a sequence generator for production of a sequence {zi}, with a sequence element zi being a function of the difference between the times ti and ti+1 associated with two successive zero crossings, and
• a calculation unit for reconstruction of the data symbol sequence {dk}, with that data symbol sequence being chosen from the possible data symbol sequences as the sought data symbol sequence {dk} for which the Euclidean distance between the sequence {zi} 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 {dk} with a coefficient sequence {hi,k} for the index k, wherein the coefficient sequences {hi,k} are obtained from the times t1 and ti+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 {dk} is understood as the data symbol sequence {dk} being fed into a filter in which the coefficients hi,k are present, and which generates an equivalent sequence to the sequence {zi} on the output side by convolutions of the data symbol sequence {dk} with the coefficient sequences {hi,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 ti+1 when the times ti and ti+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 ti+1 when a symbol clock cycle boundary is crossed between the time ti and the time ti+1.

A method for demodulation of an analog received signal which is frequency-modulated at the transmitter end with a data symbol sequence {dk}, said method comprising:

• (a) detection of zero crossings in the received signal;
• (b) generation of a sequence {zi}, with a sequence element zi being a function of the difference between the times ti and ti+1 associated with two successive zero crossings, and
• (c) reconstruction of the data symbol sequence {dk} with a Viterbi algorithm, with that data symbol sequence being chosen from the possible data symbol sequences as the sought data symbol sequence {dk} for which the Euclidean distance between the sequence {zi} 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 {dk} with a coefficient sequence {hi,k} for the index k, wherein the coefficient sequences {hi,k} are obtained from the times ti and ti+1, wherein the frequency modulation of the analog received signal with the data symbol sequence {dk} is understood as the data symbol sequence {dk} being fed into a filter in which the coefficients hi,k are present, and which generates an equivalent sequence to the sequence {zi} on the output side by convolutions of the data symbol sequence {dk} with the coefficient sequences {hi,k}, wherein a trellis diagram whose nodes represent the filter states is used for reconstruction of the data symbol sequence {dk}, 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 ti+1 when the times ti and ti+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 ti+1 when a symbol clock cycle boundary is crossed between the time ti and the time ti+1.

A method for demodulation of an analog received signal which is frequency-modulated at the transmitter end with a data symbol sequence {dk}, said method comprising:

• (a) detection of zero crossings in the received signal;
• (b) generation of a sequence {zi}, with a sequence element zi being a function of the difference between the times ti and ti+1 associated with two successive zero crossings, and
• (c) reconstruction of the data symbol sequence {dk}, with that data symbol sequence being chosen from the possible data symbol sequences as the sought data symbol sequence {dk} for which the Euclidean distance between the sequence {zi} 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 {dk} with a coefficient sequence {hi,k} for the index k, wherein the coefficient sequences {hi,k} are obtained from the times ti and ti+1, wherein the sequence elements hi,k in the coefficient sequences {hi,k} are defined in such a way that
• z
• i
• =
• ∑
• k
• =
• -
• ∞
• ∞
• ⁢
• ⁢
• d
• k
• ·
• h
• i
• ,
• k
• ,
• wherein the sequence elements zi are given by the function
• z
• i
• =
• 1
• -
• 2
• ⁢
• ω
• 0
• π
• ·
• (
• t
• i
• +
• 1
• -
• t
• i
• )
• where ω0 the carrier frequency of the unmodulated signal,
• the coefficients hi,k are given by the function hi,k=2η·[q(ti+1−k·T)−q(ti−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.