# US 2010/0166101 A1 · Method for estimating the signal-to-noise ratio for packet transmission and reception systems of signals based on m-dpsk modulations and apparatus thereof

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- Number: US 2010/0166101 A1
- Document ID: US20100166101A1
- Status: Published application
- Kind: A1
- Application number: 12/646,348
- Filed: 2009-12-23
- Published: 2010-07-01
- Earliest claimed: 2008-12-23
- Assignees: Dora S.p.A.
- Inventors: Paola Bisaglia; Simone Bois; Eleonora Guerrini
- Web page: https://patentgrep.com/patent/US20100166101A1

## CPC

- H04L 27/2331: {wherein the received signal is demodulated using one or more delayed versions of itself}
- H04B 17/346: {Noise values (signal-to-interference ratio [SIR] or carrier-to-interference ratio [CIR] H04B17/336)}
- H04L 1/206: {for modulated signals}
- H04L: TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION (arrangements common to telegraphic and telephonic communication H04M)
- H04B: TRANSMISSION

## Abstract

A method of estimating a signal-to-noise ratio from a received M-DPSK modulated signal, comprising a sequence of N known symbols, based on a division of the known symbols N and of N samples of the received signal at the output of the channel into a number of blocks B of length L with B greater than one.

## Claims

### Claim 1

A method comprising:
receiving a modulated signal, the signal comprising a sequence of N known transmitted symbols modulated using M-ary Differential Phase Shift Keying (M-DPSK) modulation with at least one carrier; and
estimating, using at least one processor, a signal-to-noise ratio based on a division of N samples of the received signal and of the N known transmitted symbols into a number of blocks B of a length L, with N, B and L being positive integer values with B>1 and L<N.

### Claim 2 (depends on 1)

The method of claim 1 wherein the estimating the signal-to-noise ratio based on the number of blocks B and the length L comprises estimating the signal-to-noise ratio based on a complex conjugate of the M-DPSK known transmitted symbols.

### Claim 3 (depends on 2)

The method of claim 2 wherein the estimating the signal-to-noise ratio based on the number of blocks B and the length L is performed according to:
SNR
=

(
1
-
1
L
)

1
B

∑
b
=
0
B
-
1


1
L

∑
k
=
l
b
l
b
+
L
-
1

r
k

a
k
*

2
1
N

∑
k
=
l
l
+
N
-
1


r
k

2
-
1
B

∑
b
=
0
B
-
1


1
L

∑
k
=
l
b
l
b
+
L
-
1

r
k

a
k
*

2
-
1
L
=
=

(
L
-
1
)

∑
b
=
0
B
-
1


1
L

∑
k
=
l
b
l
b
+
L
-
1

r
k

a
k
*

2
∑
k
=
l
l
+
N
-
1


r
k

2
-
L

∑
b
=
0
B
-
1


1
L

∑
k
=
l
b
l
b
+
L
-
1

r
k

a
k
*

2
-
1
L
wherein lb=L·b+l, l is an index denoting a position of a first known symbol of the sequence of length N in a packet, rk is a sample of the received signal at an output of a channel correspondent to a known transmitted symbol, ak is the M-DPSK known transmitted symbol, a*k is a complex conjugate of the M-DPSK known transmitted symbol and SNR indicates an estimation of the signal-to-noise ratio.

### Claim 4 (depends on 2)

The method according to claim 2 wherein when the length L of the blocks B is greater than a threshold, the estimation of the signal-to-noise ratio is given by:
SNR
=
1
B

∑
b
=
0
B
-
1


1
L

∑
k
=
l
b
l
b
+
L
-
1

r
k

a
k
*

2
1
N

∑
k
=
l
l
+
N
-
1


r
k

2
-
1
B

∑
b
=
0
B
-
1


1
L

∑
k
=
l
b
l
b
+
L
-
1

r
k

a
k
*

2
,
wherein lb=L·b+l, l is an index denoting a position of a first known symbol of the sequence of length N in a packet, rk is a sample of the received signal at an output of a channel correspondent to a known transmitted symbol, ak is the M-DPSK known transmitted symbol, a*k is a complex conjugate of the M-DPSK known transmitted symbol and SNR indicates an estimation of the signal-to-noise ratio.

### Claim 5 (depends on 2)

The method according to claim 2 wherein
B
=
N
-
L
L
-
O
+
1
≥
N
L
factor of consecutive blocks having length L, and estimation of the signal-to-noise ratio being given by:
SNR
=
(
L
-
1
)
B
·
L

∑
b
=
0
B
-
1


1
L

∑
k
=
l
b
l
b
+
L
-
1

r
k

a
k
*

2
1
B

∑
b
=
0
B
-
1

1
L

∑
k
=
l
b
l
b
+
L
-
1


r
k

2
-
1
B

∑
b
=
0
B
-
1


1
L

∑
k
=
l
b
l
b
+
L
-
1

r
k

a
k
*

2
-
1
L
,
wherein lb=L·b+l, l is an index denoting a position of a first known symbol of the sequence of length N in a packet, rk is a sample of the received signal at an output of a channel correspondent to a known transmitted symbol, ak is the M-DPSK known transmitted symbol, a*k is a complex conjugate of the M-DPSK known transmitted symbol and SNR indicates an estimation of the signal-to-noise ratio.

### Claim 6 (depends on 1)

The method according to claim 1, further comprising:
filtering the received modulated signal; and
applying non-coherent type differential demodulation to the filtered signal after estimation of the signal-to-noise ratio.

### Claim 7 (depends on 1)

The method according to claim 1 wherein the at least one carrier comprises multiple carriers.

### Claim 8

An apparatus, comprising:
a module configured to obtain a number B of blocks of a length L based on a division of a number N of known symbols and of a number N of samples of a received signal at an output of a channel, with N, B and L being positive integer values, and B greater than one; and
an estimator configured to estimate, based on the number of blocks B and the length L, a signal-to-noise ratio of the received signal comprising a sequence of the N known symbols modulated using M-ary Differential Phase Shift Keying (M-DPSK) modulation with at least one carrier signal.

### Claim 9 (depends on 8)

The apparatus of claim 8, wherein the module configured to obtain the number of blocks B comprises a divider configured to divide the N known symbols and N samples of the received signal at the output of the channel into the number of blocks B of the length L.

### Claim 10 (depends on 8)

The apparatus of claim 8 wherein the estimator is configured to estimate the signal-to-noise according to:
SNR
=

(
1
-
1
L
)

1
B

∑
b
=
0
B
-
1


1
L

∑
k
=
l
b
l
b
+
L
-
1

r
k

a
k
*

2
1
N

∑
k
=
l
l
+
N
-
1


r
k

2
-
1
B

∑
b
=
0
B
-
1


1
L

∑
k
=
l
b
l
b
+
L
-
1

r
k

a
k
*

2
-
1
L
=

(
L
-
1
)

∑
b
=
0
B
-
1


1
L

∑
k
=
l
b
l
b
+
L
-
1

r
k

a
k
*

2
∑
k
=
l
l
+
N
-
1


r
k

2
-
L

∑
b
=
0
B
-
1


1
L

∑
k
=
l
b
l
b
+
L
-
1

r
k

a
k
*

2
-
1
L
wherein lb=L·b+l, l is an index denoting a position of a first known symbol of the sequence of length N in a packet, rk is a sample of the received signal at the output of the channel correspondent to a known transmitted symbol, ak is the M-DPSK known transmitted symbol, a*k is a complex conjugate of the M-DPSK known transmitted symbol and SNR indicates an estimation of the signal-to-noise ratio.

### Claim 11 (depends on 8)

The apparatus according to claim 8 wherein if the length L of the blocks B is greater than a threshold, the estimator is configured to estimate the signal-to-noise ratio according to
SNR
=
1
B


∑
b
=
0
B
-
1


1
L

∑
k
=
l
b
l
b
+
L
-
1

r
k

a
k
*

2
1
N

∑
k
=
l
l
+
N
-
1


r
k

2
-
1
B

∑
b
=
0
B
-
1


1
L

∑
k
=
l
b
l
b
+
L
-
1

r
k

a
k
*

2
,
wherein lb=L·b+l, l is an index denoting a position of a first known symbol of the sequence of length N in a packet, rk is a sample of the received signal at the output of the channel correspondent to a known transmitted symbol, ak is the M-DPSK known transmitted symbol, a*k is a complex conjugate of the M-DPSK known transmitted symbol and SNR indicates an estimation of the signal-to-noise ratio.

### Claim 12 (depends on 8)

The apparatus according to claim 8 wherein
B
=
N
-
L
L
-
O
+
1
≥
N
L
wherein O indicates an overlapping factor of consecutive blocks having length L, and estimation of the signal-to-noise ratio being given by:
SNR
=
(
L
-
1
)
B
·
L

∑
b
=
0
B
-
1


1
L

∑
k
=
l
b
l
b
+
L
-
1

r
k

a
k
*

2
1
B

∑
b
=
0
B
-
1

1
L

∑
k
=
l
b
l
b
+
L
-
1


r
k

2
-
1
B

∑
b
=
0
B
-
1


1
L

∑
k
=
l
b
l
b
+
L
-
1

r
k

a
k
*

2
-
1
L
,
wherein lb=L·b+l, l is an index denoting a position of a first known symbol of the sequence of length N in a packet, rk is a sample of the received signal at the output of the channel correspondent to a known transmitted symbol, ak is the M-DPSK known transmitted symbol, a*k is a complex conjugate of the M-DPSK known transmitted symbol and SNR indicates an estimation of the signal-to-noise ratio.

### Claim 13 (depends on 8)

The apparatus of claim 8, further comprising:
a filter configured to filter the received signal; and
a differential demodulator configured to demodulate the received signal and to receive as an input the estimated signal-to-noise ratio.

### Claim 14 (depends on 8)

The apparatus of claim 8 wherein the at least one carrier signal comprises a plurality of carrier signals.

### Claim 15

A computer-readable memory medium whose contents cause at least one processor to perform a method, the method comprising:
obtaining a number of blocks B of a length L based on a division of a number of known symbols N and of N samples of a received signal at an output of a channel into the number of blocks B of length L, with B, L and N positive integer values, and B greater than one; and
estimating, based on the number of blocks B and the length L, a signal-to-noise ratio of a received signal comprising a sequence of the N known symbols modulated using M-ary Differential Phase Shift Keying (M-DPSK) modulation with at least one carrier signal.

### Claim 16 (depends on 15)

The computer-readable memory medium of claim 15 wherein the method further comprises differential demodulation of the received signal.

### Claim 17 (depends on 15)

The computer-readable medium of claim 15 wherein the obtaining comprises dividing the N known symbols and N samples of the received signal at the output of the channel into the number of blocks B of length L.

### Claim 18 (depends on 15)

The computer-readable medium of claim 15 wherein B is greater than N divided by L.

### Claim 19

A system, comprising:
a differential demodulator configured to demodulate a received signal comprising a sequence of N known symbols modulated using M-ary Differential Phase Shift Keying (M-DPSK) modulation with at least one carrier signal; and
an estimator configured to estimate a signal-to-noise ratio of the received signal based on a division of the N known symbols and of N samples of the received signal at an output of a channel into a number of blocks B of length L, with N, B and L being positive integer values, and B greater than one.

### Claim 20 (depends on 19)

The system of claim 19 wherein the estimator comprises a divider configured to divide the known symbols N and N samples of the received signal at the output of the channel into the number of blocks B of the length L.

### Claim 21 (depends on 19)

The system of claim 19, further comprising a filter.

### Claim 22 (depends on 19)

The system of claim 19, further comprising a transmitter configured to transmit a signal, wherein the differential demodulator and the estimator are configured to receive the transmitted signal.

### Claim 23 (depends on 19)

The system of claim 19 further comprising a transmitter configured to transmit modulated signals.

### Claim 24

A system comprising:
means for obtaining a number of blocks B of a length L based on a division of a sequence of known symbols N and of N samples of a received signal at an output of a channel into the number of blocks B; and
means for estimating, based on the number of blocks B and the length L, a signal-to-noise ratio of a received signal comprising a sequence of the N known symbols modulated using M-ary Differential Phase Shift Keying (M-DPSK) modulation with at least one carrier signal.

### Claim 25

A method for estimating a signal-to-noise ratio for a packet transmission and reception system of signals having a known data sequence by means of a M-DPSK modulation with at least one carrier, said system comprising packet transmission of a signal with a sequence of N known symbols, with N positive integer number, said transmission comprising a M-DPSK modulation of the signal to transmit by means of a M-PSK mapper and a differential block, the transmission of the M-DPSK modulated signal (s(t)) through a channel having constant gain (G) over all the N symbols and in presence of noise (w(t)) with null average, and reception of a signal (r(t)) at the output of the channel, said method comprises estimation of a signal-to-noise ratio of the received signal with the division of the N known symbols (ak) and of the N samples (rk) of the signal (r(t)) at the output of the channel into B blocks of L length with B and L positive integer numbers and B greater than one and wherein B is expressed by
B
=
N
-
L
L
-
O
+
1
≥
N
L
wherein O indicates an overlapping factor of consecutive blocks having length L and calculation of the estimation of the signal-to-noise ratio by means of an equation:
SNR
=
(
L
-
1
)
B
·
L

∑
b
=
0
B
-
1


1
L

∑
k
=
l
b
l
b
+
L
-
1

r
k

a
k
*

2
1
B

∑
b
=
0
B
-
1

1
L

∑
k
=
l
b
l
b
+
L
-
1


r
k

2
-
1
B

∑
b
=
0
B
-
1


1
L

∑
k
=
l
b
l
b
+
L
-
1

r
k

a
k
*

2
-
1
L
wherein lb=b·(L−O)+l where l is an index denoting a position of a first known symbol of the sequence of length N in the packet, rk is a sample of the received signal at the output of the channel correspondent to a known transmitted symbol, ak is the M-DPSK modulated known transmitted symbol, a*k is a complex conjugate of the M-DPSK modulated known transmitted symbol and SNR indicates the estimation of the signal-to-noise ratio.

### Claim 26 (depends on 25)

The method according to claim 25 wherein when O=0 the B blocks are expressed by
B
=
N
L
and said estimation of the signal-to-noise ratio is given by:
SNR
=

(
1
-
1
L
)

1
B

∑
b
=
0
B
-
1


1
L

∑
k
=
l
b
l
b
+
L
-
1

r
k

a
k
*

2
1
N

∑
k
=
l
l
+
N
-
1


r
k

2
-
1
B

∑
b
=
0
B
-
1


1
L

∑
k
=
l
b
l
b
+
L
-
1

r
k

a
k
*

2
-
1
L
=

(
L
-
1
)

∑
b
=
0
B
-
1


1
L

∑
k
=
l
b
l
b
+
L
-
1

r
k

a
k
*

2
∑
k
=
l
l
+
N
-
1


r
k

2
-
L

∑
b
=
0
B
-
1


1
L

∑
k
=
l
b
l
b
+
L
-
1

r
k

a
k
*

2
-
1
L
..

### Claim 27 (depends on 25)

The method according to claim 25 wherein when the length L of the blocks B is sufficient great to average the noise, said estimation of the signal-to-noise ratio is given by:
SNR
=
1
B

∑
b
=
0
B
-
1


1
L

∑
k
=
l
b
l
b
+
L
-
1

r
k

a
k
*

2
1
B

∑
b
=
0
B
-
1

1
L

∑
k
=
l
b
l
b
+
L
-
1


r
k

2
-
1
B

∑
b
=
0
B
-
1


1
L

∑
k
=
l
b
l
b
+
L
-
1

r
k

a
k
*

2
.

### Claim 28 (depends on 25)

The method according to claim 25 wherein said transmission and reception system is of a pass-band type and the reception is of a non-coherent type with differential demodulation, said estimation of the signal-to-noise ratio being effectuated before the differential demodulation of the signal.

### Claim 29 (depends on 25)

The method according to claim 25 wherein said transmission and reception system is of a multiple carrier type.

### Claim 30

An apparatus to estimate a signal-to-noise ratio for a packet transmission and reception system of signals having a known data sequence by means of a M-DPSK modulation with at least one carrier, said system comprising means for the packet transmission of a signal with a sequence of N known symbols, with N positive integer number, said transmission means comprising a M-DPSK modulator of the signal to transmit comprising a M-PSK mapper and a differential block, said M-DPSK modulated signal (s(t)) being adapted to pass through a channel having constant gain (G) over all the N symbols and in presence of noise (w(t)) with null average, said system comprises means (10) for receiving a signal (r(t)) at an output of the channel, said apparatus comprising first means adapted to divide the N known symbols (ak) and the N samples (rk) of the signal (r(t)) at the output of the channel into B blocks of L length with B and L positive integer numbers and B greater than one and said first means (101) being adapted to overlap consecutive blocks having length L of a factor O, said B blocks being expressed by
B
=
N
-
L
L
-
O
+
1
≥
N
L
wherein O indicates an overlapping factor of consecutive blocks having length L, and second means adapted to calculate the estimation of the signal-to-noise ratio by means of an equation:
SNR
=
(
L
-
1
)
B
·
L

∑
b
=
0
B
-
1


1
L

∑
k
=
l
b
l
b
+
L
-
1

r
k

a
k
*

2
1
B

∑
b
=
0
B
-
1

1
L

∑
k
=
l
b
l
b
+
L
-
1


r
k

2
-
1
B

∑
b
=
0
B
-
1


1
L

∑
k
=
l
b
l
b
+
L
-
1

r
k

a
k
*

2
-
1
L
wherein −lb=(L−O)·b+l where l is an index denoting a position of a first known symbol of the sequence of length N in the packet, rk is a sample of the received signal at the output of the channel correspondent to a known transmitted symbol, ak is the M-DPSK modulated known transmitted symbol, a*k is a complex conjugate of the M-DPSK modulated known transmitted symbol and SNR indicates the estimation of the signal-to-noise ratio.

### Claim 31 (depends on 30)

The apparatus according to claim 30 wherein O=0 and said second means being adapted to effectuate the estimation of the signal-to-noise ratio by an equation:
SNR
=

(
1
-
1
L
)

1
B

∑
b
=
0
B
-
1


1
L

∑
k
=
l
b
l
b
+
L
-
1

r
k

a
k
*

2
1
N

∑
k
=
l
l
+
N
-
1


r
k

2
-
1
B

∑
b
=
0
B
-
1


1
L

∑
k
=
l
b
l
b
+
L
-
1

r
k

a
k
*

2
-
1
L
=

(
L
-
1
)

∑
b
=
0
B
-
1


1
L

∑
k
=
l
b
l
b
+
L
-
1

r
k

a
k
*

2
∑
k
=
l
l
+
N
-
1


r
k

2
-
L

∑
b
=
0
B
-
1


1
L

∑
k
=
l
b
l
b
+
L
-
1

r
k

a
k
*

2
-
1
L
.

### Claim 32 (depends on 30)

The apparatus according to claim 30 wherein when the length L of the blocks B is sufficient great to average the noise said second means are adapted to calculate the estimation of the signal-to-noise ratio by an equation:
SNR
=
1
B

∑
b
=
0
B
-
1


1
L

∑
k
=
l
b
l
b
+
L
-
1

r
k

a
k
*

2
1
B

∑
b
=
0
B
-
1

1
L

∑
k
=
l
b
l
b
+
L
-
1


r
k

2
-
1
B

∑
b
=
0
B
-
1


1
L

∑
k
=
l
b
l
b
+
L
-
1

r
k

a
k
*

2
.

### Claim 33 (depends on 30)

The apparatus according to claim 30 wherein said transmission and reception system is of a pass-band type, said reception means of the signal effectuating a non-coherent reception and comprising a differential demodulator, said estimation apparatus being adapted to calculate the estimation of the signal-to-noise ratio of the signal at an input of the differential demodulator.

### Claim 34 (depends on 6)

The apparatus according to claim 6 wherein said transmission and reception system is of a multiple carrier type.

### Claim 35

A packet transmission and reception system of signals having a known data sequence by means of a M-DPSK modulation with at least one carrier, said system comprising means for packet transmission of a signal with a sequence of N known symbols, with N positive integer number, said transmission means comprising a M-DPSK modulator of the signal to transmit comprising a M-PSK mapper and a differential block, said M-DPSK modulated signal (s(t)) being adapted to pass through a channel having constant gain (G) over all the N symbols and in presence of noise (w(t)) with null average, said system comprising means for receiving a signal (r(t)) at the output of the channel which comprises a differential demodulator, said system including an apparatus comprising first means adapted to divide the N known symbols (ak) and N samples (rk) of the signal (r(t)) at the output of the channel into B blocks of L length with B and L positive integer numbers and B greater than one and said first means (101) being adapted to overlap consecutive blocks having length L of a factor O, said B blocks being expressed by
B
=
N
-
L
L
-
O
+
1
≥
N
L
wherein O indicates an overlapping factor of consecutive blocks having length L, and second means adapted to calculate the estimation of the signal-to-noise ratio by means of an equation:
SNR
=
(
L
-
1
)
B
·
L

∑
b
=
0
B
-
1


1
L

∑
k
=
l
b
l
b
+
L
-
1

r
k

a
k
*

2
1
B

∑
b
=
0
B
-
1

1
L

∑
k
=
l
b
l
b
+
L
-
1


r
k

2
-
1
B

∑
b
=
0
B
-
1


1
L

∑
k
=
l
b
l
b
+
L
-
1

r
k

a
k
*

2
-
1
L
wherein lb=(L−O)·b+l where l is an index denoting a position of a first known symbol of the sequence of length N in the packet, rk is a sample of the received signal at the output of the channel correspondent to a known transmitted symbol, ak is the M-DPSK modulated known transmitted symbol, a*k is a complex conjugate of the M-DPSK modulated known transmitted symbol and SNR indicates an estimation of the signal-to-noise ratio.