System and method for wireless transmission using hybrid ARQ based on average mutual information per bit
View Patent ↗A method and system for packet transmission in a hybrid automatic repeat request (ARQ) system. A modulation and a block length for a transmission are determined based on the average mutual information per bit. The average mutual information per bit is computed based on a current channel signal-to-noise ratio and a plurality of previous transmissions, each being transmitted with a respective coded block length, modulation form, and signal-to-noise ratio. A block error rate is computed for the potential block lengths and modulations based on the average mutual information per bit, and a throughput of the current transmission is determined based on the block error rate. The modulation form and the block length of the transmission are determined based on an analysis of the throughput. If the receiver cannot decode the current transmission, the transmitter repeats the computation to determine the modulation and the block length for retransmission.
1. A method for determining a modulation form and a block length of a current transmission transmitted by a transmitter comprising:
computing an average mutual information per bit based on a current channel signal-to-noise ratio and a plurality of previous transmissions, each previous transmission having a respective coded block length, modulation form, and signal-to-noise ratio;
computing a block error rate for a plurality of block lengths and modulations based on the average mutual information per bit;
determining a throughput of the current transmission using the block error rate; and
determining the modulation and the block length of the current transmission based on an analysis the throughput;
wherein the throughput is determined by
η
(
t
,
m
)
=
1
-
P
w
(
t
,
m
)
∑
j
=
1
l
-
1
n
j
/
q
(
Ω
j
)
+
n
t
/
q
(
Ω
m
)
wherein n is the throughput, P W is the block error rate,
l is a cardinality of the current transmission,
n j is a code length of the j th transmission,
Ω j is a modulation form of the j th transmission,
n t is a code length chosen so as to obtain a lower code rates,
Ω m is chosen from a plurality of predefined modulation forms, and
q( ) determines a number of bits per symbol of a particular modulation form.
2. The method of claim 1 , further comprising transmitting the current transmission to a receiver using the determined modulation and block length.
3. The method of claim 2 , further comprising:
receiving an acknowledgement from the receiver;
determining whether the receiver successfully decoded the current transmission based on the received acknowledgement; and
if the receiver did not successfully decode the current transmission, repeating the steps of computing an average mutual information per bit, computing a block error rate, determining the throughput, and determining the modulation and the block length.
4. The method of claim 3 , wherein the received acknowledgement is one of an ACK and a NACK.
5. The method of claim 1 , wherein the average mutual information per bit is determined by
I
avg
(
t
,
m
)
=
1
∑
j
=
1
l
-
1
n
j
+
n
t
(
∑
j
=
1
l
-
1
I
Ω
j
(
SNR
j
*
)
/
q
(
Ω
j
)
+
I
Ω
m
(
SNR
l
)
/
q
(
Ω
m
)
)
wherein l is a cardinality of the current transmission,
n j is a code length of the j th transmission,
n t is a code length chosen so as to obtain a lower code rates,
I( ) is the mutual information per bit for a given signal to noise ratio,
SNR j *; is an actual signal to noise ratio during the j th transmission,
SNR t is a current measurement of a signal to noise ratio,
Ω j is a modulation form of the j th transmission,
Ω m is chosen from a plurality of predefined modulation forms, and
q( ) determines a number of bits per symbol of a particular modulation form.
6. The method of claim 1 , wherein the block error rate is approximated by
P
w
(
t
,
m
)
=
Q
(
I
avg
(
t
,
m
)
-
b
t
a
t
)
,
and a t , b t ) are approximation parameters for a code rate R t determined by
R
t
=
k
(
∑
j
=
1
l
-
1
n
j
+
n
t
)
,
wherein l is a cardinality of the current transmission,
n j is a code length of the j th transmission,
n t is a code length chosen so as to obtain a lower code rates,
I avg ( ) is the average mutual information per bit, and
Q( ) determines a number of bits per symbol of a particular modulation form.
7. The method of claim 1 , wherein the modulation form includes a quadrature amplitude modulation.
8. The method of claim 1 , wherein the plurality of previous transmissions includes all previous transmissions over a channel of the current transmission.
9. The method of claim 1 , further comprising:
comparing the block length to a predetermined codeword length;
comparing the modulation of the previous transmission to the modulation of the current transmission; and
applying Chase combining to repeated coded bits of the current transmission, in response to determining the block length exceeds the predetermined codeword length and the modulation of the previous transmission is equivalent to the modulation of the current transmission, such that the average mutual information per bit is given by
I avg =I Ω j (SNR j +SNR k )/ q (Ω j )
where I Ω j is the mutual information per bit for a given signal to noise ratio,
SNR j is an actual signal to noise ratio during the j th transmission,
SNR k is a current measurement of a signal to noise ratio,
q( ) determines a number of bits per symbol of a particular modulation form, and
Ω j is a modulation form of the j th transmission.
10. The method of claim 1 , further comprising:
comparing the block length to a predetermined codeword length;
comparing the modulation of the previous transmission to the modulation of the current transmission; and
applying post-modulation bit-level combining in response to determining the block length exceeds the predetermined codeword length and the modulation of the previous transmission is not equivalent to the modulation of the current transmission, such that the average mutual information per bit is given by
I avg =I Ω b ( I Ω b −1 ( I Ω j (SNR j )/ q (Ω j ))+ I Ω b −1 ( I Ω k (SNR k )/ q (Ω k )))
where Ω b denotes the binary phase shift keying (BPSK) modulations,
SNR j is an actual signal to noise ratio during the j th transmission,
SNR k is a current measurement of a signal to noise ratio,
q( ) determines a number of bits per symbol of a particular modulation form,
Ω j is a modulation form of the j th transmission, and
Ω k is a modulation form of the current transmission.
11. A wireless adaptive hybrid automatic repeat request transmission system for packet transmission comprising:
means for computing an average mutual information per bit based on a current channel signal-to-noise ratio and a plurality of previous transmissions, each previous transmission having a respective coded block length, modulation form, and signal-to-noise ratio;
means for computing a block error rate for all possible block lengths and modulations based on the average mutual information per bit;
means for determining a throughput of the current transmission using a result of the means for computing the block error rate; and
means for determining the modulation and the block length of the current transmission based on an analysis of a result of the means for determining the throughput;
wherein the throughput is determined by
η
(
t
,
m
)
=
1
-
P
w
(
t
,
m
)
∑
j
=
1
l
-
1
n
j
/
q
(
Ω
j
)
+
n
t
/
q
(
Ω
m
)
wherein η is the throughput, P w is the block error rate,
l is a cardinality of the current transmission,
n j is a code length of the j th transmission,
Ω j is a modulation form of the j th transmission,
n t is a code length chosen so as to obtain a lower code rates,
Ω m is chosen from a plurality of predefined modulation forms, and
q( ) determines a number of bits per symbol of a particular modulation form.
12. The system of claim 11 , further comprising means for transmitting the current transmission to a receiver using the determined modulation and block length.
13. The system of claim of claim 12 , further comprising:
means for receiving an acknowledgement from the receiver; and
means for determining whether the receiver successfully decoded the current transmission based on the received acknowledgement.
14. The system of claim of claim 13 , wherein the received acknowledgement is one of an ACK and a NACK.
15. The system of claim of claim 11 , wherein the average mutual information per bit is determined by
I
avg
(
t
,
m
)
=
1
∑
j
=
1
l
-
1
n
j
+
n
t
(
∑
j
=
1
l
-
1
I
Ω
j
(
SNR
j
*
)
/
q
(
Ω
j
)
+
I
Ω
m
(
SNR
l
)
/
q
(
Ω
m
)
)
wherein l is a cardinality of the current transmission,
n j is a code length of the j th transmission,
n t is a code length chosen so as to obtain a lower code rates,
I( ) is the mutual information per bit for a given signal to noise ratio,
signal-to-noise ratio j is a signal to noise ratio of the j th transmission,
signal-to-noise ratio t is a measurement of a signal to noise ratio,
Ω j is a modulation form of the j th transmission,
Ω m is chosen from a plurality of predefined modulation forms, and
q( ) determines a number of bits per symbol of a particular modulation form.
16. The system of claim of claim 11 , wherein the block error rate is approximated by
P
w
(
t
,
m
)
=
Q
(
I
avg
(
t
,
m
)
-
b
t
a
t
)
,
and (a t , b t ) are approximation parameters for a code rate R t determined by
R
t
=
k
(
∑
j
=
1
l
-
1
n
j
+
n
t
)
,
wherein l is a cardinality of the current transmission,
n j is a code length of the j th transmission,
n t is a code length chosen so as to obtain a lower code rates,
I avg ( ) is the average mutual information per bit, and
Q( ) determines a number of bits per symbol of a particular modulation form.
17. The system of claim of claim 11 , wherein the modulation form includes a quadrature amplitude modulation.
18. The system of claim of claim 11 , wherein the plurality of previous transmissions includes all previous transmissions over a channel of the current transmission.
19. The system of claim 11 , further comprising:
means for comparing the block length to a predetermined codeword length;
means for comparing the modulation of the previous transmission to the modulation of the current transmission; and
means for applying Chase combining to repeated coded bits of the current transmission, in response to determining the block length exceeds the predetermined codeword length and the modulation of the previous transmission is equivalent to the modulation of the current transmission, such that the average mutual information per bit is given by
I avg =I Ω j (SNR j +SNR k )/ q (≠ j )
where I Ωj is the mutual information per bit for a given signal to noise ratio,
SNR j is an actual signal to noise ratio during the j th transmission,
SNR k is a current measurement of a signal to noise ratio,
q( ) determines a number of bits per symbol of a particular modulation form, and
Ω j is a modulation form of the j th transmission.
20. The system of claim 11 , further comprising:
means for comparing the block length to a predetermined codeword length;
means for comparing the modulation of the previous transmission to the modulation of the current transmission; and
means for applying post-modulation bit-level combining in response to determining the block length exceeds the predetermined codeword length and the modulation of the previous transmission is not equivalent to the modulation of the current transmission, such that the average mutual information per bit is given by
I avg =I Ω b ( I Ω b −1 ( I Ω j (SNR j )/ q (Ω j ))+( I Ω b −1 ( I Ω b (SNR k )/ q (Ω k )))
where Ω b denotes the binary phase shift keying (BPSK) modulations,
SNR j is an actual signal to noise ratio during the j th transmission,
SNR k is a current measurement of a signal to noise ratio,
q( ) determines a number of bits per symbol of a particular modulation form,
Ω j is a modulation form of the j th transmission, and
Ω k is a modulation form of the current transmission.
21. A method for determining a modulation form and a block length of a current transmission transmitted by a transmitter comprising:
computing an average mutual information per bit based on a current channel signal-to-noise ratio and a plurality of previous transmissions, each previous transmission having a respective coded block length, modulation form, and signal-to-noise ratio;
computing a block error rate for a plurality of block lengths and modulations based on the average mutual information per bit;
determining a throughput of the current transmission using the block error rate; and
determining the modulation and the block length of the current transmission based on an analysis the throughput;
wherein the average mutual information per bit is determined by
I
avg
(
t
,
m
)
=
1
∑
j
=
1
l
-
1
n
j
+
n
t
(
∑
j
=
1
l
-
1
I
Ω
j
(
SNR
j
*
)
/
q
(
Ω
j
)
+
I
Ω
m
(
SNR
l
)
/
q
(
Ω
m
)
)
wherein l is a cardinality of the current transmission,
n j is a code length of the j th transmission,
n t is a code length chosen so as to obtain a lower code rates,
I( ) is the mutual information per bit for a given signal to noise ratio,
SNR j * is an actual signal to noise ratio during the j th transmission,
SNR t is a current measurement of a signal to noise ratio,
Ω j is a modulation form of the j th transmission,
Ω m is chosen from a plurality of predefined modulation forms, and
q( ) determines a number of bits per symbol of a particular modulation form.