Method and apparatus for minimizing total transmission energy in a communication system employing retransmission of frame received in error

• US 6,771,700 B1
• Filed: 10/22/1999
• Issued: 08/03/2004
• Est. Priority Date: 10/09/1999
• Status: Expired due to Term

• Current Assignee: Qualcomm, Inc.
• Original Assignee: Qualcomm, Inc.
• Inventors: Holtzman, Jack, Lundby, Stein A., Razoumov, Leonid
• Primary Examiner(s): Tran, Khai
• Application Number:
  US09/426,016
• Time in Patent Office: 1,747 Days
• Field of Search: 375/227, 375/285, 375/219, 375/254, 375/341, 375/222, 455/522, 455/69, 455/442, 455/70, 455/67.1, 370/228, 370/328, 370/331, 370/335, 370/342, 370/479, 370/333, 370/468, 370/470, 714/18, 714/1, 714/748, 714/708, 714/794, 714/795
• US Class Current: 375/227
• CPC Class Codes: H04L 1/0026 Transmission of channel quality indication
• CPC Class Codes: H04L 1/1607 Details of the supervisory signal
• CPC Class Codes: H04L 1/1816 with retransmission of the same, encoded, message
• CPC Class Codes: H04L 1/1825 Adaptation of specific ARQ protocol parameters according to transmission conditions
• CPC Class Codes: H04L 1/1867 Arrangements specially adapted for the transmitter end
• CPC Class Codes: H04W 52/20 using error rate
• CPC Class Codes: H04W 52/50 at the moment of starting communication in a multiple access environment

Abstract

Method and apparatus for transmitting a signal at a predetermined level of reliability using retransmission of erroneously transmitted frames so as to minimize total transmission energy. The transmitting station evaluates the frame error rate (FER) as a function of energy. Next, the transmitting station determines a combination of initial transmission energies and retransmission energies that will provide the target level of reliability while minimizing the total transmission energy employed in the initial transmission and the retransmissions. The transmitting station transmits a frame with an initial transmission energy. Employing conventional feedback methods the transmitting station is alerted to the occurrence of frame errors at the receiving station. The transmitting station upon notification of a frame error retransmits the frame with an energy determined to minimize the total energy required to transmit the frame with a predetermined level of reliability.

Claims

1. A method for retransmission in a communication system, comprising the steps of:

determining a plurality of transmission energies in accordance with a predetermined reliability level and at least one characteristic of a communication channel, comprising the steps of;

measuring said at least one of characteristic of said communication channel; and

utilizing a look-up table to select pre-computed transmission energies corresponding to said measured characteristic and said reliability level;

transmitting a frame of information at a first transmission energy; and

retransmitting said frame of information at a next transmission energy from said plurality of transmission energies when said frame was received in error.

2. The method of claim 1, wherein said pre-computed transmission energies were pre-computed by the steps of:

solving for a minimal total energy <

E>

, an equation;

$〈<br><br>E〉<br><br>=E_1+f<br><br>\text{\hspace{1em}<br><br>}<br><br>\left(E_1\right)·<br><br>E_2+f<br><br>\text{\hspace{1em}<br><br>}<br><br>\left(E_1\right)·<br><br>f<br><br>\text{\hspace{1em}<br><br>}<br><br>\left(E_2\right)·<br><br>E_3+\mathrm{\dots <br><br>}+E_N<br><br>\text{\hspace{1em}<br><br>}<br><br>\underset{i=1}{\overset{N-1}{\prod <br><br>}}<br><br>\text{\hspace{1em}<br><br>}<br><br>f<br><br>\text{\hspace{1em}<br><br>}<br><br>\left(E_i\right),$

 

where;

E_i are said transmission energies;

f(E_i) are frame error rates corresponding to said transmission energies E_i;

subject to constraint;

$T_{\mathrm{FER}}=\underset{i=1}{\overset{N}{\prod <br><br>}}<br><br>\text{\hspace{1em}<br><br>}<br><br>f<br><br>\text{\hspace{1em}<br><br>}<br><br>\left(E_i\right),$

 

where;

T_FRR is a target frame error rate; and

wherein said reliability level corresponds to said target frame error rate.

3. A method for retransmission in a communication system, comprising the steps of:

determining a plurality of transmission energies in accordance with a predetermined reliability level and at least one characteristic of a communication channel, comprising the steps of;

measuring at least one of said characteristic of said communication channel;

utilizing a look-up table to select a predetermined relationship between a frame error rate and a transmission energy corresponding to said measured parameters;

solving for a minimal total energy <

E>

in accordance with the equation;

$〈<br><br>E〉<br><br>=E_1+f<br><br>\text{\hspace{1em}<br><br>}<br><br>\left(E_1\right)·<br><br>E_2+f<br><br>\text{\hspace{1em}<br><br>}<br><br>\left(E_1\right)·<br><br>f<br><br>\text{\hspace{1em}<br><br>}<br><br>\left(E_2\right)·<br><br>E_3+\mathrm{\dots <br><br>}+E_N<br><br>\text{\hspace{1em}<br><br>}<br><br>\underset{i=1}{\overset{N-1}{\prod <br><br>}}<br><br>\text{\hspace{1em}<br><br>}<br><br>f<br><br>\text{\hspace{1em}<br><br>}<br><br>\left(E_i\right),$

 

where;

E_i are said transmission energies,

f(E_i) are frame error rates corresponding to said transmission energies E_i;

subject to constraint;

$T_{\mathrm{FER}}=\underset{i=1}{\overset{N}{\prod <br><br>}}<br><br>\text{\hspace{1em}<br><br>}<br><br>f<br><br>\text{\hspace{1em}<br><br>}<br><br>\left(E_i\right),$

 

where;

T_FRR is a target frame error rate; and

wherein said reliability level corresponds to said target frame error rate;

transmitting a frame of information at a first transmission energy; and

retransmitting said frame of information at a next transmission energy from said plurality of transmission energies when said frame was received in error.

4. A method for retransmission in a communication system, comprising the steps of:

determining a plurality of transmission energies in accordance with a predetermined reliability level and at least one characteristic of a communication channel, comprising the step of;

determining a relationship between a frame error rate and a transmitting energy;

solving for a minimal total energy <

E>

, in accordance with the equation;

$〈<br><br>E〉<br><br>=E_1+f<br><br>\text{\hspace{1em}<br><br>}<br><br>\left(E_1\right)·<br><br>E_2+f<br><br>\text{\hspace{1em}<br><br>}<br><br>\left(E_1\right)·<br><br>f<br><br>\text{\hspace{1em}<br><br>}<br><br>\left(E_2\right)·<br><br>E_3+\mathrm{\dots <br><br>}+E_N<br><br>\text{\hspace{1em}<br><br>}<br><br>\underset{i=1}{\overset{N-1}{\prod <br><br>}}<br><br>\text{\hspace{1em}<br><br>}<br><br>f<br><br>\text{\hspace{1em}<br><br>}<br><br>\left(E_i\right),$

 

where;

E_i are said transmission energies, and

f(E_i) are frame error rates corresponding to said transmission energies E_i;

subject to constraint;

$T_{\mathrm{FER}}=\underset{i=1}{\overset{N}{\prod <br><br>}}<br><br>\text{\hspace{1em}<br><br>}<br><br>f<br><br>\text{\hspace{1em}<br><br>}<br><br>\left(E_i\right),$

 

where;

T_FRR is a target frame error rate; and

wherein said reliability level corresponds to said target frame error rate;

transmitting a frame of information at a first transmission energy; and

retransmitting said frame of information at a next transmission energy from said plurality of transmission energies when said frame was received in error.

5. A method, for retransmission in a communication system, comprising the steps of:

determining two transmission energies in accordance with a predetermined reliability level and at least one characteristic of a communication channel;

transmitting a frame of information at a first transmission energy; and

retransmitting said frame of information at a next transmission energy from said plurality of transmission energies when said frame was received in error.

6. A method for retransmission in a communication system, comprising the steps of:

determining a plurality of transmission energies in accordance with an equation for estimating a minimum aggregate transmission energy;

transmitting a frame of information at a first transmission energy; and

retransmitting said frame of information at a next transmission energy from said plurality of transmission energies when said frame was received in error.

7. An apparatus for retransmission in a communication system, comprising:

a control processor configured to;

determine a plurality of transmission energies in accordance with a predetermined reliability level and at least one characteristic of a communication channel by;

measuring said at least one of characteristic of said communication channel; and

utilizing a look-up table to select pre-computed transmission energies corresponding to said measured characteristic and said reliability level;

provide a first set of signals indicative of a first transmission energy of said plurality of transmission energies for a frame of information; and

provide at least one additional set of signals indicative of next transmission energy of said plurality of transmission energies for retransmitting said frame of information when said frame of information was received in error.

8. The apparatus of claim 7, wherein said control processor pre-computes said transmission energies by having been configured to:

solve for a minimal total energy <

E>

, an equation;

$〈<br><br>E〉<br><br>=E_1+f<br><br>\text{\hspace{1em}<br><br>}<br><br>\left(E_1\right)·<br><br>E_2+f<br><br>\text{\hspace{1em}<br><br>}<br><br>\left(E_1\right)·<br><br>f<br><br>\text{\hspace{1em}<br><br>}<br><br>\left(E_2\right)·<br><br>E_3+\mathrm{\dots <br><br>}+E_N<br><br>\text{\hspace{1em}<br><br>}<br><br>\underset{i=1}{\overset{N-1}{\prod <br><br>}}<br><br>\text{\hspace{1em}<br><br>}<br><br>f<br><br>\text{\hspace{1em}<br><br>}<br><br>\left(E_i\right),$

 

where;

E_i are said transmission energies;

f(E_i) are frame error rates corresponding to said transmission energies E_i;

subject to constraint;

$T_{\mathrm{FER}}=\underset{i=1}{\overset{N}{\prod <br><br>}}<br><br>\text{\hspace{1em}<br><br>}<br><br>f<br><br>\text{\hspace{1em}<br><br>}<br><br>\left(E_i\right),$

 

where;

T_FRR is a target frame error rate; and

wherein said reliability level corresponds to said target frame error rate.

9. An apparatus for retransmission in a communication system, comprising:

a control processor configured to;

determine a plurality of transmission energies in accordance with a predetermined reliability level and at least one characteristic of a communication channel by;

measuring at least one of said characteristic of said communication channel;

utilizing a look-up table to select a predetermined relationship between a frame error rate and a transmission energy corresponding to said measured parameters;

solving for a minimal total energy <

E>

in accordance with the equation;

$〈<br><br>E〉<br><br>=E_1+f<br><br>\text{\hspace{1em}<br><br>}<br><br>\left(E_1\right)·<br><br>E_2+f<br><br>\text{\hspace{1em}<br><br>}<br><br>\left(E_1\right)·<br><br>f<br><br>\text{\hspace{1em}<br><br>}<br><br>\left(E_2\right)·<br><br>E_3+\mathrm{\dots <br><br>}+E_N<br><br>\text{\hspace{1em}<br><br>}<br><br>\underset{i=1}{\overset{N-1}{\prod <br><br>}}<br><br>\text{\hspace{1em}<br><br>}<br><br>f<br><br>\text{\hspace{1em}<br><br>}<br><br>\left(E_i\right),$

 

where;

E_i are said transmission energies,

f(E_i) are frame error rates corresponding to said transmission energies E_i;

subject to constraint;

$T_{\mathrm{FER}}=\underset{i=1}{\overset{N}{\prod <br><br>}}<br><br>\text{\hspace{1em}<br><br>}<br><br>f<br><br>\text{\hspace{1em}<br><br>}<br><br>\left(E_i\right),$

 

where;

T_FRR is a target frame error rate; and

wherein said reliability level corresponds to said target frame error rate;

provide a first set of signals indicative of a first transmission energy of said plurality of transmission energies for a frame of information; and

provide at least one additional set of signals indicative of next transmission energy of said plurality of transmission energies for retransmitting said frame of information when said frame of information was received in error.

10. An apparatus for retransmission in a communication system, comprising:

a control processor configured to;

determine a plurality of transmission energies in accordance with a predetermined reliability level and at least one characteristic of a communication channel by;

determining a relationship between a frame error rate and a transmitting energy;

solving for a minimal total energy <

E>

, in accordance with the equation;

$〈<br><br>E〉<br><br>=E_1+f<br><br>\text{\hspace{1em}<br><br>}<br><br>\left(E_1\right)·<br><br>E_2+f<br><br>\text{\hspace{1em}<br><br>}<br><br>\left(E_1\right)·<br><br>f<br><br>\text{\hspace{1em}<br><br>}<br><br>\left(E_2\right)·<br><br>E_3+\mathrm{\dots <br><br>}+E_N<br><br>\text{\hspace{1em}<br><br>}<br><br>\underset{i=1}{\overset{N-1}{\prod <br><br>}}<br><br>\text{\hspace{1em}<br><br>}<br><br>f<br><br>\text{\hspace{1em}<br><br>}<br><br>\left(E_i\right),$

 

where;

E_i are said transmission energies, and

f(E_i) are frame error rates corresponding to said transmission energies E_i;

subject to constraint;

$T_{\mathrm{FER}}=\underset{i=1}{\overset{N}{\prod <br><br>}}<br><br>\text{\hspace{1em}<br><br>}<br><br>f<br><br>\text{\hspace{1em}<br><br>}<br><br>\left(E_i\right),$

 

where;

T_FRR is a target frame error rate; and

wherein said reliability level corresponds to said target frame error rate;

provide a first set of signals indicative of a first transmission energy of said plurality of transmission energies for a frame of information; and

provide at least one additional set of signals indicative of next transmission energy of said plurality of transmission energies for retransmitting said frame of information when said frame of information was received in error.

11. An apparatus for retransmission in a communication system, comprising:

a control processor configured to;

determine two transmission energies in accordance with a predetermined reliability level and at least one characteristic of a communication channel;

provide a first set of signals indicative of a first transmission energy of said plurality of transmission energies for a frame of information; and

provide at least one additional set of signals indicative of next transmission energy of said plurality of transmission energies for retransmitting said frame of information when said frame of information was received in error.

12. An apparatus for retransmission in a communication system, comprising:

a control processor configured to;

determine a plurality of transmission energies by solving an equation for estimating a minimum aggregate transmission energy;

provide a first set of signals indicative of a first transmission energy of said plurality of transmission energies for a frame of information; and

provide at least one additional set of signals indicative of next transmission energy of said plurality of transmission energies for retransmitting said frame of information when said frame of information was received in error.

13. An apparatus for retransmission in a communication system, comprising:

a control processor configured to;

determine a plurality of transmission energies in accordance with a predetermined reliability level and at least one characteristic of a communication channel by;

measuring said at least one of characteristic of said communication channel; and

utilizing a look-up table to select pre-computed transmission energies corresponding to said measured characteristic and said reliability level; and

a transmitter for;

transmitting a frame of information at a first transmission energy of said plurality of transmission energies; and

retransmitting said frame of information with a next transmission energy from said plurality of transmission energies when said frame was received in error.

14. The apparatus of claim 13, wherein said control processor pre-computes said transmission energies by having been configured to:

solve for a minimal total energy <

E>

, an equation;

$〈<br><br>E〉<br><br>=E_1+f<br><br>\text{\hspace{1em}<br><br>}<br><br>\left(E_1\right)·<br><br>E_2+f<br><br>\text{\hspace{1em}<br><br>}<br><br>\left(E_1\right)·<br><br>f<br><br>\text{\hspace{1em}<br><br>}<br><br>\left(E_2\right)·<br><br>E_3+\mathrm{\dots <br><br>}+E_N<br><br>\text{\hspace{1em}<br><br>}<br><br>\underset{i=1}{\overset{N-1}{\prod <br><br>}}<br><br>\text{\hspace{1em}<br><br>}<br><br>f<br><br>\text{\hspace{1em}<br><br>}<br><br>\left(E_i\right),$

 

where;

E_i are said transmission energies;

f(E_i) are frame error rates corresponding to said transmission energies E_i;

subject to constraint;

$T_{\mathrm{FER}}=\underset{i=1}{\overset{N}{\prod <br><br>}}<br><br>\text{\hspace{1em}<br><br>}<br><br>f<br><br>\text{\hspace{1em}<br><br>}<br><br>\left(E_i\right),$

 

where;

T_FRR is a target frame error rate; and

wherein said reliability level corresponds to said target frame error rate.

15. An apparatus for retransmission in a communication system, comprising:

a control processor configured to;

determine a plurality of transmission energies in accordance with a predetermined reliability level and at least one characteristic of a communication channel by;

measuring at least one of said characteristic of said communication channel;

utilizing a look-up table to select a predetermined relationship between a frame error rate and a transmission energy corresponding to said measured parameters;

solving for a minimal total energy <

E>

in accordance with the equation;

$〈<br><br>E〉<br><br>=E_1+f<br><br>\text{\hspace{1em}<br><br>}<br><br>\left(E_1\right)·<br><br>E_2+f<br><br>\text{\hspace{1em}<br><br>}<br><br>\left(E_1\right)·<br><br>f<br><br>\text{\hspace{1em}<br><br>}<br><br>\left(E_2\right)·<br><br>E_3+\mathrm{\dots <br><br>}+E_N<br><br>\text{\hspace{1em}<br><br>}<br><br>\underset{i=1}{\overset{N-1}{\prod <br><br>}}<br><br>\text{\hspace{1em}<br><br>}<br><br>f<br><br>\text{\hspace{1em}<br><br>}<br><br>\left(E_i\right),$

 

where;

E_i are said transmission energies,

f(E_i) are frame error rates corresponding to said transmission energies E_i;

subject to constraint;

$T_{\mathrm{FER}}=\underset{i=1}{\overset{N}{\prod <br><br>}}<br><br>\text{\hspace{1em}<br><br>}<br><br>f<br><br>\text{\hspace{1em}<br><br>}<br><br>\left(E_i\right),$

 

where;

T_FRR is a target frame error rate; and

wherein said reliability level corresponds to said target frame error rate; and

a transmitter for;

transmitting a frame of information at a first transmission energy of said plurality of transmission energies; and

retransmitting said frame of information with a next transmission energy from said plurality of transmission energies when said frame was received in error.

16. An apparatus for retransmission in a communication system, comprising:

a control processor configured to;

determine a plurality of transmission energies in accordance with a predetermined reliability level and at least one characteristic of a communication channel by;

determining a relationship between a frame error rate and a transmitting energy;

solving for a minimal total energy <

E>

, in accordance with the equation;

$〈<br><br>E〉<br><br>=E_1+f<br><br>\text{\hspace{1em}<br><br>}<br><br>\left(E_1\right)·<br><br>E_2+f<br><br>\text{\hspace{1em}<br><br>}<br><br>\left(E_1\right)·<br><br>f<br><br>\text{\hspace{1em}<br><br>}<br><br>\left(E_2\right)·<br><br>E_3+\mathrm{\dots <br><br>}+E_N<br><br>\text{\hspace{1em}<br><br>}<br><br>\underset{i=1}{\overset{N-1}{\prod <br><br>}}<br><br>\text{\hspace{1em}<br><br>}<br><br>f<br><br>\text{\hspace{1em}<br><br>}<br><br>\left(E_i\right),$

 

where;

E_i are said transmission energies, and

f(E_i) are frame error rates corresponding to said transmission energies E_i;

subject to constraint;

$T_{\mathrm{FER}}=\underset{i=1}{\overset{N}{\prod <br><br>}}<br><br>\text{\hspace{1em}<br><br>}<br><br>f<br><br>\text{\hspace{1em}<br><br>}<br><br>\left(E_i\right),$

 

where;

T_FRR is a target frame error rate; and

wherein said reliability level corresponds to said target frame error rate; and

a transmitter for;

transmitting a frame of information at a first transmission energy of said plurality of transmission energies; and

retransmitting said frame of information with a next transmission energy from said plurality of transmission energies when said frame was received in error.

17. An apparatus for retransmission in a communication system, comprising:

a control processor configured to;

determine two transmission energies in accordance with a predetermined reliability level and at least one characteristic of a communication channel; and

a transmitter for;

transmitting a frame of information at a first transmission energy of said plurality of transmission energies; and

retransmitting said frame of information with a next transmission energy from said plurality of transmission energies when said frame was received in error.

18. An apparatus for retransmission in a communication system, comprising:

a control processor configured to;

determine a plurality of transmission energies by solving an equation for estimating a minimum aggregate transmission energy; and

a transmitter for;

transmitting a frame of information at a first transmission energy of said plurality of transmission energies; and

retransmitting said frame of information with a next transmission energy from said plurality of transmission energies when said frame was received in error.

19. An apparatus for retransmission in a communication system, comprising:

a control processor configured to;

determine a plurality of transmission energies in accordance with a predetermined reliability level and at least one characteristic of a communication channel by;

measuring said at least one of characteristic of said communication channel; and

utilizing a look-up table to select pre-computed transmission energies corresponding to said measured characteristic and said reliability level;

provide a first set of signals indicative of a first transmission energy of said plurality of transmission energies for a frame of information; and

provide at least one additional set of signals indicative of next transmission energy from said plurality of transmission energies for retransmitting said frame of information when said frame was received in error; and

a receiver for providing an indication to said control processor whether said frame was received in error.

20. The apparatus of claim 19, wherein said control processor pre-computes said transmission energies by having been configured to:

solve for a minimal total energy <

E>

, an equation;

$〈<br><br>E〉<br><br>=E_1+f<br><br>\text{\hspace{1em}<br><br>}<br><br>\left(E_1\right)·<br><br>E_2+f<br><br>\text{\hspace{1em}<br><br>}<br><br>\left(E_1\right)·<br><br>f<br><br>\text{\hspace{1em}<br><br>}<br><br>\left(E_2\right)·<br><br>E_3+\mathrm{\dots <br><br>}+E_N<br><br>\text{\hspace{1em}<br><br>}<br><br>\underset{i=1}{\overset{N-1}{\prod <br><br>}}<br><br>\text{\hspace{1em}<br><br>}<br><br>f<br><br>\text{\hspace{1em}<br><br>}<br><br>\left(E_i\right),$

 

where;

E_i are said transmission energies;

f(E_i) are frame error rates corresponding to said transmission energies E_i;

subject to constraint;

$T_{\mathrm{FER}}=\underset{i=1}{\overset{N}{\prod <br><br>}}<br><br>\text{\hspace{1em}<br><br>}<br><br>f<br><br>\text{\hspace{1em}<br><br>}<br><br>\left(E_i\right),$

 

where;

T_FRR is a target frame error rate; and

wherein said reliability level corresponds to said target frame error rate.

21. An apparatus for retransmission in a communication system, comprising:

a control processor configured to;

determine a plurality of transmission energies in accordance with a predetermined reliability level and at least one characteristic of a communication channel by;

measuring at least one of said characteristic of said communication channel;

utilizing a look-up table to select a predetermined relationship between a frame error rate and a transmission energy corresponding to said measured parameters;

solving for a minimal total energy <

E>

in accordance with the equation;

$〈<br><br>E〉<br><br>=E_1+f<br><br>\text{\hspace{1em}<br><br>}<br><br>\left(E_1\right)·<br><br>E_2+f<br><br>\text{\hspace{1em}<br><br>}<br><br>\left(E_1\right)·<br><br>f<br><br>\text{\hspace{1em}<br><br>}<br><br>\left(E_2\right)·<br><br>E_3+\mathrm{\dots <br><br>}+E_N<br><br>\text{\hspace{1em}<br><br>}<br><br>\underset{i=1}{\overset{N-1}{\prod <br><br>}}<br><br>\text{\hspace{1em}<br><br>}<br><br>f<br><br>\text{\hspace{1em}<br><br>}<br><br>\left(E_i\right),$

 

where;

E_i are said transmission energies,

f(E_i) are frame error rates corresponding to said transmission energies E_i;

subject to constraint;

$T_{\mathrm{FER}}=\underset{i=1}{\overset{N}{\prod <br><br>}}<br><br>\text{\hspace{1em}<br><br>}<br><br>f<br><br>\text{\hspace{1em}<br><br>}<br><br>\left(E_i\right),$

 

where;

T_FRR is a target frame error rate; and

wherein said reliability level corresponds to said target frame error rate;

provide a first set of signals indicative of a first transmission energy of said plurality of transmission energies for a frame of information; and

provide at least one additional set of signals indicative of next transmission energy from said plurality of transmission energies for retransmitting said frame of information when said frame was received in error; and

a receiver for providing an indication to said control processor whether said frame was received in error.

22. An apparatus for retransmission in a communication system, comprising:

a control processor configured to;

determine a plurality of transmission energies in accordance with a predetermined reliability level and at least one characteristic of a communication channel by;

determining a relationship between a frame error rate and a transmitting energy;

solving for a minimal total energy <

E>

, in accordance with the equation;

$〈<br><br>E〉<br><br>=E_1+f<br><br>\text{\hspace{1em}<br><br>}<br><br>\left(E_1\right)·<br><br>E_2+f<br><br>\text{\hspace{1em}<br><br>}<br><br>\left(E_1\right)·<br><br>f<br><br>\text{\hspace{1em}<br><br>}<br><br>\left(E_2\right)·<br><br>E_3+\mathrm{\dots <br><br>}+E_N<br><br>\text{\hspace{1em}<br><br>}<br><br>\underset{i=1}{\overset{N-1}{\prod <br><br>}}<br><br>\text{\hspace{1em}<br><br>}<br><br>f<br><br>\text{\hspace{1em}<br><br>}<br><br>\left(E_i\right),$

 

where;

E_i are said transmission energies, and

f(E_i) are frame error rates corresponding to said transmission energies E_i;

subject to constraint;

$T_{\mathrm{FER}}=\underset{i=1}{\overset{N}{\prod <br><br>}}<br><br>\text{\hspace{1em}<br><br>}<br><br>f<br><br>\text{\hspace{1em}<br><br>}<br><br>\left(E_i\right),$

 

where;

T_FRR is a target frame error rate; and

wherein said reliability level corresponds to said target frame error rate;

provide a first set of signals indicative of a first transmission energy of said plurality of transmission energies for a frame of information; and

provide at least one additional set of signals indicative of next transmission energy from said plurality of transmission energies for retransmitting said frame of information when said frame was received in error; and

a receiver for providing an indication to said control processor whether said frame was received in error.

23. An apparatus for retransmission in a communication system, comprising:

a control processor configured to;

determine two transmission energies in accordance with a predetermined reliability level and at least one characteristic of a communication channel;

provide a first set of signals indicative of a first transmission energy of said plurality of transmission energies for a frame of information; and

provide at least one additional set of signals indicative of next transmission energy from said plurality of transmission energies for retransmitting said frame of information when said frame was received in error; and

a receiver for providing an indication to said control processor whether said frame was received in error.

24. An apparatus for retransmission in a communication system, comprising:

a control processor configured to;

determine a plurality of transmission energies by solving an equation for estimating a minimum aggregate transmission energy;

provide a first set of signals indicative of a first transmission energy of said plurality of transmission energies for a frame of information; and

provide at least one additional set of signals indicative of next transmission energy from said plurality of transmission energies for retransmitting said frame of information when said frame was received in error; and

a receiver for providing an indication to said control processor whether said frame was received in error.

25. An apparatus for retransmission in a communication system, comprising:

a control processor configured to;

determine a plurality of transmission energies in accordance with a predetermined reliability level and at least one characteristic of a communication channel by;

measuring said at least one of characteristic of said communication channel; and

utilizing a look-up table to select pre-computed transmission energies corresponding to said measured characteristic and said reliability level;

a receiver for providing an indication to said control processor whether said frame has been received in error; and

a transmitter for;

transmitting a frame of information at a first transmission energy of said plurality of transmission energies; and

retransmitting said frame of information with a next transmission energy from said plurality of transmission energies when said frame was received in error.

26. The apparatus of claim 25, wherein said control processor pre-computes said transmission energies by having been configured to:

solve for a minimal total energy <

E>

, an equation;

$〈<br><br>E〉<br><br>=E_1+f<br><br>\text{\hspace{1em}<br><br>}<br><br>\left(E_1\right)·<br><br>E_2+f<br><br>\text{\hspace{1em}<br><br>}<br><br>\left(E_1\right)·<br><br>f<br><br>\text{\hspace{1em}<br><br>}<br><br>\left(E_2\right)·<br><br>E_3+\mathrm{\dots <br><br>}+E_N<br><br>\text{\hspace{1em}<br><br>}<br><br>\underset{i=1}{\overset{N-1}{\prod <br><br>}}<br><br>\text{\hspace{1em}<br><br>}<br><br>f<br><br>\text{\hspace{1em}<br><br>}<br><br>\left(E_i\right),$

 

where;

E_i are said transmission energies;

f(E_i) are frame error rates corresponding to said transmission energies E_i;

subject to constraint;

$T_{\mathrm{FER}}=\underset{i=1}{\overset{N}{\prod <br><br>}}<br><br>\text{\hspace{1em}<br><br>}<br><br>f<br><br>\text{\hspace{1em}<br><br>}<br><br>\left(E_i\right),$

 

where;

T_FRR is a target frame error rate; and

wherein said reliability level corresponds to said target frame error rate.

27. An apparatus for retransmission in a communication system, comprising:

a control processor configured to;

determine a plurality of transmission energies in accordance with a predetermined reliability level and at least one characteristic of a communication channel by;

measuring at least one of said characteristic of said communication channel;

utilizing a look-up table to select a predetermined relationship between a frame error rate and a transmission energy corresponding to said measured parameters;

solving for a minimal total energy <

E>

in accordance with the equation;

$〈<br><br>E〉<br><br>=E_1+f<br><br>\text{\hspace{1em}<br><br>}<br><br>\left(E_1\right)·<br><br>E_2+f<br><br>\text{\hspace{1em}<br><br>}<br><br>\left(E_1\right)·<br><br>f<br><br>\text{\hspace{1em}<br><br>}<br><br>\left(E_2\right)·<br><br>E_3+\mathrm{\dots <br><br>}+E_N<br><br>\text{\hspace{1em}<br><br>}<br><br>\underset{i=1}{\overset{N-1}{\prod <br><br>}}<br><br>\text{\hspace{1em}<br><br>}<br><br>f<br><br>\text{\hspace{1em}<br><br>}<br><br>\left(E_i\right),$

 

where;

E_i are said transmission energies,

f(E_i) are frame error rates corresponding to said transmission energies E_i;

subject to constraint;

$T_{\mathrm{FER}}=\underset{i=1}{\overset{N}{\prod <br><br>}}<br><br>\text{\hspace{1em}<br><br>}<br><br>f<br><br>\text{\hspace{1em}<br><br>}<br><br>\left(E_i\right),$

 

where;

T_FRR is a target frame error rate; and

wherein said reliability level corresponds to said target frame error rate;

a receiver for providing an indication to said control processor whether said frame has been received in error; and

a transmitter for;

transmitting a frame of information at a first transmission energy of said plurality of transmission energies; and

retransmitting said frame of information with a next transmission energy from said plurality of transmission energies when said frame was received in error.

28. An apparatus for retransmission in a communication system, comprising:

a control processor configured to;

determine a plurality of transmission energies in accordance with a predetermined reliability level and at least one characteristic of a communication channel by;

determining a relationship between a frame error rate and a transmitting energy;

solving for a minimal total energy <

E>

, in accordance with the equation;

$〈<br><br>E〉<br><br>=E_1+f<br><br>\text{\hspace{1em}<br><br>}<br><br>\left(E_1\right)·<br><br>E_2+f<br><br>\text{\hspace{1em}<br><br>}<br><br>\left(E_1\right)·<br><br>f<br><br>\text{\hspace{1em}<br><br>}<br><br>\left(E_2\right)·<br><br>E_3+\mathrm{\dots <br><br>}+E_N<br><br>\text{\hspace{1em}<br><br>}<br><br>\underset{i=1}{\overset{N-1}{\prod <br><br>}}<br><br>\text{\hspace{1em}<br><br>}<br><br>f<br><br>\text{\hspace{1em}<br><br>}<br><br>\left(E_i\right),$

 

where;

E_i are said transmission energies, and

f(E_i) are frame error rates corresponding to said transmission energies E_i;

subject to constraint;

$T_{\mathrm{FER}}=\underset{i=1}{\overset{N}{\prod <br><br>}}<br><br>\text{\hspace{1em}<br><br>}<br><br>f<br><br>\text{\hspace{1em}<br><br>}<br><br>\left(E_i\right),$

 

where;

T_FRR is a target frame error rate; and

wherein said reliability level corresponds to said target frame error rate;

a receiver for providing an indication to said control processor whether said frame has been received in error; and

a transmitter for;

transmitting a frame of information at a first transmission energy of said plurality of transmission energies; and

retransmitting said frame of information with a next transmission energy from said plurality of transmission energies when said frame was received in error.

29. An apparatus for retransmission in a communication system, comprising:

a control processor configured to;

determine two transmission energies in accordance with a predetermined reliability level and at least one characteristic of a communication channel;

a receiver for providing an indication to said control processor whether said frame has been received in error; and

a transmitter for;

transmitting a frame of information at a first transmission energy of said plurality of transmission energies; and

retransmitting said frame of information with a next transmission energy from said plurality of transmission energies when said frame was received in error.

30. An apparatus for retransmission in a communication system, comprising:

a control processor configured to;

determine a plurality of transmission energies by solving an equation for estimating a minimum aggregate transmission energy;

a receiver for providing an indication to said control processor whether said frame has been received in error; and

a transmitter for;

transmitting a frame of information at a first transmission energy of said plurality of transmission energies; and

retransmitting said frame of information with a next transmission energy from said plurality of transmission energies when said frame was received in error.