Apparatus, computer readable medium, transmission medium, and method for synchronizing a received signal based on a maximum likelihood principle using a bisection technique

• US 20030021364A1
• Filed: 05/08/2001
• Published: 01/30/2003
• Est. Priority Date: 05/08/2001
• Status: Active Grant

• Current Assignee: COMSAT Corporation (Reorganized ISA SA)
• Original Assignee: COMSAT Corporation (Reorganized ISA SA)
• Inventors: Fan, Yigang, Chakravarthi, Prakash
• Granted Patent: US 6,744,836 B2
• Time in Patent Office: Days
• US Class Current: 375/341
• CPC Class Codes: H04L 7/041 using special codes as synchronising signal
• CPC Class Codes: H04L 7/10 Arrangements for initial synchronisation

Abstract

The present invention relates to burst mode digital communication systems where data transmission is preceded by a preamble for acquisition of carrier and clock synchronization using maximum likelihood (ML) principle. The preamble is sampled and the set of samples obtained is processed using the optimization algorithms of the present invention to provide the ML timing estimate. The optimization algorithms in the present invention consist of three parts. The first part deals with isolating the desired optimal estimate from non-optimal extremes satisfying the same necessary condition, and provides the initial conditions for activating the binary search schemes. The second part performs the binary search for the optimal timing estimate that guarantees the convergence. On the basis of the obtained iterative sequence, the last part constructs a more rapidly convergent sequence to obtain the ML symbol timing estimate. Using the obtained symbol timing estimate, the ML carrier phase estimate can be computed explicitly, and synchronization performed.

Claims

1. A method for synchronizing a received signal based on a maximum likelihood (ML) principle using a bisection technique comprising:

(a) directly sampling the received signal in a preamble period;

(b) obtaining an initial condition for initiating an iterative search by bisection method based on isolating an optimal estimate from non-optimal extremes;

(c) performing said iterative search by bisection method;

(d) generating another sequence using said bisection sequence, that converges to an ML timing estimate more rapidly;

(e) computing an ML carrier-phase using said ML timing estimate; and

(f) synchronizing the received signal based on said ML timing estimate and said ML carrier-phase.

2. A method for synchronizing a received signal using a maximum likelihood (ML) principle based on a bisection technique according to claim 1, wherein an Aitken'"'"'s Δ

² process is used to construct a rapidly convergent sequence based on said iterative sequence generated by said bisection method to increase a speed of convergence of said ML timing estimate.

3. A method for synchronizing a received signal based on a maximum likelihood (ML) principle using a bisection technique according to claim 1, wherein said received signal is stored in a memory.

4. A method for synchronizing a received signal based on a maximum likelihood (ML) principle using a bisection technique according to claim 1, wherein said steps (a)-(f) are performed by a processor.

5. A method for synchronizing a received signal based on a maximum likelihood (ML) principle using a bisection technique according to claim 1, wherein during said direct sampling, the signal is sampled 2m times per symbol period, m samples with sampling instants

6. A method according to claim 5, farther comprising sampling at boundaries where

7. A method for synchronizing a received signal using a maximum likelihood (ML) principle based on a bisection technique according to claim 1, wherein said bisection method is based on an algorithm comprising:

Step 1 Set i=1.

Step 2 While i<

N perform Steps 3-6.

$\mathrm{Step}<br><br>\text{\hspace{1em}<br><br>}<br><br>3<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{Set}<br><br>\text{\hspace{1em}<br><br>}<br><br>{\mathrm{\tau <br><br>}}_i={\mathrm{\tau <br><br>}}_a+\frac{{\mathrm{\tau <br><br>}}_b-{\mathrm{\tau <br><br>}}_a}{2}.<br><br>\mathrm{Step}<br><br>\text{\hspace{1em}<br><br>}<br><br>4<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{If}<br><br>\text{\hspace{1em}<br><br>}<br><br>f<br><br>\left({\mathrm{\tau <br><br>}}_i\right)=0<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{or}<br><br>\text{\hspace{1em}<br><br>}<br><br>\frac{{\mathrm{\tau <br><br>}}_b-{\mathrm{\tau <br><br>}}_a}{2}<<br><br>\mathrm{TOL}<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{then}$

OUTPUT(Ti);

(Procedure completed successfully.)

Stop;

Step 5 Set i=i+1.

Step 6 If f(τ

_a)f(τ

_b)>

0 then set τ

_a=τ

_i

else set τ

_b=τ

_i.

Step 7 OUTPUT (‘

N iterations are completed’

);

Stop;

wherein τ

_a, τ

_b are endpoints determined by said isolating an optimal estimate from non-optimal extremes, TOL is a tolerance, and N is a maximum number of iterations.

8. A computer readable medium, on which is stored a computer program for synchronizing a received signal based on a maximum likelihood (ML) principle using a bisection technique, said computer program storing instructions which, when executed, will perform the steps of:

(a) directly sampling the received signal in a preamble period;

(b) obtaining an initial condition for initiating an iterative search by bisection method based on isolating an optimal estimate from non-optimal extremes;

(c) performing said iterative search by bisection method;

(d) generating another sequence using said bisection sequence that converges to a ML timing estimate more rapidly;

(e) computing an ML carrier-phase using said ML timing estimate; and

(f) synchronizing the received signal.

9. A computer readable medium according to claim 8 wherein an Aitken'"'"'s Δ

² process is used to construct a rapidly convergent sequence based on said iterative sequence generated by said bisection method to increase a speed of convergence of said ML timing estimate without adding much complexity.

10. A computer readable medium according to claim 8 wherein said received data is stored in a memory.

11. A communications apparatus for synchronizing a received signal based on a maximum likelihood (ML) principle using a bisection technique, comprising:

(a) a receiver for receiving a signal;

(b) a memory for storing said received signal, and synchronization process iterations; and

(c) a processor, wherein said processor is used for;

directly sampling the received signal in a preamble period;

obtaining an initial condition for initiating an iterative search by bisection method based on isolating an optimal estimate from non-optimal extremes;

performing said iterative search by bisection method;

generating another sequence using said bisection sequence that converges to a ML timing estimate more rapidly;

computing an ML carrier-phase using said ML timing estimate; and

synchronizing the received signal based on said ML timing estimate and said ML carrier-phase.

12. A communications apparatus for synchronizing a received signal based on a maximum likelihood (ML) principle using a bisection technique according to claim 11, wherein said processor also uses an Aitken'"'"'s Δ

² process to construct a rapidly convergent sequence based on said iterative sequence generated by said bisection method to increase a speed of convergence of said ML timing estimate.

13. A transmission medium for transmitting a program for synchronizing a received signal based on a maximum likelihood (ML) principle using a bisection technique, the program comprising the steps of:

(a) directly sampling the received signal in a preamble period;

(b) obtaining an initial condition for initiating an iterative search by bisection method based on isolating an optimal estimate from non-optimal extremes;

(c) performing said iterative search by bisection method;

(d) generating another sequence using said bisection sequence that converges to a ML timing estimate more rapidly;

(e) computing an ML carrier-phase using said ML timing estimate; and

(f) synchronizing the received signal based on said ML timing estimate and said ML carrier-phase.

14. A transmission medium for transmitting a program for synchronizing a received signal using a maximum likelihood (ML) principle based on a bisection technique according to claim 13, wherein an Aitken'"'"'s Δ

² process is used to construct a rapidly convergent sequence based on said iterative sequence generated by said bisection method to increase a speed of convergence of said ML timing estimate.

15. A transmission medium for transmitting a program for synchronizing a received signal based on a maximum likelihood (ML) principle using a bisection technique according to claim 13, wherein said received signal is stored in a memory.

16. A transmission medium for transmitting a program for synchronizing a received signal based on a maximum likelihood (ML) principle using a bisection technique according to claim 13, wherein said steps (a)-(f) are performed by a processor.