Quantization method for OFDM
View Patent ↗A quantization method for OFDM is described. In an embodiment, the method uses an objective function which is defined as a function of the quantization error of the OFDM signal in frequency summed over data subcarriers. A search algorithm is used to optimize the objective function and the solution found is quantized by rounding. The quantized value of the solution may then be fed back into the objective function to compute a value of that function and if the value is less than the value computed in a previous iteration of the method, the method is repeated using the quantized value of the solution as the new starting point for the search algorithm. If the value of the function is, however, not less than the value computed in a previous iteration, the new solution is discarded and the quantized value of the solution from the previous iteration is output.
1. A computer implemented method of quantizing an OFDM signal, the method comprising:
defining an objective function as a function of a quantization error of the OFDM signal in frequency summed over data subcarriers;
optimizing, by a processor, the objective function using a search algorithm to generate a real number solution; and
quantizing the real number solution to generate a quantized solution.
2. The method according to claim 1 , further comprising:
storing the quantized solution in a look-up table in an OFDM transmitter.
3. The method according to claim 2 , further comprising:
transmitting the quantized solution from the OFDM transmitter.
4. The method according to claim 1 , wherein the OFDM signal comprises long training fields.
5. The method according to claim 1 , further comprising:
computing a value of the objective function using the quantized solution; and
for a first iteration and in subsequent iterations if the computed value is less than a value of the objective function computed in a previous iteration, repeating the method using the quantized solution as a starting point for optimizing the objective function.
6. The method according to claim 5 , further comprising, in subsequent iterations if the computed value is not less than the value of the objective function computed in the previous iteration:
using the quantized solution from the previous iteration.
7. The method according to claim 1 , wherein the data subcarriers comprise payload data subcarriers and pilot subcarriers.
8. The method according to claim 1 , wherein the objective function is defined as a square of quantization error in frequency summed over data subcarriers.
9. The method according to claim 8 , wherein the objective function is:
F
(
x
Q
(
n
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)
=
∑
k
d
Q
(
k
)
-
d
(
k
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2
where k is over the data carrying subcarriers, n is the time index, d(k)=FFT(x(n)), x Q (n) is a quantized representation of the time-domain signal x(n) and d Q (k)=FFT(x Q (n)).
10. The method according to claim 9 , wherein the search algorithm comprises a non-linear least squares optimization algorithm.
11. A method of quantizing an OFDM long training field comprising:
defining an objective function as a square of quantization error in frequency summed over data subcarriers;
generating a starting search point;
using a search algorithm and the starting search point to optimize the objective function and compute a solution by a processor;
quantizing the solution and using the quantized solution to compute a value of the objective function;
in a first iteration, storing the computed value and the quantized solution and repeating the optimization and quantization using the stored solution; and
in a subsequent iteration, comparing the computed value to the stored value, and if the computed value is less than the stored value, storing the computed value and the quantized solution and repeating the optimization and quantization using the stored solution, and
if the computed value is not less than the stored value, outputting the stored solution.
12. The method according to claim 11 , further comprising repeating the method for each symbol in the OFDM long training field.
13. The method according to claim 12 , further comprising storing the output solutions in a look-up table in an OFDM transmitter module.
14. The method according to claim 11 , wherein the objective function is defined as a square of quantization error in frequency summed over data subcarriers.
15. The method according to claim 11 , wherein the objective function is:
F
(
x
Q
(
n
)
)
=
∑
k
d
Q
(
k
)
-
d
(
k
)
2
where k is over the data carrying subcarriers, n is the time index, d(k)=FFT(x(n)), x Q (n) is a quantized representation of the time-domain signal x(n) and d Q (k)=FFT(x Q (n)).
16. An apparatus for quantizing an OFDM signal, the apparatus comprising:
an input for receiving an OFDM signal;
a processor;
an output for outputting a quantized OFDM signal; and
a memory arranged to store executable instructions which when executed cause the processor to:
optimize an objective function using a search algorithm to generate a real number solution, the objective function comprising a square of quantization error of the OFDM signal in frequency summed over data carrying subcarriers;
round the real number solution to generate a quantized solution; and
store the quantized solution.
17. The apparatus according to claim 16 , wherein memory is further arranged to store executable instructions which when executed cause the processor to:
compute a value of the objective function using the quantized solution; and
repeat the method using the quantized solution as a starting point for optimizing the objective function if the computed value is less than a value of the objective function computed in a previous iteration.
18. The apparatus according to claim 17 , wherein the memory is further arranged to store executable instructions which when executed cause the processor to:
discard the quantized solution if the computed value is not less than the value of the objective function computed in the previous iteration; and
output the quantized solution from the previous iteration.
19. The apparatus according to claim 16 , wherein the objective function is:
F
(
x
Q
(
n
)
)
=
∑
k
d
Q
(
k
)
-
d
(
k
)
2
where k is over the data subcarriers, n is the time index, d(k)=FFT(x(n)), x Q (n) is a quantized representation of the time-domain signal x(n) and d Q (k)=FFT(x Q (n)).
20. The apparatus according to claim 16 , wherein the OFDM signal comprises long training fields.