Low complexity method for reducing PAPR in FRFT-OFDM systems
The invention relates to a method for reducing the PAPR in FRFT-OFDM systems, which belongs to the field of broadband wireless digital communications technology. The method is based on fractional random phase sequence and fractional circular convolution theorem, which can effectively reduce the PAPR of the system. The method of the invention has the advantages of simple system implementation and low computational complexity. In this method, the PAPR of the system can be effectively reduced while maintaining the reliability of the system. When the number of candidate signals is the same, the PAPR performance of the present method was found to be almost the same as that of SLM and better than that of PTS. More importantly, the present method has lower computational complexity than that of SLM and PTS methods.
1. A method for reducing peak-to-average power ratio (PAPR) in a fractional Fourier transform-orthogonal frequency division multiplexing (FRFT-OFDM) communication system, comprising the steps of:
1) at a transmitting end of the FRFT-OFDM communication system, performing an N-point inverse discrete fractional Fourier transform (IDFRFT) of digitalized complex input data X of length N and converting it into time domain to obtain FRFT-OFDM subcarrier signal x(n), wherein n is 1, 2, . . . , N;
2) performing a p-order chirp periodic extension of the FRFT-OFDM subcarrier signal x(n) to obtain an extended chirp sequence, x((n)) P,N , wherein chirp refers to a linear frequency modulation and p is the order of Fractional Fourier Transform, and wherein conversion equation for the p-order chirp periodic extension is:
x
(
n
-
N
)
e
j
1
2
cot
α
•
(
n
-
N
)
2
Δ
t
2
=
x
(
n
)
e
-
j
1
2
cot
α
•
n
2
Δ
t
2
wherein α=pπ/2, Δt is sampling interval;
3) shifting x((n)) P,N to right by iM (i is 1, 2, . . . , L) points to get x((n−iM)) P,N , which further multiplies by R N (n) to obtain chirp circular displacement of FRFT-OFDM signal, x((n−iM)) P,N R N (n), wherein L is the length of a random phase sequence; M=N/L,
R
N
(
n
)
=
{
1
1
≤
n
≤
N
-
1
0
other
;
4) multiplying x((n−iM)) P,N R N (n) by
η
(
n
,
i
)
=
e
j
1
2
cot
α
•
[
-
2
•
iM
•
n
+
(
i
M
)
2
]
Δ
t
2
point-by-point to obtain φ(n,i) as the following:
φ( n,i )= x (( n−iM )) P,N R N ( n )□η( n,i ), i= 0,1 . . . L− 1, n= 0,1, . . . , N− 1
5) multiplying φ(n,i) by weighting factors, r (l) (i), and using a combiner to obtain candidate signals {tilde over (x)} (l) (n) of FRFT-OFDM in time domain as the following:
x
~
(
l
)
(
n
)
=
∑
i
=
0
L
-
1
r
(
l
)
(
i
)
•
φ
(
n
,
i
)
,
n=0, 1 . . . N−1, l=1, 2, . . . S
wherein r (l) (i) is a weighting factor with L-length, and S is the number of alternative Fractional random phase sequence;
6) transmitting a weighting factor r(i) opt that makes PAPR of candidate signals minimum as sideband information of FRFT-OFDM signals, wherein
r
(
i
)
opt
=
argmin
PARP
{
r
(
l
)
(
i
)
,
…
,
r
(
s
)
}
{
x
~
(
l
)
(
n
)
}
8) using a Digital-to-Analog Converter to convert the transmitting FRFT-OFDM signals with minimum PAPR to analog signals which are further amplified by a High-Power Amplifier after modulated by carrier; and
9) submitting the amplified analog signals to a transmitting antenna.