Spectrum shaping method for generating signal having almost constant envelope in communication system, and transmitter performing same
Provided is a discrete Fourier transform (DFT)-spread orthogonal frequency division multiplexing (OFDM) transmission method and transmitter including a phase shifter configured to generate a pi/2-binary phase shift keying (BPSK) symbol vector by phase-shifting a vector including M BPSK symbols, a DFT spreader configured to generate a DFT-spread pi/2-BPSK symbol vector by spreading the pi/2-BPSK symbol vector using an M-point DFT matrix, a circular extender configured to generate a circularly extended pi/2-BPSK symbol vector by periodically extending the DFT-spread pi/2-BPSK symbol vector, a frequency domain spectrum shaper configured to generate a frequency domain spectrum shaped pi/2-BPSK symbol vector by multiplying each element of the circularly extended pi/2-BPSK symbol vector by each element of a first shaping vector, and a subcarrier allocator configured to allocate the frequency domain spectrum shaped pi/2-BPSK symbol vector to subcarriers in an allocated frequency range.
1. A discrete Fourier transform (DFT)-spread orthogonal frequency division multiplexing (OFDM) transmitter comprising:
a phase shifter configured to generate a pi/2-binary phase shift keying (BPSK) symbol vector d by phase-shifting a vector b including M BPSK symbols;
a DFT spreader configured to generate a DFT-spread pi/2-BPSK symbol vector x by spreading the pi/2-BPSK symbol vector d by using an M-point DFT matrix W M ;
a circular extender configured to generate a circularly extended pi/2-BPSK symbol vector y by periodically extending the DFT-spread pi/2-BPSK symbol vector x ,
a frequency domain spectrum shaper configured to generate a frequency domain spectrum shaped pi/2-BPSK symbol vector z by multiplying each element of the circularly extended pi/2-BPSK symbol vector y by each element of a first shaping vector s T ;
a subcarrier allocator configured to allocate the frequency domain spectrum shaped pi/2-BPSK symbol vector z to subcarriers in an allocated frequency range; and
an inverse DFT (IDFT) unit and a cyclic prefix (CP) adder configured to generate a DFT-spread OFDM transmission signal by performing an IDFT and inserting a CP to the pi/2-BPSK symbol vector z allocated to the subcarriers,
wherein the frequency domain spectrum shaped pi/2-BPSK symbol vector z is obtained by performing a Hadamard product of the circularly extended pi/2-BPSK symbol vector y and the first shaping vector s T,
wherein the first shaping vector s T is determined according to the M and a number L of the subcarriers to be used,
wherein an l-th element of the first shaping vector s T is determined to be a value obtained by equidistant sampling of continuous-time Fourier transform of a minimum shift keying (MSK) waveform defined by the following equation:
P
(
f
)
=
sin
c
(
-
2
f
+
1
2
)
+
sin
c
(
2
f
+
1
2
)
and
wherein the value is a sampled value at a certain location defined by the following equation
s
T
,
l
=
△
sin
c
(
-
2
l
+
L
+
2
M
+
1
2
)
+
sin
c
(
2
l
-
L
-
2
M
+
1
2
)
where l=1, 2, . . . , L.
2. The DFT-spread OFDM transmitter of claim 1 , wherein the number L of the subcarriers is determined by the following equation
L
=
(
k
+
1
2
)
M
where k is an arbitrary natural number.
3. The DFT-spread OFDM transmitter of claim 1 , wherein the frequency domain spectrum shaper is configured to perform frequency domain spectrum shaping with a second shaping vector s T2 generated by obtaining a Hadamard product of the first shaping vector s T and a window vector w of one of Hamming, Hanning, Keiser, Gaussian, Tukey, Blackmann and Dolph-Chebyshev.
4. A discrete Fourier transform (DFT)-spread orthogonal frequency division multiplexing (OFDM) transmission method performed by a DFT-spread OFDM transmitter, the DFT-spread OFDM transmission method comprising:
generating a pi/2-binary phase shift keying (BPSK) symbol vector d by phase-shifting a vector b including M BPSK symbols;
generating a DFT-spread pi/2-BPSK symbol vector x by spreading the pi/2-BPSK symbol vector d by using an M-point DFT matrix W M ;
generating a circularly extended pi/2-BPSK symbol vector y by periodically extending the DFT-spread pi/2-BPSK symbol vector x ,
generating a frequency domain spectrum shaped pi/2-BPSK symbol vector z by multiplying each element of the circularly extended pi/2-BPSK symbol vector y by each element of a first shaping vector s T ; and
allocating the frequency domain spectrum shaped pi/2-BPSK symbol vector z to subcarriers in an allocated frequency range; and
generating a DFT-spread OFDM transmission signal by performing an inverse DFT (IDFT) and inserting a cyclic prefix (CP) to the pi/2-BPSK symbol vector allocated to the subcarriers,
wherein the frequency domain spectrum shaped pi/2-BPSK symbol vector z is obtained by performing a Hadamard product of the circularly extended pi/2-BPSK symbol vector y and the first shaping vector s T,
wherein the first shaping vector s T is determined according to the M and a number L of the subcarriers to be used,
wherein an l-th element of the first shaping vector s T is determined to be a value obtained by equidistant sampling of continuous-time Fourier transform of a minimum shift keying (MSK) waveform defined by the following equation:
P
(
f
)
=
sin
c
(
-
2
f
+
1
2
)
+
sin
c
(
2
f
+
1
2
)
and
wherein the value is a sampled value at a certain location defined by the following equation
s
T
,
l
=
△
sin
c
(
-
2
l
+
L
+
2
M
+
1
2
)
+
sin
c
(
2
l
-
L
-
2
M
+
1
2
)
where l=1, 2, . . . , L.
5. The DFT-spread OFDM transmission method of claim 4 , wherein the number L of the subcarriers is determined by the following equation
L
=
(
k
+
1
2
)
M
where k is an arbitrary natural number.
6. The DFT-spread OFDM transmission method of claim 4 , wherein the generating of the frequency domain spectrum shaped pi/2-BPSK symbol vector z comprises performing frequency domain spectrum shaping with a second shaping vector s T2 generated by obtaining a Hadamard product of the first shaping vector s T and a window vector w of one of Hamming, Hanning, Keiser, Gaussian, Tukey, Blackmann and Dolph-Chebyshev.