Page 82 - Kaleidoscope Academic Conference Proceedings 2021

2021 ITU Kaleidoscope Academic Conference

data in the adjacent subcarriers can be expressed by where W (i) is the additive noise in J g,i (D , ∆ f ), and
∗
0
∗
Y m,l (Ω(m) + i) = sin(π(∆ f − i))
∗
a i = (16)
sin(π(∆ f − i)) ∗ .
jπ(∆f (N−1−2D)−i(N−1))/N N sin(π(∆ f − i)/N)
h(m, l)e
N sin(π(∆ f − i)/N) 0 2
j2π∆f (m(N C P +LN)+lN)/N −j2πDΩ(m)/N Without loss of generality, assume W (i) ∼ CN(0, σ ) which
× e e is independent for i = −1, 0, 1. Then the additive noise in
J g (D , ∆ f ) satisfies
ˆ
∗
∗
+ W m,l (Ω(m) + i),
(11)
i = −1, 0, 1; m = 0, . . ., M − 1; l = 0, . . ., L − 1. q
Õ 0 2 2 2 2
In order to generate the correlation peak, it is straightforward a i W (i) ∼ a −1 + a + a · CN(0, σ ). (17)
0
1
to combine the received power in the three subcarriers in i=−1,0,1
Equation (11) by using corresponding phase rotations and Meanwhile, the correlation peak in [8] is
weights. The combination is in two steps as shown in ∗
∗
∗
0
Equation (12) and Equation (13). J g (D , ∆ f ) = a 0 QLh g e j2π∆f (N−1−2D)/N + W (0). (18)
J g,i (D, ∆ f ) = q
Because of a 2 + a + a ≥ |a 0 |, in the proposed method,
2
2
(g+1)Q−1 L−1 −1 0 1
Õ Õ the increase of the power of the received signal is larger than
Y m,l (Ω(m) + i) that of the received noise.
m=gQ l=0
× e −j2π∆f (m(N C P +LN)+lN)/N j2πDΩ(m)/N . (12) 3.3.2 Interference from other UEs
e
The correlated values in Equation (12) are coherently Preamble from other UEs in adjacent subcarriers also will
combined as
interfere with the preamble detection. We suppose the TO
ˆ
J g (D, ∆ f ) = and FO of the interfering UE are D 1 and ∆ f 1 , respectively.
Õ jπi(N−1)/N sin(π(∆ f − i)) When the BS tries to detect a preamble, the leaked power
J g,i (D, ∆ f )e . of the interfering preamble will form a correlation peak in
N sin(π(∆ f − i)/N)
ˆ
i=−1,0,1 J g (D 1 , ∆ f 1 ) because of the property of FFT. In the proposed
(13) method, the interference is suppressed by the weights in
It is worth noting that in equations (12) and (13), the phases Equation (13). The reason for this is two-fold. First, the
of all the terms in Equation (11) are aligned and combined. majority of interfering power is in the adjacent subcarrier but
Meanwhile the combination weights in Equation (13) is will be allocated a relatively small weight. Second, with the
based on the amplitudes in the three subcarriers, by which combination weights, the interfering signals in the detected
J g (D, ∆ f ) will combine the received power. Subsection 3.3 subcarrier and in the adjacent subcarrier always have opposite
ˆ
theoretically proves that this design of weights can improve signs. As with Equation (16), let b i denote the weight for
the performance. J g (D 1 , ∆ f 1 ). The change of b i with respect to ∆ f 1 is presented
ˆ
Finally, the TO and FO in the channel are estimated by in Figure 3.
L/Q−1
∗
∗
(D , ∆ f ) = arg max Õ ˆ 2 (14)
J g (D, ∆ f ) .
D,∆f g=0
3.3 Theoretical analysis
In Equation (13), the received signals in the three adjacent
subcarriers are combined with different weights. In the
meantime, the noise in the subcarriers are also cumulating.
In this subsection, the weighted combination is theoretically
proved to be able to improve the NPRACH preamble detection
performance.
3.3.1 Interference from AWGN
Because the h(m, l) is consistent in Q symbol groups, assume
the channel coefficients in J g are h g . Suppose the real TO Figure 3 – The combination weights of different subcarriers
ˆ
and FO are D and ∆ f , respectively, then the correlation
∗
∗
peak of the proposed receiver is Suppose the interfering preamble is transmitted in the (Ω(m)+
∗
∗
ˆ
J g (D , ∆ f ) = 1)-th subcarrier, then the interfering signals in the Ω(m)-th
and (Ω(m) + 1)-th subcarriers have coefficients b −1 and b 0 ,
∗
Õ
∗
2 j2π∆f (N−1−2D )/N 0
ˆ
a QLh g e (15) respectively. However, in the correlation peak J g (D 1 , ∆ f 1 ),
i + a i W (i),
i=−1,0,1 the two interfering signals are combined by weights b 0 and
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