Page 80 - Kaleidoscope Academic Conference Proceedings 2021

2021 ITU Kaleidoscope Academic Conference

• The proposed receiver is theoretically proved to be able the sampling number of the CP part, respectively.
to improve the performance. The interference from other
subcarriers will be suppressed because of the design of 2.1 Influence of FO and TO on received preamble
the combination weights.
Let ∆ f denote the residual FO which is normalized by the
This paper is organized as follows. Section 2 briefly SCS, and D ∈ {0, 1, . . ., N CP − 1} denote the residual TO in
introduces the structure of NPRACH preamble, and derives the receiver side. As is pointed in [8], the NPRACH preamble
the effect of TO/FO on the received signal. Section is constrained in a narrowband, so the channel can be modeled
3 describes both the reference method in [8] and the as a one-tap channel. Without loss of generality, assume the
proposed receiver. The improvement on the performance power scaling factor β N PRACH is 1/N. Then the received
is theoretically analyzed in Subsection 3.3. In Section 4, signal of the l−th symbol in the m−th symbol group can be
the performance is evaluated by numerical simulation, which denoted by
is compared with the receiver in [8]. Finally, Section 5
concludes this paper.
y m,l (n) =h(m, l)e j2πΩ(m)(n−D+lN)/N
2. NPRACH PREAMBLE × e j2π∆f (m(N C P +LN)+lN+n−D)/N /N + w m,l (n)

An NPRACH preamble consists of single-subcarrier OFDM =Ae j2πn(Ω(m)+∆f )/N + w m,l (n),
symbols with frequency hopping[7]. As shown in Figure 1, a n = 0, 1, . . ., N − 1 (2)
N PRACH
preamble has N rep repetition units. Each repetition
unit contains P symbol groups. A symbol group is the where w m,l (n) denotes the Additive White Gaussian Noise
concatenation of L single-subcarrier OFDM symbols and a (AWGN). The term h(m, l) is the channel coefficient and
CP. The OFDM symbols in the same symbol group are in the
same subcarrier, and different symbol groups are hopping in A = h(m, l) e j2π(∆f (m(N C P +LN)+lN−D)−DΩ(m))/N . (3)
the frequency domain. The hopping pattern is determined by N
the subcarrier index of the first symbol group, the preamble After receiving the time domain signal, the BS will perform
format and the physical cell identity. FFT on it to detect the preamble in the frequency domain.
The obtained frequency domain signal in the k-th subcarrier
can be denoted by

N−1
Õ
Y m,l (k) = y m,l (n)e −j2πkn/N
n=0
N−1
Õ
=A e j2πn(Ω(m)+∆f )/N · e −j2πkn/N + W m,l (k) (4)
n=0

Define θ = π(Ω(m) + ∆ f − k)/N and assume e j2θ , 1. It
follows that
Figure 1 – An example of NPRACH preamble N−1
Õ
j2θn + W m,l (k)
e
Y m,l (k) =A
The NPRACH procedure consists of 4 messages, and the n=0
NPRACH preamble is regarded as Msg1. In order to initialize jθN jθN −jθN
wireless access, an NB-IoT UE needs to choose one subcarrier =A e (e − e ) + W m,l (k)
index for the first symbol group from the candidate indices e (e jθ − e −jθ )
jθ
and send the corresponding NPRACH preamble. The BS =Ae jθ(N−1) sin(θN) + W m,l (k) (5)
will try to detect in which subcarrier the preamble exists to sin(θ)
identify the accessing UE. The FO and TO will be further In Equation (5), the received power in the k-th subcarrier
estimated for some compensation steps such as time advance. is determined by the term sin(θN)/sin(θ). Suppose the ∆ f
However, when the FO is large, the power of the preamble will is increasing from 0 to 1/2, then the received power in the
leak into the adjacent subcarriers, which adversely affects the Ω(m)-th subcarrier will decrease and the received power in
performance of the NPRACH detection. the (Ω(m)+1)-th subcarrier will increase. When |∆ f | is large,
Let N denote the sampling number of an OFDM symbol. As it will largely affect the NPRACH preamble detection.
is defined in [7], the equivalent baseband signal of the m-th
symbol group in time domain can be expressed by
3. NPRACH RECEIVER
s m (n) = β N PRACH e j2πΩ(m)n/N , n = −N CP , . . ., LN − 1, 3.1 Reference method
(1)
where β N PRACH , Ω(m), N CP denote the power scaling The receiver in [8] takes full advantage of all the OFDM
factor, the subcarrier index of the m-th symbol group and symbols in the NPRACH preamble to make a joint estimation,

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