1. Introduction
Device-to-device (D2D) communication is a prime enabler that creates direct interaction between 5G-enabled user devices without the participation of the cellular network [
1]. Sidelink D2D communication is considered a key technology in advancing wireless cellular networks from 4G long-term evolution-advanced (LTE-A) to 5G new radio (NR). Standardization developments towards 5G NR in 3rd-generation partnership project (3GPP) releases 16 and 17 focus on feature enhancements for cellular vehicle-to-everything (V2X) communication using NR sidelink [
2,
3,
4]. The main scenario of NR sidelink addresses D2D-enabled V2X use cases, such as vehicle platooning, advanced driving, extended sensors, and remote driving [
5,
6,
7]. A main challenge in 5G NR-V2X applications is meeting the rigorous reliability and latency demands while simultaneously enhancing coverage using relays [
8]. In order to achieve these goals, releases 16 and 17 establish the role of 5G in supporting advanced V2X services and ensuring vehicle quality of service (QoS) support. Thus, V2X communication is anticipated to play a pivotal role in 5G NR systems [
4].
In NR-V2X cellular communication, synchronization information can be periodically broadcasted with source user equipment (UE) to increase the synchronization coverage of a synchronization source and to facilitate multiple UE devices to align the time reference with each other [
9,
10]. When UE devices are in different, non-synchronized cells, or one or more UE devices are out of coverage, UE devices have to synchronize with one another via sidelink synchronization signal (SLSS) [
11], which is transmitted within a sidelink synchronization signal block (SL-SSB).
Figure 1 illustrates the synchronization modes of V2X networks. As shown in
Figure 1, achieving synchronization across a network, especially in situations with partial coverage and in out-of-coverage scenarios where V2X UE devices communicate directly among themselves, poses a big challenge. In each SL-SSB, a sidelink primary synchronization signal (SL-PSS) and a sidelink secondary synchronization signal (SL-SSS) together carry information such as the source identifier of the transmitting UE, as well as synchronization information. At the beginning of communication, the SLSS is used for timing- and frequency-offset estimation. By identifying the SLSS transmitted by a source UE device, nearby UE devices can be synchronized with the source UE device and can estimate the symbol timing offset (STO) as well as carrier frequency offset (CFO) [
12]. Once the initial STO and CFO have been removed from the time domain, a UE device attempts to acquire a sidelink identity by decoding the sidelink synchronization identity (SSID) information transmitted by the SLSS, which includes both the in-coverage indicator and the SLSS identifier (SLSSID) [
13]. The problem of detecting the SLSS can be primarily divided into two main challenges. Firstly, the V2X UE device lacks information about the system timing, and secondly, the frequency of the local oscillator is not fully synchronized with the network [
14]. Consequently, significant time and frequency uncertainties may be present between the V2X UE and the network, posing a substantial challenge to initial sidelink acquisition [
15]. To establish robust synchronization under such demanding conditions, various synchronization strategies have been investigated in the existing literature [
14,
15,
16,
17,
18].
The first step of the synchronization procedure on the UE side is the detection of the SL-PSS and the determination of the in-coverage indicator transmitted in the SL-PSS. After SL-PSS detection, the UE device attempts to detect the SLSSID transmitted in the SL-SSS [
16]. Generally, there are two main strategies for detecting the SL-SSS, which can be performed in a coherent or non-coherent manner [
17,
18,
19]. Once the SL-PSS has been identified, the UE device becomes ready for obtaining channel state information (CSI) to coherently detect the following SL-SSS. However, an interfering SL-PSS received from a neighboring next-generation nodeB (gNodeB) may deteriorate the performance of the initial CSI estimation. Due to the difficult task of CSI estimation, differential detection is commonly used for non-coherent SL-SSS detection (NSD), thereby avoiding any CSI estimation [
19]. In this way, the effect of multipath fading and timing offset is removed from the received SL-SSS without resorting to the use of CSI. In spite of its simple implementation and robustness to Doppler frequency, the performance of the NSD approach heavily depends on the amount of frequency selectivity over the signal bandwidth. Since the SL-PSS is transmitted on two consecutive orthogonal frequency division multiplexing (OFDM) symbols, average channel estimation of the SL-PSS becomes feasible and thus provides an improved CSI estimate. Using available CSI, various coherent SL-SSS detection (CSD) schemes have been proposed in the literature [
17,
18]. However, in situations where the time selectivity of the channel prevents accurate CSI estimation and the Doppler effect can be high enough, the performance of the CSD methods deteriorates accordingly. In [
18], the two binary m-sequences comprising a SL-SSS can be detected independently without relying on mutual information, which contributes to simplifying the complexity of the SL-SSS detector. Nevertheless, this computational advantage comes at the expense of sacrificing detection performance. After successfully detecting SL-SSS, the UE device gains access to important system information transmitted via a physical broadcast channel (PBCH). To decode PBCH successfully, it is essential to track and eliminate the remaining residual CFO (RCFO) since it persists even after CFO compensation. For this reason, it is important to design a cost-effective and still high-performance SL-SSS detection method for 5G V2X vehicular communications. Additionally, the initial synchronization procedure in 5G NR-V2X systems becomes notably challenging due to the necessity to evaluate 336 potential SL-SSS candidates for detection.
This paper presents a reduced-complexity formulation for SL-SSS detection in cellular V2X communication systems, supported by a coherent algorithm based on a priori knowledge of the CSI. The main contributions of this paper are stated as follows.
By utilizing the cyclic-shifted property of SL-SSS derived from m-sequence and adopting the maximum likelihood (ML) detection principle, we design a computationally efficient SL-SSS detection method to simultaneously estimate the SLSSID and RCFO in a decoupled manner without sacrificing detection performance.
The benefit of employing the identical correlation function for SLSSID detection is the capability to concurrently estimate the RCFO, thus resulting in a more straightforward design for the synchronization receiver.
Such a design makes it easier to achieve robust joint detection of the SLSSID and RCFO in the presence of significant frequency-selective fading and STO.
In order to validate the viability of the proposed SL-SSS detection method, we compare the performance of the proposed and conventional SL-SSS detectors in terms of detection probability and computational complexity.
Simulation results confirm that the proposed SL-SSS detection method is computationally efficient and achieves detection performance comparable with that of existing approaches, thereby making it as a strong candidate for synchronization receivers in 5G NR-V2X systems.
The reminder of this paper is as follows.
Section 2 presents the system model for 5G NR-V2X communication.
Section 3 highlights the reduced-complexity SL-SSS synchronization method. The numerical results, demonstrating the benefits of the proposed detector, are presented in
Section 4. Finally, the paper is summarized in
Section 5.
3. Proposed SL-SSS Detection Method for V2X Systems
This section presents joint synchronization of SL-SSS and RCFO, which is based on the ML detection principle. In order to evaluate the usefulness of the proposed SL-SSS detector, we develop a simplified alternative and calculate its corresponding analytical detection probability.
For a simple presentation, assume that the SL-PSS with an in-coverage indicator
u is present on the
l-th OFDM symbol within each SSB such that
and
. To counteract the impacts of interference and fading channel, we use the average correlation among the received four consecutive SLSSs. As seen from (
6), the SL-SSS can be represented by the concatenation of two m-sequences as follows:
for
and
, where
and
stand for m-sequences mapped from
and
in a subcarrier-wise manner, respectively. Based on in-coverage indicator
u detected using the SL-PSS,
forms one of three m-sequences created by applying a cyclic shift of length
to a basic code and
is designed with the same sequence for all three sequences
’s (
), therefore generating a total number of 336 SLSSIDs. According to this formulation, an SLSSID
s is associated with a pair
in such a way that
.
3.1. Approximate ML Detection Scheme
In this section, we consider that the OFDM receiver collects four observation SLSS vectors of length
,
, to detect the SLSSID and RCFO. Denote
(
). For the simplicity of notations, let us consider a situation where the ICFO
and in-coverage indicator
u are perfectly known at the UE receiver. Furthermore,
, where
is the possible identifier of
and
is the possible identifier of
. Applying the ML estimation principle, one can obtain the conditional joint probability density function (PDF) of the SLSS vectors
(
) as
where
stands for the appropriate noise variance,
, and
stands for the received signal from which the SL-SSS sequence is compensated during the fourth and fifth OFDM symbol periods of each SSB.
The ML optimization problem is to jointly choose the SLSSID and RCFO in order to maximize the conditional PDF
with respect to
, which is described as
Since
has already been detected before the process of detecting SL-SSS, the UE device tries to jointly detect the SLSSID and RCFO by performing
where
After some arithmetic calculations, (
13) is simplified as
where
stands for a real part of the enclosed quantity,
and
Since
is independent of both
a and
b, it can be dropped from the optimization task in (
12), resulting in an approximate ML (AML) estimate of
simply as
For each trial value of
, the AML estimator performs an exhaustive search of
by appropriately quantizing the possible RCFO values, which incurs a heavy computational load. In order to solve the complexity issue involved with maximizing (
17) with respect to
, a low-complexity alternative is presented in the following section.
3.2. Low-Complexity SL-SSS Detection Scheme
Since the superscripts
are omitted from
and it is apparent from (
13) that
is negative, the cost function
reaches its maximum when
is maximized. To achieve this goal, it is necessary that
. Based on this implication,
can be estimated in a closed form as follows:
where
∠ is the angle operation. Note that the estimation range of (
18) is limited by
. Using the fact that
and putting this notation in
, it is obvious that the quantity
is reduced to
. By using this formulation, a simplified estimation
is performed as
which implies that the detection problem of (
17) is decoupled in a sequential manner. By collecting the estimated pair
, we can determine
as
. Then, one can estimate
in a decoupled manner by substituting
into (
18).
As seen from (
19), we perform a hypothesis test for potential SL-SSS candidates to decide one of the 336 SLSSIDs, which still remains computationally very demanding. To address this complexity problem, we propose a low-complexity SLSSID detection method without compromising the detection performance of (
19). A close looking at (
6) informs us that
and
are generated by cyclically shifting
. Therefore, three m-sequences are related to each other as
, where
for
is the phase difference factor between
and
’s for
that are cyclic-shifted versions of
. Inspired by this observation, the cost function is rewritten by
where
is the partial SL-SSS for
and
whose possible number of candidate sequences is 112. Using the cyclic-shifted property of m-sequence, two different auto-correlations with local template
for the remaining hypothesized values
and
can be implemented by simply compensating only the polarity of the pre-computed autocorrelation for
. This compensation is performed on a per-subcarrier basis according to the phase difference factor
(
). To complete (
20), therefore, only one auto-correlation needs to be calculated for each trial value of
b, which helps reduce the computational burden by minimizing the number of required multiplication operations. Substituting (
3) into (
20), we have
where
is a complex Gaussian random variable (RV),
and
Note that
and
are treated as zero-mean complex Gaussian RVs with variances
and
, respectively. Assuming
(hypothesis
), substituting (
3) into (
20) yields
where we assume
.
3.3. Performance Analysis
3.3.1. SL-SSS Detection
In this subsection, the detection probability of (
19) is derived in a closed form. For ease of derivation, we suppose that the flat-fading channel is slowly time-variant, i.e.,
. Let
denote the expected value of the enclosed quantity. The detection probability
is the probability that
(or equivalently
s) are correctly decided. First, we consider the hypothesis
that
in (
24). Conditioned on
, we find that
with
and
, where
,
,
, and
. In this assumption, the PDF of
in (
24) is Rician distributed and is given by
where
denotes the modified Bessel function of the first kind and zeroth order. In the case when
(null hypothesis
),
. For
, it can be seen that
. As a consequence,
is Rayleigh-distributed as
.
Thus, making use of
and
, the probability that
are correctly detected and conditioned on
becomes
With the aid of binomial expansion,
is found to be
where
is the ratio of mean to standard deviation of a complex random variable
. In (
27),
is defined as
where
is the instantaneous signal-to-noise ratio (SNR) and
is the instantaneous signal-to-ICI ratio (SIR). In order to find a closed-form formula, (
27) is averaged over
, namely
where
is the PDF of
. If the SNR is relatively high, the second squaring term of the denominator of (
28) is negligible. Ignoring this term,
is approximated as
Substituting (
30) into (
29), and after some mathematical simplifications, one obtains the following unconditional probability
where
is the average SNR and
is the average SIR.
3.3.2. RCFO Estimation
We consider the scenario in which the estimates
are available to the receiver without any error. With this assumption, it is easy to see that instead of (
21), we now have
where
and
. Assuming a significantly large SNR and applying power boosting to the SLSS, we can confidently assert that
. Consequently, for high SNR, it follows that
where
,
,
represents the imaginary part and
refers to the arctangent function applied to a real number
x. It is important to mention that
and
hold the same statistical equivalence as
and
, respectively. Since the estimated error
is significantly small and
approximates
with increasing SNR, we can easily conclude that
It is clear from (
34) that the MSE of the RCFO estimation scheme is represented by
and we have
. Upon observing (
22) and (
23), it becomes apparent that the variances of
and
are computed as
,
, respectively. Hence, it is evident that
and
By combining (
35)–(
37), we eventually arrive at