Uplink Sensing in Perceptive Mobile Networks with Asynchronous Transceivers

The emerging joint communication and radar sensing (JCAS) techniques, aka, dual-functional radar-communications (DFRC), integrate communication and radar sensing functions into one system by sharing a single transmitted signal and many hardware and signal processing modules [1, 2, 3, 4, 5, 6]. The integration not only achieves immediate benefits of reduced size, power consumption, cost, and improved spectrum efficiency but also helps to establish a communication link using sensing information or vise versa [7]. The perceptive mobile network (PMN) [8, 9, 10, 11] is a recently proposed next-generation mobile network based on the JCAS techniques. The concept of PMN was first introduced in [8] and then elaborated in [9]. Evolving from the current communication-only mobile network, PMN is expected to serve as a ubiquitous radar-sensing network, whilst providing uncompromising mobile communication services.

Although PMN and its systematic framework were introduced in [8], JCAS technologies have been actively studied in the past decade, particularly the technologies closely related to modern mobile networks. In [12], the orthogonal-frequency-division-multiplexing (OFDM) signal was used for sensing and communication simultaneously. Also using the OFDM signals, the authors in [13] developed a smoothing approach that jointly estimates the delay and Doppler frequency of targets moving at high speed. In the scenario of multiuser systems, the authors in [14] proposed an interleaved OFDM signal model to mitigate the multiuser interference (MUI). The authors in [15] analyzed the MUI tolerance of a multiple-input multiple-out (MIMO) JCAS system in terms of the resulting radar signal-to-interference-plus-noise ratio (SINR), using the signal model in [14]. In [16], the authors used separated antenna arrays to realize dual-function JCAS systems. A multi-objective function was further applied to trade off the similarity of the generated waveform to the desired one in [17]. It is noted that all these papers use a co-located DFRC transceiver, similar to a mono-static radar, and face an essential requirement of the full-duplex capability of the transceiver [18]. Alternative solutions other than full-duplex transceiver exist but require changes to existing network infrastructure, e.g., the authors in [19] used a synchronized single-antenna sensing receiver that is sufficiently separated from the transmitter.

Since the full-duplex technology is not quite mature, there exists an optional transceiver setup for realizing JCAS in PMNs, similar to a bi-static radar [20], where the sensing receiver is physically separated from the transmitter. This setup is consistent with the uplink sensing as defined in [9]. Such a setup can be implemented with minimal network changes only and is a favorite option in the near term. Some works have been done for realizing JCAS for the uplink channels [21, 22]. In [21], the authors investigated the uplink sensing in a 5G cellular network using massive MIMO and coexisting with a radar in the same frequency band. The authors adopted broadband OFDM modulation and obtained the uplink channel via minimum-mean-squared-error (MMSE) or zero-forcing (ZF) based processing schemes. In [22], the authors proposed a receiver architecture for DFRC systems and obtained its corresponding uplink communication channel capacity and radar channel capacity, respectively. The main challenges for realizing this setup in PMNs are (1) the unavailability of clock-level synchronization between the sensing receiver and the transmitter; (2) the relatively low angle-of-arrival (AoA) estimation accuracy due to the rich multi-path environment in mobile networks [9]. Perfect synchronization was assumed in most recent papers about JCAS, whereas the asynchrony between the sensing receiver and the transmitter is not addressed yet. Some papers on cognitive radio have dealt with the asynchronous issues [23, 24] but they are unrelated to JCAS. These works analyzed the interferences caused by asynchrony but did not provide an effective way for parameter estimation. Without clock-level synchronization between the sensing receiver and the transmitter, both timing offsets (TOs) and carrier frequency offsets (CFOs) can occur [25, 26], leading to sensing ambiguity and degraded accuracy in estimating delay and Doppler frequency of targets.

To handle the asynchronous transceivers, a limited number of works on passive WiFi sensing have been proposed based on a cross-antenna cross-correlation (CACC) method [25, 26, 27]. The underlying principle of CACC is that TOs can be removed by computing the cross-correlation between signals of multiple receiving antennas and exploiting the same TO across multiple antennas in one device. In [25], CACC is applied to resolve the AoA estimation problem for device-free human tracking with commodity WiFi devices. In [26], CACC is used to resolve the ranging estimation problem for passive human tracking using a single WiFi link. Unfortunately, there exists a derivative problem with the CACC method, i.e., the outputs from CACC contain mirrored unknown parameters. The mirrored parameters double the number of unknown parameters and also obscured the sign of Doppler frequencies, leading to a degraded sensing accuracy. The author in [25] proposed an add-minus suppression (AMS) method that suppresses the mirrored parameters and extracts the actual ones. However, the AMS method needs the power of static paths to be much stronger than that of the dynamic paths, otherwise the mirrored component is suppressed slightly in a rich multi-path environment.

To overcome the challenge of low AoA estimation accuracy in the physically-separated transceiver, techniques based on spatial smoothing and combining measurements in spatial and other domains have been proposed [28, 29, 30]. In [28], the authors proposed a high-resolution two-dimension (2D) MUSIC estimator via spatial smoothing, to obtain accurate AoA estimates with a small scale of antennas. In [29], the authors jointly combined spatial and temporal measurements to obtain high-resolution AoA estimation. In [30], the authors defined a spatial path filter that is used to separate signals from multiple propagation paths and obtained the AoAs via CACC outputs. All these methods are designed for narrowband systems and they do not have the capability of jointly estimating AoAs and other parameters such as delay and Doppler frequency.

In this paper, we propose a broadband uplink sensing scheme for PMNs with physically-separated asynchronous transceivers and OFDM modulation. There are two key novelties in our scheme. Firstly, since the mirrored components derived from the CACC outputs have not been addressed properly in prior works, we propose a mirrored-MUSIC algorithm that jointly processing the actual and mirrored parameters to overcome the mirrored parameter problem associated with CACC. Secondly, noting that the estimates of AoAs are not included in the proposed mirrored-MUSIC algorithm, we propose a high-resolution AoA estimation algorithm that can obtain high-resolution estimates of AoAs by combining spatial and other domain measurements. Our proposed scheme is applicable for practical scenarios requiring a single static user equipment (UE) and a line-of-sight (LOS) path between the static transmitter and the base station (BS). Our major contributions are summarized as follows.

• •

  We provide a practical radar sensing scheme that can be implemented in mobile networks without the requirement of clock-level synchronization between the transmitter and receiver. By using a CACC method to mitigate the TOs and CFOs resulted from asynchrony, our scheme relaxes stringent clock-level synchronization between physically-separated transceivers. The mean-squared-error (MSE) between the CACC output and our desired signal also keeps at a minimum level.

• •

  We propose a mirrored-MUSIC algorithm to handle the mirrored outputs of the CACC method and a general problem where the test basis vectors show mirror symmetry. The algorithm, which halves the unknown variables without introducing any approximation, has lower complexity and better performances compared to conventional MUSIC. This algorithm can also be applied to many other applications, such as traditional harmonic retrieval problems with the sinusoidal modulated signals [31, 32], ESPRIT [29], and the matrix pencil method [33].

• •

  We develop a high-resolution MUSIC-based AoA estimation algorithm that combines measurements from spatial, temporal, and frequency domains. This algorithm equivalently increases the samples in the spatial domain and hence significantly improves the resolution of AoAs, compared with estimating the AoAs in the spatial domain only. In particular, a new issue of “ambiguity of basis vectors” occurs when integrating multiple parameters into one domain measurement. Our algorithm resolves this critical issue in combining multi-domain measurements by selecting multiple peaks from the MUSIC outputs.

The rest of this paper is organized as follows. Section II introduces system and channel models. Section III presents the CACC method. Section IV introduces the proposed mirrored-MUSIC algorithm for estimating the actual delays and Doppler frequencies. Section V presents the high-resolution AoA estimation scheme. Extensive simulation results are presented in Section VI. Finally, conclusions are drawn in Section VII.

Notations: $\rm\bf a$ denotes a vector, $\rm\bf A$ denotes a matrix, italic English letters like $N$ and lower-case Greek letters $\alpha$ are a scalar, $\angle a$ is the phase angle of complex value $a$. $|{\rm\bf A}|,{\rm\bf A}^{T},{\rm\bf A}^{H},{\rm\bf A}^{\dagger}$ represent determinant value, transpose, conjugate transpose, pseudo inverse, respectively. We denote Frobenius norm of a matrix as $\|{\rm\bf A}\|_{F}$. We use ${\rm diag}(\alpha_{1},\cdots,\alpha_{k})$ to denote a diagonal matrix. $[{\rm\bf A}]_{N}$ is the $N$th column of a matrix and $[{\rm\bf A}]^{N}$ is the $N$th row of a matrix.

We consider the uplink communication and sensing in a PMN, as shown in Fig. 1. Multiple UEs communicate with a BS. The BS is physically static and uses received uplink signals for both communication and sensing. Each UE has one antenna and the BS has a limited number of $N$ antennas. Our proposed scheme in this paper requires the following setups:

• •

  The signals used for sensing are from a specific UE of which location is fixed and known to the BS.

• •

  There is a LOS propagation path between the BS and the UE used for sensing. The power of the LOS path is much larger than that of non-LOS (NLOS) paths.

This setup is practically feasible for PMNs. The fixed UE can be a node that provides fixed broadband access in the mobile network. We can adopt the millimeter-wave frequency band to guarantee the dominating power of the LOS path. In PMN, several types of signals may be used for sensing. Referring to the fifth-generation (5G) mobile network, they can be demodulation reference signals (DMRSs) that are specifically provided for channel estimation, synchronization signal blocks (SSBs), and even demodulated data symbols [34, 35, 36, 37]. Without loss of generality, we consider sensing via the uplink signal from a specific UE, denoted as UE 1.

At all UEs, we adopt a simplified packet structure, as shown in Fig. 2. In each packet, training symbols, denoted as preambles, are followed by a sequence of data symbols. OFDM modulation is applied across the whole packet. These data symbols can be empty if the packet is a DMRS. We only use the OFDM preambles for sensing. The preambles can also be used for synchronization and channel estimation for communications, which needs different processing at the BS. In this paper, we would like to use the preambles for sensing multiple targets in the PMN. The parameters of targets including the propagation delay, Doppler frequency, and AoA need to be obtained. Our proposed scheme can also be applied to other systems with similar signal structure, such as WiFi systems.

Without losing generality, we assume each packet has only one preamble. For both preamble symbol and data symbol, each of them has $G$ subcarriers with a subcarrier interval of $1/T$, where $T$ denotes the length of an OFDM symbol. Each of the OFDM symbols is prepended by a cyclic prefix (CP) of period $T_{\rm C}$. Our scheme works if and only if a segment of subcarriers with an interleaved interval is available for UE 1. When multiple UEs communicate with the BS, each UE occupies a unique segment of subcarriers with the interleaved interval as in [15]. For notational simplicity, we assume that UE 1 occupies the whole preamble symbol here. Mathematically, the $m$th preamble symbol can be expressed as [13, 14]

where $x[m,g]$ is a modulated symbol transmitted on the $g$th subcarrier of the $m$th preamble symbol and ${\rm rect}\left(\frac{t}{T+T_{\rm C}}\right)$ denotes a rectangular window of length $T+T_{\rm C}$.

The BS receives the preambles using a uniform linear array (ULA) of $N$ antennas. The uplink channel between receiver at BS and the transmitter at UE 1 has $L$ NLOS paths reflected or refracted from $L$ targets, together with a dominating LOS path, where the index of the LOS path is denoted as $l=0$. Let $\alpha_{l}$, $f_{{\rm D},l}$, $\tau_{l}$ and $\theta_{l}$ denote the channel gain, the Doppler frequency, the propagation delay, and the AoA of the $l$th path, respectively. Due to the fixed locations of BS and UE 1, we assume that the parameters, $\tau_{0}$ and $\theta_{0}$, which correspond to the LOS path, are known at the BS, and $f_{{\rm D},0}$ is $0$. We also assume that $|\alpha_{0}|\gg|\alpha_{l}|,\forall l\in\{1,\cdots,L\}$. Note that the Doppler frequency of the $l$th path comes from the $l$th target of the channel, which can be either positive or negative depending on the moving directions.

We assume that $M$ packets are sent at the same interval, denoted as $T_{\rm A}$, at the UE baseband. Since there is typically no synchronization at clock level between BS and UE 1, the received signal has an unknown time-varying TO, denoted as $\delta_{\tau}(m)$, associated with the clock asynchrony, even if the packet level synchronization is achieved. Hence, the total time delay during signal propagation for the $l$th target as seen by BS equals $\tau_{l}+\delta_{\tau}(m)$. In [26], it is shown that there also exists an unknown time-varying CFO due to the asynchronous carrier frequency, denoted as $\delta_{f}(m)$. The received time-domain signal corresponding to the preamble symbol in the $m$th packet can be represented as [26]

where the vector, ${\bf a}(\Omega_{l})=\exp[j\Omega_{l}(0,1,\cdots,N-1)]^{T}$, is the array response vector of size $N\times 1$, with $\Omega_{l}$ being $\frac{2\pi d}{\lambda}\cos\theta_{l}$, $d$ denoting the antenna interval, $\lambda$ denoting the wavelength, and $\theta_{l}$ being the AoA from the $l$th target, and ${\bf z}(t|m)$ is a complex additive-white-Gaussian-noise (AWGN) vector with zero mean and variance of $\sigma^{2}$. TO is typically time-varying and has a random value that changes during any two discontinuous transmissions. The CFO may slowly vary over time. It is noted that TO and CFO are mixed with the actual propagation delay and the actual Doppler frequency, respectively. Hence they can directly cause ambiguity of ranging and velocity measurements. They also make the total delay and total Doppler frequency vary with time and prevent from aggregating signals for joint processing. It should be noted that, for the communication purpose, there is no need to distinguish the actual parameters with these offsets, since they can be estimated as a whole value and then be removed. As for the radar sensing purpose, these offsets have to be mitigated since the range and the velocity of targets only depend on actual parameters. Note that we use the approximation $e^{j2\pi m(T_{\rm A}+\delta_{\tau}(m)+\tau_{l})(f_{{\rm D},l}+\delta_{f}(m))}\approx e^{j2\pi mT_{\rm A}(f_{{\rm D},l}+\delta_{f}(m))}$, since the timing values of $(\delta_{\tau}(m)+\tau_{l})$ are much smaller than $T_{\rm A}$ and $(f_{{\rm D},l}+\delta_{f}(m))$ is also small in relation to the sampling rate.

After removing CP from the received time-domain signal, we then transform the signal into frequency domain via $G$-point fast-Fourier-transform (FFT)’s. Referring to (II), the received frequency-domain signal is

where $y_{n}[m,g]$ is the received frequency-domain signal on the $g$th subcarrier at the $n$th receiving antenna of the $m$th OFDM preamble symbol, and $z_{n}[m,g]$ is a complex AWGN with zero mean and variance of $\sigma^{2}$. The actual value of $|x[m,g]|^{2}$ has insignificant impact on our proposed scheme. For simplicity, we assume $|x[m,g]|^{2}=1$.

As we mentioned in Section II, the actual delays and the actual Doppler frequencies are mixed with TOs and CFOs, respectively. In this section, we adopt and extend the CACC method to generate signals with TOs and CFOs being removed, in order to obtain the delay and the Doppler frequency of targets.

We decompose the received signals into three parts, i.e.,

where $D_{n}[m,g]$ denotes the received signal from the LOS path, given by

and $I_{n}[m,g]$ is the received signals reflected or refracted from the targets, given by

The CACC operation makes it possible to mitigate both TO and CFO. This operation computes the cross-correlation between different antennas and is generally used in estimating the AoA with hybrid subarrays [30]. We select one antenna that has the largest received average power as reference antenna. Without losing generality, we assume that the reference antenna is the $0$th antenna. Neglecting the noise term, the CACC operation between the $n$th antenna and the $0$th antenna generates

where $y_{0}[m,g]$ is the received signal at the reference antenna, $\rho_{n}^{(1)}[m,g]=D_{n}[m,g]D_{0}^{H}[m,g]$, $\rho_{n}^{(2)}[m,g]=I_{n}[m,g]I_{0}^{H}[m,g]$, $\rho_{n}^{(3)}[m,g]=D_{n}[m,g]I_{0}^{H}[m,g]$, and $\rho_{n}^{(4)}[m,g]=I_{n}[m,g]D_{0}^{H}[m,g]$. For those CACC outputs, we have the following proposition.

According to Proposition 1, by using a 2D high-pass filter with respect to $m$ and $g$, we can remove the invariant component from the CACC outputs and obtain $\hat{\xi}_{n}[m,g]\approx\rho_{n}^{(3)}[m,g]+\rho_{n}^{(4)}[m,g]$. The cut-off frequency of the 2D high-pass filter depends on the bandwidth of $\hat{\xi}_{n}[m,g]$. From Appendix A, the cut-off frequency of $\hat{\xi}_{n}[m,g]$ is $(\omega_{f},\omega_{\tau})=\left(\min\left|\pi T_{\rm A}f_{{\rm D},l}\right|,\min(\pi(\tau_{l}-\tau_{0})/T)\right)$.

From the expression of $\rho_{n}^{(3)}[m,g]+\rho_{n}^{(4)}[m,g]$, we note that $\hat{\xi}_{n}[m,g]$ contains the actual sensing parameters without TOs and CFOs. The output from the high-pass filter can be represented as

where $\bar{\rho}_{n}$ is the low-pass component in $\rho_{n}[m,g]$. Note that the delays in (III) become relative values, i.e., $\tau_{l}-\tau_{0}$, $(0<\tau_{0}<\tau_{l})$. Since $\tau_{0}$ is assumed to be known at the BS, the problem of estimating $\tau_{l}$ becomes how to estimate the relative delays. The error between $\hat{\xi}_{n}[m,g]$ and $\xi_{n}[m,g]$ is resulted from $\rho_{n}^{(2)}[m,g]$ and hence not affected by the noise. We define this error as the input error, i.e. $e^{2}=\mathbb{E}\|\hat{\xi}_{n}[m,g]-\xi_{n}[m,g]\|^{2}$.

In $\xi_{n}[m,g]$, $\rho_{n}^{(3)}[m,g]$ can be seen as the side product, which is mixed with the actual component of interest, $\rho_{n}^{(4)}[m,g]$, since $\rho_{n}^{(4)}[m,g]$ already contains all sensing parameters. It would be redundant to estimate $\rho_{n}^{(3)}[m,g]$ and the estimation would require a doubled number of samples if conventional methods are used to estimate the actual component and the side product together. One idea is to separate $\rho_{n}^{(3)}[m,g]$ from $\rho_{n}^{(4)}[m,g]$, which is a challenging task. The AMS method was proposed in [26] and [25] to remove the side product. However, this method does not always work, particularly when the number of signal propagation paths is large in a rich multi-path propagation environment. In Appendix B, we briefly describe the AMS method and compare its input error with $\xi_{n}[m,g]$ that is adopted in our scheme. We show that our adopted $\xi_{n}[m,g]$ has a smaller input error than that of the AMS method.

In this section, we propose a mirrored-MUSIC algorithm that is tailored to directly estimating conjugated variables from signals similar to the one in (III).

MUSIC-based algorithms have been widely used for estimating different parameters of channels, including delay, Doppler frequency, and AoA [20, 26, 29]. With a given signal matrix, conventional MUSIC finds the formulation of basis vectors of the signal matrix. Utilizing the fact that the basis vectors fall into the null-space of the signal matrix, the parameter can be obtained by checking if the candidate basis vector with a testing parameter falls into the null-space of the signal matrix. Conventional MUSIC would construct $\xi_{n}[m,g]$ into a matrix. The matrix corresponding to $\xi_{n}[m,g]$ has a doubled number of parameters to be estimated. We will exploit this redundancy, and the estimation of both delay and Doppler frequency will be transformed into an equivalent problem with halved unknown variables. This can achieve significantly improved performance compared to the conventional MUSIC algorithms.