Joint Mobile User Positioning and Passive Target Sensing using Optimized Sequential Beamforming Aymen Hamrouni∗ , Sofie Pollin∗† , Hazem Sallouha∗
∗ WaveCoRE, Department of Electrical Engineering (ESAT), KU Leuven, Leuven, Belgium † Interuniversity Microelectronics Centre (IMEC), Leuven, Belgium
arXiv:2605.15808v1 [eess.SP] 15 May 2026
Email: {aymen.hamrouni, sofie.pollin, hazem.sallouha}@kuleuven.be
Abstract—Integrated sensing and communication (ISAC) relies on monostatic sensing (MS) and bistatic positioning (BP) to enable comprehensive environmental awareness and user localization. However, existing frameworks predominantly assume static geometries and optimize these modalities independently, neglecting user mobility and sequential information sharing. In this paper, we propose a velocity-aware sequential beamforming framework that dynamically couples MS and BP in time. We derive the Cramér-Rao bounds (CRBs) in the position domain to formulate a non-convex resource allocation problem. Instead of relying on static weighted-sum tradeoffs, we introduce a sequential Bayesian optimization strategy where MS is executed first to construct a reliable structural prior on the UE and passive targets (PTs). This covariance prior is subsequently passed to the UE to regularize the BP estimation stage. We demonstrate that optimizing a single shared beamformer globally across both phases yields superior synergistic gains compared to a two-stage greedy approach. Simulation results validate that the shared sequential design efficiently balances limited symbol resources, achieving centimeter-level positioning accuracy for both the UE and PTs, robust velocity estimation, and a significantly reduced computational runtime. Index Terms—Bistatic positioning, monostatic sensing, user mobility, joint beamforming design.
I. I NTRODUCTION Integrated sensing and communication (ISAC) has emerged as a fundamental design paradigm for future wireless networks, unifying communication, localization, and environmental awareness within a single infrastructure [1]. By exploiting shared spectrum and hardware, ISAC enables multiantenna systems to simultaneously support data transmission and sensing functionalities [2]. Within this framework, sensing functionalities can be broadly categorized into Monostatic Sensing (MS) and Bistatic Positioning (BP), two complementary yet intrinsically coupled modalities that are both essential for comprehensive situational awareness [3], [4]. MS utilizes the Base Station’s (BS) co-located transmit and receive arrays to analyze round-trip echoes for environmental mapping and detection of Passive Targets (PTs) [3]. In contrast, BP leverages the spatially separated link between the BS and the User Equipment (UE), where the latter processes downlink signals to estimate its own position and velocity relative to the infrastructure [4]. When MS and BP operations share a common multi-antenna transmitter infrastructure, they fundamentally serve distinct operational requirements that compete for the same resources. From the UE perspective, high-precision positioning and ve-
BS
PT 2
UE PT1
MS BP
Fig. 1. Illustration of MS and BP in an urban canyon scenario. The BS simultaneously performs i) MS (orange dotted lines) to detect UE and PTs (e.g., stationary cars) and ii) BP (blue dashed lines) to enable localization and velocity estimation for the mobile UE.
locity estimation favor bistatic measurements that leverage the geometric diversity between spatially separated transmit and receive platforms to enhance the observability of the UE’s spatial-temporal state. Conversely, from the environment sensing perspective, PT detection and tracking favor monostatic radar operations, where the co-located transmitter and receiver enable coherent round-trip measurements. Consider an autonomous vehicle navigating a dense urban canyon. In such GPS-denied environments, bistatic measurements provide a crucial absolute, drift-free position and velocity reference [5]. These RF-based updates are essential to bound the cumulative drift inherent to onboard inertial measurement units (IMUs) within sensor fusion algorithms [6]. By anchoring the relative sensors, the vehicle maintains the stringent Position Error Bounds (PEB) and Velocity Error Bounds (VEB) required for safe, autonomous trajectory planning. Simultaneously, the serving Base Station utilizes MS to scan the surrounding environment to detect PTs including static objects and dynamic obstacles like pedestrians or legacy vehicles. Fundamental spatial and time-frequency tradeoffs have been thoroughly analyzed for conventional monostatic configurations [7]. However, to overcome the limited coverage, severe path-loss scaling, and self-interference geometric con-
straints, the research community has increasingly shifted toward bistatic and multi-static deployments. For instance, Bauhofer et al. [8] proposed fusion techniques for processing information from multiple spatially separated sensing nodes to enable robust multi-target localization. Similarly, cooperative ISAC frameworks utilizing multiple base stations have demonstrated significant enhancements in PT localization [9]. Advanced multi-static architectures have been developed to improve target localization accuracy under both Line-of-Sight (LoS) and Non-Line-of-Sight (NLoS) conditions [10]. Despite these advancements in spatial observability, only recently have attempts been made to characterize these joint tradeoffs when MS and BP are jointly executed from a shared infrastructure. In these recent attempts, Cramér-Rao bound (CRB) plays a central role. The CRB enables a principled quantification of sensing and positioning accuracy in terms of transmit covariance, capturing the spatial power allocation and beamforming strategy, and array geometry, which determines the system’s spatial resolution and parameter identifiability. Among the few works addressing this, Ge et al. [11] explored fusion at the filtering stage, proposing an extended Kalman-Poisson multi-Bernoulli sequential filter to integrate maps from both monostatic and bistatic sensing modalities in 5G mmWave scenarios. Zhang et al. [12] recently investigated the performance tradeoff between BP and MS within a MIMO-OFDM system, proposing a multi-objective optimization framework based on a weighted-sum CRB to design optimal spatial beamformers. Nevertheless, existing work predominantly assumes static scenarios, neglecting the inherent mobility of practical wireless systems. In reality, UE exhibits non-negligible velocities over the sensing interval. Ignoring this mobility not only compromises model realism but also discards the valuable information embedded in Doppler shifts, which can significantly enhance both positioning and sensing performance. Furthermore, such joint operations create a fundamental resource allocation dilemma: MS demands radar-centric beamforming patterns that maximize the illumination of uncooperative environmental scatterers, whereas BP requires beamforming strategies that guarantee robust signal reception at the mobile vehicle. MS and BP directly compete for finite symbol resources within a fixed coherence interval. To the best of our knowledge, the joint BP and MS with mobile user scenarios, along with the corresponding beamforming design problem, are open research questions. In this paper, we propose a joint MS and BP sensing framework that explicitly models UE mobility and exploits the information coupling between both sensing modalities. Unlike existing static approaches, we develop a velocityaware, sequential beamforming design that dynamically balances positioning and environmental sensing over time. Our main contributions are summarized as follows: •
We derive the CRB for joint MS and BP in a practical mmWave MIMO-OFDM system under UE mobility. By extracting delay, angle, and Doppler parameters in the channel domain, we map them to 2D position and 2D velocity to formulate a non-convex beamforming opti-
TABLE I CPI FOR UE C ONSTANT-V ELOCITY A SSUMPTION BY S CENARIO Scenario Pedestrian Vehicle (urban) High-speed vehicle UAV (mmWave)
fc (GHz) 28 28 28 60
vU (m/s) 5 30 50 50
TCPI ≲ 1.0 ms ≲ 180 µs ≲ 100 µs ≲ 50 µs
mization under a fixed energy budget. We establish a sequential strategy that executes MS first to construct a reliable prior on both the UE state and environmental PTs. This prior is then parameterized via its covariance and passed to the BP stage. This ordering is critical since standalone BP is poorly conditioned for PT estimation due to limited geometric diversity and nuisance parameters (e.g., clock bias). However, injecting the MS-derived covariance regularizes the problem, enabling the UE to jointly sense the PTs and refine its own position. • We introduce an adaptive temporal allocation policy that optimizes the distribution of finite symbol resources between the two stages, balancing direct measurement quality with the gains of covariance-level information sharing. Our simulation results reveal that, within a given coherent block, optimizing separate greedy beamformers for the MS and BP fails to maximize the joint posterior information. Instead, a single shared beamformer, optimized globally across both stages achieves superior UE PEB, PTs PEB, and UE VEB. This performance gain stems from coherent coupling as shared illumination pattern simultaneously strengthens both the MS prior and the BP likelihood, whereas separate beamformers dilute energy through stage-wise reconfiguration. Furthermore, this proposed shared formulation requires significantly less computational runtime than the two-stage greedy approach by avoiding beam-switching, reducing the effective search space. •
II. S YSTEM M ODEL AND P ROBLEM F ORMULATION A. System Setup We consider a MIMO–OFDM setup with M subcarriers, where a BS equipped with NB co-located transmit-receive antennas sends pilot signals over L slots at center frequency fc to a UE with NU antennas. The UE exploits these received pilots to determine its position and velocity in BP. In MS, the BS collects the echoes from PTs to infer their positions and from the UE to infer its position and velocity. In this configuration, each PT contributing to MS corresponds to a single multipath component in BP. We assume the UE has a position pU ∈ R2 and moving with a constant velocity vector vU ∈ R2 , , where vU = ∥vU ∥ denotes its speed magnitude, during a coherent processing interval (CPI). The K PTs reflectors are assumed to be static during CPI (e.g., roadside infrastructure, building facades, or parked vehicles) with unknown positions. Considering the BS’s positioning signals across L slots, we assume that each slot has a duration of Tslot and contains P OFDM pilot symbols
each of duration Tsym . The transmission start time of the (l, p)th pilot symbol is tl,p = (l − 1)Tslot + (p − 1)Tsym , where l = 1, . . . , L, p = 1, . . . , P . The constant-velocity assumption holds provided that TCPI = tL,P ≤ Tc , where the coherence time, Tc , is approximated from the maximum Doppler spread as [13]: λ Tc ≈ , (1) 2vrel with wavelength λ = c/fc and relative velocity vrel = vU since the BS and PTs are assumed static. Under this condition, the small-scale fading coefficients remain approximately constant over the CPI. Table I provides quantitative CPI limits for practical scenarios based on realistic carrier frequencies and UE velocities [14]. The transmit signal on the m-th subcarrier of the p-th symbol in the l-th slot is xl,p,m = fl sp,m , (2) where fl ∈ CNB is the beamformer used in slot l, and sp,m is a unit-modulus pilot on subcarrier m of symbol p. For clarity, we adopt the following notation convention: variables denoted as X́ correspond to MS-related quantities, while variables denoted as X̋ correspond to BP-related quantities. B. Receive Signal for MS and BP The signal collected for MS at the co-located BS receiver is denoted as [12]: ýl,p,m = H́l,p,m xl,p,m + źl,p,m , (3) 2 with źl,p,m ∼ CN (0, σ INB ) is the AWGN at the BS and H́l,p,m ∈ CNB ×NB is the round-trip BS-PTs/UE channel at subcarrier m, symbol p, and slot l, expressed as: H́l,p,m = β́0 e−j2πm∆f τ́0 ej2πν́0 tl,p aB (θ0 )aH B (θ0 ) +
K X
β́k e−j2πm∆f τ́k aB (θk )aH B (θk ),
(4)
k=1
Here, K denotes the number of PTs and for path k, β́k , τ́k , and θk are the complex gain, delay, and angle-of-departure (AOD), respectively. The UE is treated as a PT in MS and indexed by k = 0 and Doppler ν́0 exists only for LoS UE path. The noise power is σ 2 = F N0 ∆f , where F is the noise figure, N0 is the single-sided noise PSD, and ∆f is the subcarrier spacing. The vector aB (·) ∈ CNB denotes the steering vectors at the BS. The received signal at the UE for BP is expressed as [12]: y̋l,p,m = WH H̋l,p,m xl,p,m + z̋l,p,m , (5) where z̋l,p,m ∼ CN (0, σ 2 INU ) denotes AWGN at the UE and W ∈ CNU ×NURF is the analog combining matrix at the UE, with NURF denoting the number of RF chains. The matrix H̋l,p,m ∈ CNU ×NB is the BS–UE channel at subcarrier m, symbol p, and slot l, modeled as: K X H̋l,p,m = β̋k e−j2πm∆f τ̋k ej2πν̋k tl,p aU (ψk )aH B (θk ), (6) k=0
where ψk denotes the angle-of-arrival (AOA) at the UE from path k and Doppler term ej2πν̋k tl,p accounts for the phase evolution due to relative motion from all paths k. Here, the
LoS component is indexed by k = 0 and the vector aU (·) ∈ CNU denotes the steering vectors at the UE. C. CRB-Based Performance Metrics The localization process in both MS and BP is modeled as a two-stage process where, in the first stage, channel-domain parameters are estimated, and in a second stage, these channeldomain parameters are mapped to position-domain parameters. For MS, we define the channel-domain parameter vector as: T T ξ́ = θ T , τ́ T , ν́ T , β́R , β́IT ∈ R4K+5 , (7) where θ = [θ0 , . . . , θK ]T , τ́ = [τ́0 , . . . , τ́K ]T , ν́ = [ν́0 , 0, . . . , 0]T , β́R = [ℜ{β́0 }, . . . , ℜ{β́K }]T , β́I = [ℑ{β́0 }, . . . , ℑ{β́K }]T . The MS position-domain parameters are written as: T T T T T T ή = pT ∈ R4K+6 . (8) U , vU , p1 , . . . , pK , β́R , β́I The (i, j)-th element of the MS channel-domain Fisher Information Matrix (FIM), IChan (ξ́), is given by [15]: ) ( L P M ∂ µ́H 2 XX X l,p,m ∂ µ́l,p,m , (9) ℜ [IChan (ξ́)]i,j = 2 σ ∂[ξ́]i ∂[ξ́]j p=1 m=1 l=1
where µ́l,p,m = H́l,p,m xl,p,m is the noise-free observation in Eq. (3). The MS position-domain FIM can then be obtained as IPos (ή) = J́T IChan (ξ́)J́, with J́ denoting the Jacobian matrix relating the position-domain parameters ή and channel-domain parameters ξ́. Hence, the lower bound on the estimation error variance for UE position and velocity and PTs positions is written as follows: CRBMS (pU , vU , pk ) = tr [IPos (ή)−1 ]1:2K+4, 1:2K+4 , (10) with tr(.) denoting the trace operation. For BP, we define the vector of channel-domain parameters as: T T ξ̋ = θ T , ψ T , τ̋ T , ν̋ T , β̋R , β̋IT ∈ R6K+6 , (11) T T where ψ = [ψ0 , . . . , ψK ] and ν̋ = [ν̋0 , . . . , ν̋K ] . The position-domain parameters for BP are collected as: T T T T T T η̋ = pT ∈ R4K+8 , U , vU , p1 , . . . , pK , ∆φ, ∆t, β̋R , β̋I (12) The parameter ∆φ denotes the BS orientation in the UE’s local frame, and ∆t is the clock bias capturing BS–UE asynchronism. Analogously to MS, the BP position-domain FIM is written as: IPos (η̋) = J̋T IChan (ξ̋)J̋, (13) with [J̋]i,j = ∂[ξ̋]i /∂[η̋]j . The CRB for UE parameters of interests (i.e., position and velocity) estimation in BP is written as: CRBBP (pU , vU ) = tr [IPos (η̋)−1 ]1:4,1:4 . (14) D. MS-BP Trade-off Problem Formulation To initially characterize the MS-BP tradeoff, we adopt a classical weighted-sum method for MOO problems, as in [12], which yields a weak Pareto frontier between MS and BP. The formulation can be written as: (P1) min (1 − α) CRBMS (pU , vU , pk ) + α CRBBP (pU , vU ) F
s.t.
tr(FFH ) ≤
PB , M
(15)
where F = [f1 , . . . , fL ] ∈ CNB ×L is the beamformer matrix that F collects the L beamformers and PB is the BS transmit power budget. The constraint is normalized so that the total power across all M subcarriers equals PB . α ∈ [0, 1] controls the objective trade-off between MS and BP. The problem (P1) is non- convex but can be relaxed to a convex SemiDefinite Programming (SDP) and can be solved efficiently using standard solvers such as CVX [12]. III. BAYESIAN - BASED S EQUENTIAL MS-BP D ESIGN The previous formulation (P1) considers the beamforming design of MS and BP independently through a weighted-sum objective, ignoring time resources and information sharing between the two operations. We extend the state-of-the-art MS-BP joint optimization framework to a sequential setting in which the spatial beamformers for BP and MS are jointly optimized, along with the pilot allocation ratio between MS and BP. In this setting, MS is executed first so the BS obtains prior information about the UE and PTs. Then, BP is optimized to refine the UE state and infer the PTs positions given this prior. Both the BS and UE share a common symbol resource. Let that be the total number of pilot symbols κTotal in the coherence time Tc . κTotal is partitioned into three distinct phases and is written as: κTotal = κMS + κMS-BP + κBP , (16) where κMS and κBP are the total active sensing/positioning symbols, and κMS-BP represents the number of symbols needed for the BS to transmit the computed MS covariance matrix to the UE for BP via a communication control channel. We define the active MS allocation ratio ρMS as the fraction of the remaining allocable symbols dedicated to the monostatic sensing, which is given by: κMS , 0 ≤ ρMS ≤ 1. (17) ρMS ≜ κTotal − κMS-BP The parameter ρMS dictates the optimal switching point between MS and BP, directly controlling the performance of MS at the BS and the amount of prior information versus the remaining resources available for the BP posterior. While MS and BP observe the same physical parameters (i.e., UE and PTs states), their measurements are collected over the disjoint pilot slots κMS and κBP and are affected by distinct nuisance parameters (e.g., different hardware and clock biases). Let theshared position-domain parameter vector T T T be defined as1 ηp = pT U , vU , p1 , . . . , pK . By marginalizing out the stage-specific nuisances via the Schur complement [16], we parameterize the FIM over the same parameter vector ηp and obtain the equivalent position-domain FIMs for each stage, denoted as ÍPos and I̋Pos , for MS and BP, respectively. The posterior distribution via Bayes’ theorem is then expressed as: p(ηp |ý, y̋) ∝ p(y̋|ηp ) p(ηp |ý) . (18) | {z } MS-based Prior
1 Note that the channel gain parameters β́ , β́ , β̋ , β̋ , are excluded, R I R I as their contribution to the position estimation is negligible [12]. In the 2D position and 2D velocity estimation, the BP clock offset ∆t and orientation offset ∆φ are likewise marginalized.
Consequently, the posterior FIM for ηp is then additive, representing the sum of the equivalent information derived from the MS-based prior and the BP likelihood. The resulting BP posterior FIM obtained from MS prior during ρMS and from BP phase during 1 − ρMS is written as: I̋seq (FMS , FBP , ρMS ) = ÍPos (FMS , ρMS ) + I̋Pos (FBP , 1 − ρMS ). (19) Here, the covariance matrix obtained from the MS stage, Í−1 Pos , is passed as a prior to the UE during the κMS-BP symbols. In practical ISAC systems, ensuring reliable localization requires that estimation errors remain below predefined safety thresholds. Motivated by this, we aim to minimize the deviation error obtained in the MS and BP sequential phases from predefined thresholds. We define the set containing the threshold of UE position and velocity and PTs positions as S. For example, the threshold of the PEB for UE in the MS ∈ S. phase is denoted as γpMS U A least-squares (LS) optimization problem can then be formulated as: (P2) min L I̋seq (FMS , FBP , ρMS )−1 , S FMS , FBP , ρMS
PB tr(FMS FH MS ) ≤ M ,
s.t.
PB tr(FBP FH BP ) ≤ M ,
(20)
0 ≤ ρMS ≤ 1. where L(., .) is a weighted squared posterior cost taking into account the deviation of the extracted bounds in the sequential MS and posterior BP from their respective thresholds in S. Weighting in L(., .) could define the task priority (e.g., if emphasis is on obtaining better BP VEB and PEB, weights on the deviation of these terms with respect to their thresholds can be set higher). This problem tackles the tradeoff between allocating more BP symbols to improve BP estimation and allocating more MS symbols to build a more informative prior, which in turn improves BP. Solving (P2) jointly over all three variables would require a bilevel optimization: for each candidate FMS , the inner FBP problem must be solved conditioned on the resulting prior, which is computationally prohibitive. We therefore consider two tractable approaches. A greedy two-stage approximation to (P2) in which the MS beamformer F⋆MS is independently from (P1), with α = 0 as follows: F⋆MS = arg min LMS ÍPos (F, ρMS )−1 , S , (21) F
where LMS (., .) is the LS MS-only cost from (P1) with respect to S. The beamformer F⋆MS is then used during the symbol allocation ρ⋆MS to build environmental prior relative to the UE and PTs position thresholds. Then, F⋆BP is subsequently optimized to minimize the posterior cost given the fixed prior ÍPos (F⋆MS , ρMS ). In this approach, the optimal beamformers are explicitly tailored and optimized to their respective phases. We refer to it as the separate sequential beamformer approach. While this beamforming optimization approach provides spatial degrees of freedom and optimizes each beamformer for its respective phase, hardware or signaling constraints may dictate a single shared beamformer across the two phases. Moreover, and as it relies on a greedy two-stage procedure
2
4
mber of Targets
6
101 Performance Thresholds 100 UE PEB for MS γpMS U BP UE PEB0 for1 BP2 4 6 γpU 0 UE VEB for BP of Targets γvMS Number U PTs PEB for BP γpBPk PTs PEB for MS γpMS k
50 cm 1 102cm 4 6 10 m/sof Targets Number 20 cm 100 cm
where F∗MS is first optimized for the MS cost alone in (P1), and F∗BP is subsequently optimized for the posterior given with fixed prior from the MS, the MS beamformer might not be the optimal beamformer to produce the best prior for downstream BP. It prioritizes MS first and minimizes the MS estimation error during ρ∗MS rather than the quality of the prior it provides to the BP stage, since it is optimized under LMS (., .), not the end-to-end posterior cost L(., .). By contrast, a single shared beamformer F∗seq used across both phases (i.e., F∗MS = F∗BP = F∗seq ) could be optimized directly against the final posterior cost, allowing it to jointly balance the MS prior quality and BP measurement quality in a single coupled optimization. Therefore, we define the following optimization problem: (P3) min L I̋seq (Fseq , ρMS )−1 , S Fseq , ρMS
s.t.
PB tr(Fseq FH seq ) ≤ M ,
20
20
(a) MS (α = 0)
BS UE PTs
20
10
0
x [m]
10 50 20
15
0
20
20
50
Array angle [deg]
(b) BP (α = 1)
(22)
0 ≤ ρMS ≤ 1, where the optimal shared beamformer F∗seq is shared across both phases in Eq. (19). We refer to this approach as the shared sequential beamformer approach. IV. E XPERIMENTAL R ESULTS In this section, we evaluate the positioning and velocity estimation performance of the sequential MS-BP configuration. Unless stated otherwise, all results are obtained for the parameters mentioned in Table II. The channel-domain FIMs for BP and MS are computed using the Slepian-Bangs formula [15] and mapped to the position–velocity domain via the corresponding Jacobians. The FIM of the channel parameters follows the standard diagonal assumption with no coupling
1011
BP MS
104 103 102 101
BP MS (Snap) MS Ext
109 107 105 103 101
100 0
1
2
4
Number of Targets
(a) PEB vs. number of PTs
6
VEB Radial (cm/s)
10 dB 3.5 8 dB 10 m2 10 m2
σshadow σRCS,k103 σRCS,0
10
105
UE PEB (cm)
VEB Ratio (T/R)
VEB Tangential (cm/s)
BP BP 7 (Snap) MS (Snap) Noise andMS Environmental 10Model MS Noise Power Spectral Density N0 −173 dBm/HzMS F 5 10 n
0
x [m]
10
Fig. 2. Beamforming design for MS and BP. The UE and PTs are placed symmetrically at equal distances to isolate distance-dependent path-loss disparities, focusing on beamforming for MS and BP.
106
Noise 104 figure Path loss exponent Shadow fading 2 PTs10RCS (MS) UE RCS (MS)
10
Normalized gain [dB]
20
0 T2: -5.5dB 0 T1: -5.5dB Beampattern 5 10 10
0
Gain [dB]
0
System and Signal Configuration BS antenna elements NBS 64 UE antenna elements NUE 16 Carrier frequency fc 28 GHz System bandwidth B 120 MHz Number of subcarriers M 1024 BS transmit power budget PB −20 dBm Number of slots L 16 Symbols per slot P 100 Clock bias ∆t 1 µs Relative orientation offset ∆φ T=R 110◦
Gain [dB]
10
VEB Performance vs Number of Targets (Random Geometry)
BP MS (Snap) MS
y [m]
Value
205 10 10 15 0 20
UE VEB (cm/s)
Symbol
20
y [m]
Parameter
JO-FDB =0.0UE:- Angular JO-FDB =1.0 - Spatial 0.0dB
0
Normalized gain [dB]
JO-FDB =0.0 - Spatial
TABLE II S YSTEM , C HANNEL , AND S IMULATION PARAMETERS
100
10 1
10 2 0
1
2
4
Number of Targets
6
(b) VEB vs. number of PTs
Fig. 3. PEB (log-scale) vs. number of PTs and VEB (log-scale) vs. number of PTs for BP, Snapshot MS, and Extended MS.
between delay, angle, Doppler, and channel gain estimates across different propagation paths [17]. This approximation is justified under large array apertures and high signal bandwidth conditions, where angular and temporal resolution effectively decorrelate the parameter estimation errors. A. Beamforming Analysis To fundamentally understand the underlying spatial allocation strategies of the two MS and BP modalities, Fig. 2 visualizes the optimized spatial beam patterns for pure MS, α = 0, and pure BP, α = 1. To isolate the inherent estimation requirements of each modality from path-loss biases, the simulation geometry is deliberately constructed symmetrically. As observed in Fig. 2a, the MS optimization allocates spatial energy directly toward both the PTs and the UE with more focus on the UE. This asymmetric power distribution in MS is driven by the UE velocity estimation, which relies entirely on the Doppler shift observed from the direct LoS echo. Conversely, Fig. 2b demonstrates a radically different spatial strategy for BP. The UE receives substantially lower LoS illumination energy, with the PTs on the right receiving higher energy compared to the MSs case. This occurs because FIM for BP position and velocity estimation derives critical information not only from the LoS but also from the rich signatures of the NLoS multipath components reflected off the PTs. Illuminating these PTs provides the geometric diversity required to resolve the full position and velocity. Furthermore, the highest beamforming gain is directed specifically toward the rightmost PT, due to the UE antenna array’s right-tilted orientation as included in Table. II, thereby maximizing the
0
10
Random Trajectories
30
10
10
3
2 20
Speed (m/s)
10 1 10
30
10
20
Speed (m/s)
30
10 10
20
Speed (m/s)
requirement, the BP configuration rapidly becomes Tang=Rad moreBP inBP 2 2 100 MS-Ext MS-Ext 3 performance. formative and surpasses the MS In contrast, the 3 2 10 100 3 PEB of MS increases with the number of PTs,80as multiple 101 10 10 16 16 101 16 spatial beams must be steered toward 2 different60 directions, 3 reducing the energy and directivity available along LoS path 2 1 10 3 40 in Fig.3b 100 to the2 user equipment. The same trend is reflected 100 3 for the VEB. Both the 10 snapshot and extended MS 20 estimators 10 10 0 10 20 2 10 exhibit performance degradation with additional targets for the x [m] 10 20 30 10 20 30 10 20 30 10 20 10 same reason: the transmit power and beamforming gain are (m/s) Speed (m/s) Speed (m/s) Speed (m/s) Speed increasingly distributed over non-LoS directions. The degraFig. 4. VEB (log-scale) vs. speed for BP, Snapshot MS, and Extended MS dation is more pronounced for the extended MS case, which with 4 PTs. The numbers represent the number of effective slots Leff ≤ L of strongly depends on the resolvability of the tangential velocity observation of the UE. component, particularly sensitive to the UE relative position during the second observation interval. The snapshot MS, in receivable NLoS signal power and the overall spatial-temporal contrast, derives its velocity information indirectly from the information gain at the UE. position covariance, resulting in a more gradual performance loss as the number of PTs grows. B. UE Position and Velocity Estimation Study Fig. 4 analyzes velocity estimation. We plot the UE VEB All the following simulations are Monte Carlo simulations versus speed for Snapshot MS, Extended MS, and BP. As the with 200 independent channel realizations, including random speed increases, the VEB degrades for Snapshot MS and Expositions of UE and PTs, to ensure statistically reliable esti- tended MS. This trend is explained by the reduced number of mates of PEB and VEB. The UE and PTs are generated to be effective observation slots within a CPI as higher Doppler acwithin [5, 100]m from the broadside of the BS. celerates the phase rotation across symbols/subcarriers, which We analyze the performance of UE velocity estimation and shortens the interval over which the assumed parametric model investigate the inherent coupling between position and velocity remains informative and thereby lowering the usable Fisher across the MS and BP sensing modalities. Estimating velocity information. BP consistently perform better than Snapshot MS via MS relies purely on the Doppler shift observed from the and Extended MS. direct LoS echo, which only captures the radial component of the UE’s motion vector. Consequently, if the UE has a non- C. MS/BP Allocation and Sequential Optimization negligible tangential velocity, the monostatic FIM becomes illIn Fig.5, we consider different UE velocities in [5, 30](m/s) conditioned, leading to unbounded velocity error bounds. To and also different numbers of PTs between 2 and 4, and we evaluate this limitation and compare it against our proposed compare the full MS, full BP, the shared sequential beam2 BP framework, we consider two distinct velocity estimators : former, and the separate sequential beamformer approaches by • Snapshot MS: In this approach, we simplify (P1) by evaluating the UE PEB, UE VEB, PTs PEB, and computation completely removing velocity and Doppler from the estitime. We can see that the shared and separate sequential mation stage, effectively treating the UE as static within beamformer approach consistently yields better performances each coherence interval. Two temporally separated MS compared to full MS and full BPs. In particular, both sequensnapshots are then considered, each yielding a position tial designs achieve cm-level positioning accuracy for the UE estimate with its associated covariance. The velocity and the PTs over the considered scenarios. Parametrizing the is subsequently inferred by finite differencing the two BP FIM via the separate and shared beamformers improves position estimates. conditioning, enabling the UE estimation of PTs positions, • Extended MS: This approach exploits Doppler measureunlike in the full BP baseline. Fig. 5 also reveals that full MS ments from two temporal instants under a constantperformance degrades with decreasing ρMS ratio, illustrating velocity model. Because the UE moves between obserthe fundamental tradeoff between monostatic prior quality vations, the Doppler shifts project the velocity onto two and the posterior information available from the BP stage in distinct LoS directions, enabling the joint reconstruction the sequential designs. The optimization problems (P2) and of both radial and tangential velocity components. (P3) resolve this tradeoff by determining the optimal ρ⋆MS that Fig.3 illustrates the evolution of the PEB and VEB with minimizes the desired bounds. respect to the number PTs. In Fig. 3(a), the PEB for BP Fig. 5a, Fig. 5b, and Fig. 5c show that the shared sequential is initially unresolved when a single PT is present, since beamformer consistently outperforms the separate sequential the system lacks sufficient geometric diversity to infer both design in both UE and PTs positioning, despite the latter position and synchronization parameters. Once 2 or more having more spatial degrees of freedom. This behavior origtargets are introduced, matching the minimum dimensional inates from the joint spatio-temporal structure imposed by 102
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the shared beamformer, which maintains a consistent illumination pattern across the MS and BP stages. Because the same beams coherently interrogate the scene over time, the
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0 0 20 20 40 40 60 60 80 80 100 100 100 20 40 2020 4040 6060 8080 100 00 20 60 80 100 (%) MS (%) MS(%) MS (%) MS MS (%) (b) UE VEB (log scale) (d) Computational runtime (ms) 10103 3 (c) PTs PEB (log scale) MS MS BP BP BP 20000 20000 88 10 Shared Seq. MS Shared Shared Seq.5. Performance of full MS, full BP, shared sequential, and separate sequential beamforming designs vs.10 Fig. the MS symbol ratio ρMS . Seq. Shared Seq. 2 2 Seperate Seq. 10 Shared Seq. Seperate Seq. 1 Seperate Seq. 1 10 17500 Seperate Seq. 10 10 17500 Seperate Seq. 6 0.7 0.7 6 10 10 15000 15000 BPwith R EFERENCES Doppler and delay shifts associated BP both the UE and1010 11 BP MS MS 0.6 0.6 MS 12500 Shared PTs become more accurately12500 captured, effectively enhancing Seq. Shared Seq. K. Wu, Seq. Z. Wang, S.-L. Chen, J. A. 1044Zhang, and Y. J. Guo, “Isac: From 10 0 [1] Shared Seperate Seq. Seq. Seperate 0.5 0.5 resolvability. Furthermore, Seperate 10000 10000 velocity humanSeq. to environmental sensing,” IEEE Journal of Selected Topics in parameter estimation relies10100 25 2550 5075 75 Electromagnetics, Antennas and Propagation, vol. 1, no. 1, 2025. 0 75007500measurement, to which the101 1 1022 100 10predominantly on the BP Doppler 10 10 [2] Z. Cui and S. Pollin, “Extracting the communication channel from MS stage contributes only the5000 radial 5000 component. By contrast, monostatic sensing channels: From0 propagation to impact analysis,” 102 2 100 10 IEEE Transactions on Antennas and Propagation, the separate approach commits F⋆MS 20 20 40 40 60 60 80 80 100 100 0 0based 20 20 40solely 80 the 100 20 40 40vol. 73, 60 no.80 808, 2025. 100 40 60 60on 80 100MS 10010 0 0 2020 4040 6060 8080 100 00 20 60 100 [3] Z. Ye, F. Junaid, E. Ibrahim, R. Nilsson, and J. Van De Beek, “Mono(%) (%) (%) MS (%) MS (%) MS MS MS (%) power more broadly across MSdirections cost, distributing and (%) (%) MS MS static sensing for passive ris localization and tracking,” IEEE Wireless 3 103 10thus weakening the prior information passed to the BP stage Communications Letters, vol. 13, no. 5, pp. 1260–1264, 2024. BP BP BP BP 8 8 10 all 10 the metrics show [4] M. Bauhofer, M. Henninger, T. Wild, S. Ten Brink, and S. Mandelli, MS MSnode. Also, Shared Seq. Seq. for each individual that MS Shared 2 10 102 Shared Seq. Seq. Seperate Seq. Seq. Seperate “Bistatic information fusion for positioning and tracking in integrated prior dominates Seperate theShared lack of BP 6symbols. Seq. Seq. Seperate sensing and communication,” in 2025 IEEE Wireless Communications 10 106 101 101 Finally, we compare the computational running time of and Networking Conference (WCNC), 2025, pp. 1–6. [5] H. Sallouha, S. Saleh, S. De Bast, Z. Cui, S. Pollin, and H. Wymeersch, the different designs in Fig.1045d. 4 The separate sequential 10 0 10 100 “On the ground and in the sky: A tutorial on radio localization in groundbeamformer exhibits a noticeably higher runtime than the air-space networks,” IEEE Communications Surveys & Tutorials, vol. 27, 2 102 implemented as a twocounterpart due to it 10being 1 10 110 shared no. 1, pp. 218–258, 2025. [6] M. Tommingas, T. Laadung, S. Varbla, I. Müürsepp, and stage greedy optimization: it first optimizes FMS and then, 2 0 10 10 2 10 100 M. Mahtab Alam, “Uwb and gnss sensor fusion using ml-based conditioned over second 0 0 20 20 40 40on 60 this 0 0F20 40 40a 60 100 100 BP 20 60 80choice, 80 100 100optimizes 60 80 80search positioning uncertainty estimation,” IEEE Open Journal of the (%) (%) MS MS (%) the shared formulation solves MS MSa (%) space. In contrast, single global Communications Society, vol. 6, pp. 2177–2189, 2025. [7] M. F. Keskin, M. M. Mojahedian, J. O. Lacruz, C. Marcus, O. Eriksson, optimization problem over a common beamformer used in A. Giorgetti, J. Widmer, and H. Wymeersch, “Fundamental trade-offs in both stages, which effectively reduces the dimensionality and monostatic isac: A holistic investigation toward 6g,” IEEE Transactions decouples the search from stage-specific reconfiguration. on Wireless Communications, vol. 24, no. 9, pp. 7856–7873, 2025. [8] M. Bauhofer et al., “Multi-target localization in multi-static integrated V. C ONCLUSION sensing and communication deployments,” in 2023 2nd International Conference on 6G Networking (6GNet), 2023, pp. 1–4. In this paper, we proposed a velocity-aware, sequential [9] H. Liu, Y. Zhuo, S. Jin, and Z. Wang, “Multi-bs multi-target localization beamforming framework for joint monostatic sensing (MS) for isac systems,” in 2024 IEEE/CIC International Conference on Communications in China (ICCC), 2024, pp. 586–590. and bistatic positioning (BP). By executing MS first, the K. Khosroshahi, P. Sehier, S. Mekki, and M. Suppa, “Localization base station constructs a spatial-temporal prior regarding the [10] accuracy improvement in multistatic isac with los/nlos condition using environment and the mobile user, which is then utilized to 5g nr signals,” in 2025 IEEE Wireless Communications and Networking Conference (WCNC), 2025, pp. 1–6. regularize the subsequent BP estimation. Our results demonY. Ge, H. Kim, L. Svensson, H. Wymeersch, and S. Sun, “Integrated strate that optimizing a single shared beamformer globally [11] monostatic and bistatic mmwave sensing,” in GLOBECOM 2023 - 2023 across both stages outperforms stage-specific greedy designs. IEEE Global Communications Conference, 2023, pp. 3897–3903. This shared approach effectively maximizes the joint posterior [12] Y. Zhang, H. Chen, P. Zheng, B. Ning, H. Niu, H. Wymeersch, and T. Y. Al-Naffouri, “Joint bistatic positioning and monostatic sensing: information, achieving centimeter-level positioning and robust Optimized beamforming and performance tradeoff,” IEEE Transactions velocity estimation with reduced computational complexity. on Cognitive Communications and Networking, vol. 11, no. 5, 2025. Future work will extend this framework to a dynamic time- [13] L. Cheng et al., “Doppler spread and coherence time of rural and highway vehicle-to-vehicle channels at 5.9 ghz,” in IEEE GLOBECOM series model, continuously adapting symbol allocation to the 2008 - 2008 IEEE Global Telecommunications Conference, 2008. evolving network geometry, ultimately evolving into a multi- [14] T. McKelvey and P. Dammert, “A waveform model for bistatic radar with arbitrary long coherent processing interval,” in 2025 33rd European static online beamforming. Signal Processing Conference (EUSIPCO), 2025, pp. 2232–2236. [15] M. F. Keskin et al., “Optimal spatial signal design for mmwave positionACKNOWLEDGMENT ing under imperfect synchronization,” IEEE Transactions on Vehicular This work is supported by the EU-HORIZON-MSCA-2022Technology, vol. 71, no. 5, 2022. DN 6thSense project, Grant Agreement N°101119652, under [16] Y. Shen and M. Z. Win, “Fundamental limits of wideband localization— part i: A general framework,” IEEE Transactions on Information Theory, the EU’s Programme for Research and Innovation. vol. 56, no. 10, pp. 4956–4980, 2010. [17] T. Wilding, S. Grebien, U. Mühlmann, and K. Witrisal, “Accuracy bounds for array-based positioning in dense multipath channels,” Sensors, vol. 18, no. 12, p. 4249, 2018.
Radial VEB (cm/s) Radial VEB (cm/s)
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