Coordinated Spectrum Coexistence Across Heterogeneous Commercial and Federal Services

This paper has been accepted for publication at IEEE MILCOM 2026. This is the author’s accepted version of the paper.

Coordinated Spectrum Coexistence Across Heterogeneous Commercial and Federal Services Minh Dat Nguyen, Paolo Testolina, Pedram Johari, Michele Polese, Tommaso Melodia

arXiv:2608.07789v1 [cs.NI] 7 Aug 2026

Institute for Intelligent Networked Systems, Northeastern University, Boston, MA, U.S.A. {minhd.nguyen, p.testolina, p.johari, m.polese, melodia}@northeastern.edu Abstract—Future wireless networks are expected to support the coexistence of cellular communications, radio frequency (RF) sensing, radionavigation, and radiolocation radar—among others—over congested federal sub-6 GHz spectrum under heterogeneous Quality of Service (QoS) requirements, driven by escalating cellular traffic demand, the proliferation of 6G sensing and positioning services, and regulatory pressure to repurpose federal bands without displacing incumbents. We develop a unified framework in which all four services dynamically share a common Physical Resource Block (PRB) pool under centralized coordination, formulating weighted cellular sum-rate maximization subject to duty-cycle, orthogonality, sensing signal-to-noise ratio (SNR), and Cramér–Rao-based positioning constraints. The resulting Mixed-Integer Nonlinear Program (MINLP) is solved by alternating optimization across PRB assignment, scheduling, and successive convex approximation for power allocation, complemented by a low-complexity QoS-aware greedy heuristic. Sitespecific ray-tracing simulations on the BostonTwin urban digital twin show substantial gains in spectrum efficiency and cellular throughput while strictly meeting sensing and positioning QoS, establishing coordinated multi-service sharing as a viable architecture for cellular-federal-radar coexistence in next-generation military and civilian networks. Index Terms—Spectrum sharing, federal-band coexistence, RF sensing, radionavigation, radiolocation, resource allocation, MINLP.

I. I NTRODUCTION The design and standardization of Sixth Generation (6G) cellular systems is creating increasing interest in understanding spectrum coexistence mechanisms in multiple sub-6 GHz bands. This includes assessments of whether sharing is possible across commercial cellular deployments and incumbent federal services (high-power radars, radionavigation infrastructure, and sensing systems) [1], each governed by distinct Quality of Service (QoS) requirements and regulatory dutycycle constraints [2], [3]. Static frequency partitioning leaves spectrum idle during off-duty intervals of intermittent services while failing to meet cellular peak-throughput demands [4]. Citizens Broadband Radio Service (CBRS) demonstrated that three-tier dynamic This work was partially supported by the U.S. National Science Foundation under Grant CNS-2434081. This effort was also sponsored by the U.S. Government under Other Transaction number W15QKN-21-9-5599 between the National Spectrum Consortium (NSC) and the Government. The U.S. Government is authorized to reproduce and distribute reprints for Governmental purposes notwithstanding any copyright notation herein. The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of the U.S. Government. DISTRIBUTION STATEMENT A. APPROVED FOR PUBLIC RELEASE; DISTRIBUTION IS UNLIMITED

sharing between satellite downlink, Navy radars, and LongTerm Evolution (LTE) or NR carriers is feasible, but only with limited temporal dynamics and integration, preventing performance gains from tight multiplexing of different waveforms. Integrated Sensing and Communication (ISAC) has emerged as a leading paradigm for joint spectrum utilization [5]. Early radar-cellular coexistence work [6] provided an analytical model for opportunistic cellular access during radar off-duty intervals but is restricted to a two-service model without subcarrier-level optimization or positioning constraints. Subsequent ISAC research has advanced joint subcarrier-power allocation for multicarrier and dual-function radar-communication systems [7], while a parallel thread has examined sensingcommunication trade-offs [8] and joint sensing-localization energy minimization [9]. Despite these advances, two critical gaps remain. First, radionavigation, a co-primary occupant mandated by ITU-R and national regulators [3] and present in nearly every contested federal band (e.g., aeronautical surveillance and maritime navigation radars), has not been incorporated as an explicit coexisting service with positioning-accuracy constraints in any prior resource allocation framework. Most ISAC frameworks adopt a two-service model (communication + sensing/radar) and treat localization as a by-product of ISAC waveform design at the UE level, rather than as an independent service with its own infrastructure, users, and regulatory constraints. Navigation accuracy depends jointly on the received signal quality (signal-to-interference-plus-noise ratio (SINR)) and the geometric diversity of the available infrastructure anchors, naturally captured by a Cramér-Rao lower bound (CRLB)based ranging model and a Fisher information matrix-based position error bound (PEB) [10]. Second, the joint modeling of heterogeneous duty cycles across different service types within a unified coordination architecture has not been addressed. To bridge these gaps, this paper proposes a coordinated multi-service spectrum sharing framework, in which cellular, sensing, navigation, and radiolocation share a unified Physical Resource Block (PRB) resource pool. The formulation is not limited to these four services; the resource grid and constraint structure extend naturally to additional service classes (e.g., passive radio astronomy, satellite earth-station receivers). A centralized coordinator is instantiated as an rApp within the Open Radio Access Network (O-RAN) Non-RT RAN Intelligent Controller (RIC), as it operates over policy-level horizons (seconds to minutes) matching the optimization timescale and has access to RAN-wide telemetry and external data. In this

Core Network

Fig. 1: Multi-service network architecture. regard, we further assume an extended coordination plane in which sensing, radionavigation, and radar nodes expose minimal telemetry (activity schedules, target/anchor lists, QoS thresholds) and accept resource grants via O1/E2-like interfaces, a system-design assumption aligned with the broader Dynamic Spectrum Operations (DSO) vision for contested federal bands [11], requiring standardization beyond current O-RAN scope. The framework jointly optimizes long-term PRB allocation and transmit-power allocation, maximizing the weighted cellular sum-rate subject to service-specific QoS: minimum sensing signal-to-noise ratio (SNR) and a CRLBbased PEB for radionavigation. The contributions of this paper are as follows: 1) Multi-service system model with radionavigation. We develop the first unified resource allocation framework to incorporate radionavigation as a co-primary coexisting service, characterized by a CRLB-based ranging model and a Fisher information matrix-based PEB. 2) Heterogeneous duty-cycle model with dynamic PRB allocation. We introduce a generalized activity model capturing heterogeneous duty cycles across all four service types within a unified scheduling framework, coupled with dynamic service-level PRB assignment over the full spectrum grid. 3) Mixed-Integer Nonlinear Program (MINLP) formulation and decomposition. We formulate the problem as an MINLP, establish NP-hardness via reduction from 0/1 knapsack, and develop a three-stage alternating optimization with monotone-convergence guarantees, complemented by a QoS-aware greedy algorithm that is linear in PRBs and time slots. 4) Site-specific evaluation. We build an evaluation platform on the BostonTwin Sionna-RT scene [12], calibrated to FCC/NTIA frequency assignments in the 2.7–3.7 GHz federal-band cluster [13] and 3GPP NR resource structure [14], and quantify the cost of QoS enforcement under realistic urban propagation. II. S YSTEM M ODEL AND P ROBLEM F ORMULATION A. Network Architecture and Spectrum Coordination We consider a multi-service wireless network supporting the service set I ≜ {c, s, ν, r}, where c, s, ν, r denote cellular, radio frequency (RF) sensing, radionavigation, and radiolocation radar, respectively (Fig. 1). Each service i has

transmitters indexed by k ∈ Si and endpoints: cellular UEs Uc associated with gNBs by a strongest-power rule; navigation users Uν each connected to a visible anchor set Sν (u) ⊆ Sν ; sensing/radar nodes monitoring target sets Mi,k for i ∈ {s, r}. Time is slotted, t ∈ T ≜ {1, . . . , T }, with slot duration τ . A slot aggregates one or more Orthogonal Frequency Division Multiplexing (OFDM) symbols at the chosen numerology (e.g., τ = 1 ms with ∆f = 30 kHz corresponds to a 14-symbol slot). For non-cellular services, τ represents the minimum coordination granularity at which resource grants are updated; it does not require those services to use OFDM waveforms internally. We adopt a generalized PRB abstraction: total bandwidth B is divided into NPRB elementary units of width Brb = B/NPRB , matching the 3GPP NR PRB definition for cellular (Brb = 12∆f , ∆f ∈ {15, 30, 60, 120} kHz) and the minimum allocable spectral chunk for the other services. Let N ≜ {1, . . . , NPRB }. Large-scale propagation parameters are quasi-static within the horizon, while small-scale fading varies independently across PRBs and slots and is described in detail in the following section. B. Resource Allocation Variables Let Oi,k (t) ∈ {0, 1} denote the activityPof transmitter k ∈ Si , with the duty-cycle pre-condition T1 t Oi,k (t) ≤ δi enforced by external protocol design (radar pulse repetition intervals, navigation beacon periodicity) and treated as a known input rather than an optimization variable; cellular activity is scheduler-controlled with δc ≈ 1. Two binary variables encode allocation. The grant variable (n) xi (t) ∈ {0, 1} assigns PRB n to service i; the scheduling (n) variable ai,k,u (t) ∈ {0, 1} allocates PRB n from transmitter k to endpoint u. Inter-service exclusivity and intra-service OFDMA orthogonality require, respectively, X (n) xi (t) ≤ 1, ∀n, t, (1) i∈I

X

(n)

(n)

ai,k,u (t) ≤ xi (t) Oi,k (t), ∀i, k, n, t.

(2)

u∈Ui

Eq. (2) couples the two binary variables: transmitter k of service i may schedule endpoint u on PRB n only if (i) PRB (n) n has been granted to service i (xi = 1) and (ii) transmitter k is active in slot t (Oi,k (t) = 1). P (n) (n) The PRB usage indicator zi,k (t) ≜ u ai,k,u (t) ∈ {0, 1} (n) follows from (2). Power allocation pi,k (t) ≥ 0 satisfies P (n) max Oi,k (t), ∀i, k, t, (3) n pi,k (t) ≤ Pi (n)

(n),max

0 ≤ pi,k (t) ≤ Pi

(n)

zi,k (t), ∀i, k, n, t,

(4)

where Pimax is the total transmit power budget of transmitter (n),max on service i, Pi is the per-PRB peak-power cap. C. Channel and SINR Models For the link from transmitter ℓ ∈ Si to receiver u at distance di,ℓ,u , path loss is Li,ℓ,u = L0,i +10αi log10 (di,ℓ,u /d0 )+ξi,ℓ,u , where L0,i is the reference path loss at the reference distance d0 for service i, αi is the path-loss exponent, and 2 ξi,ℓ,u ∼ N (0, σξ,i ) is a log-normal shadow-fading term.

(n)

The effective channel power gain on PRB n is gi,ℓ,u (t) = (n) Gi,ℓ,u |hi,ℓ,u (t)|2 10−Li,ℓ,u /10 , with Gi,ℓ,u the antenna gain (n) and hi,ℓ,u a Rayleigh/Rician fading coefficient. For endpoint u served by k on PRB n, (n) (n) pi,k (t) gi,k,u (t) (n) , (5) SINRi,k,u (t) = (n) Ii,u (t) + N0 Brb where N0 is the one-sided thermal-noise power spectral density at the receiver, so that N0 Brb is the noise power per PRB. The intra-service interference (universal frequency reuse P (n) (n) (n) (n) within a service) is Ii,u (t) = ℓ∈Si ,ℓ̸=k pi,ℓ (t) gi,ℓ,u (t) zi,ℓ (t).

with θk,u q the corresponding azimuth angle. The PEB is

PEBu (t)= tr(J−1 u (t)) [16], and the navigation QoS is T X 1 PEBu (t) ≤ ϵmax , ∀u ∈ Uν , (8) T t=1 where ϵmax > 0 is time-averaged positioning-error tolerance. E. Joint Optimization Problem The coordinated multi-service resource allocation problem, with the objective of maximizing the weighted cellular sum rate, can be formulated as: X (P): max w u Ru (9) {x,a,p}

D. Service-Specific QoS Models

s.t.

Cellular throughput. The aggregate throughput of u∈Uc is X (n)
(n) Ru ≜ ac,kc (u),u (t) Brb log2 1 + SINRc,kc (u),u (t) , (6) t,n

where kc (u) ∈ Sc denotes the gNB serving cellular user u. Sensing/radar SNR. Adopting a monostatic topology and the radar range equation [15], we define the (slot-independent under quasi-static range/Radar Cross-Section (RCS)) echo2 2 (Gtx (n) i,k ) λi σRCS,m , ∀i ∈ {s, r}, gain coefficient as ηi,k,m ≜ (4π) 3 d4 Lsys,i k,m

where Gtx i,k denotes the transmit antenna gain of transmitter k in service i, λi is the carrier wavelength, σRCS,m is the RCS of target m, dk,m is the one-way range between transmitter k and target m, and Lsys,i ≥ 1 aggregates implementation losses (cabling, mismatch, and processing). The echo power (n) is therefore linear in the per-PRB transmit power pi,k (t): (n) (n) (n) Pecho,k,m (t) = ηi,k,m pi,k (t). Under equal-weight integration across active PRBs (a robust low-complexity combiner [15]), the effective sensing SNR for target m ∈ Mi,k when the sensing-mode indicator Oi,k (t) = 1 is SINRsen i,k,m (t) = (n) (n) (n) n zi,k (t) ηi,k,m pi,k (t) (n) (n) n zi,k (t) Ii,k (t)+N0 Brb

P P

. Therefore, the detection QoS is

sen SINRsen i,k,m (t) ≥ γi ,

(7)

where the threshold γisen is calibrated to the desired probability of false alarm. Navigation accuracy. For anchor k ∈ Sν (u), the PRB-aggregated ranging SINR and effective bandwidth P (n) (n) (n) n aν,k,u (t)pν,k (t)gν,k,u (t) nav
, Beff,u,k (t) = are [10]: Γu,k (t) = P (n) (n) n aν,k,u (t) Iν,u (t)+N0 Brb P (n) Brb n aν,k,u (t). The CRLB-inspired ranging variance is 2 2 σu,k (t) = c20 /[8π 2 Beff,u,k (t)(Γnav u,k (t) + ε0 )] [10], [16], where c0 denotes the speed of light and Beff,u,k (t) is a proxy for the root-mean-square (RMS) signal bandwidth and ε0 > 0 is a regularization constant (ε0 = 10−3 in our experiments). The proxy Beff,u,k (t) is exact under uniform spectral allocation and upper-bounds the true CRLBbased variance otherwise (since contiguous allocations minP (n) imize the RMS bandwidth for a given | n aν,k,u (t)|); the resulting PEB constraint is therefore conservative. Defin(n) 2 (n) ing βu,k (t) ≜ 8π 2 Brb gν,k,u (t)/c20 , the 2D Fisher informaP −2 T tion matrix is Ju (t) = k∈Sν (u) σu,k (t) vk,u vk,u , where vk,u = [cos θk,u , sin θk,u ]T is the unit line-of-sight direction vector from anchor k to user u in the 2D plane,

u∈Uc

(1)–(4), (7), (8),

(n) (n) xi (t), ai,k,u (t) ∈ {0, 1}, (9a) (n) (n) where x = {xi (t), ∀i, n, t}, a = {ai,k,u (t), ∀i, k, u, n, t}, (n) p = {pi,k (t), ∀i, k, n, t}, and wu is the priority weight of

cellular user u. Problem (P) prioritizes cellular throughput while enforcing sensing and positioning as hard QoS constraints, reflecting the asymmetric urgency of these services in federal-band sharing. (P) is a MINLP due to binary variables and nonconcave SINR coupling, and is NP-hard: restricting to I = {c}, T = 1, (n) and fixed equal power pc,k = p̄ reduces (P) to maximizing P (n) P (n) max , where Rn ≜ n ac,k,u Rn subject to n ac,k,u p̄ ≤ Pc (n) wu Brb log2 (1 + p̄ gc,k,u /(N0 Brb )) is the weighted per-PRB rate, which is exactly the 0/1 knapsack problem, known to be NP-hard [17]. III. D ECOMPOSITION -BASED O PTIMIZATION Due to its NP-hard nature, we decompose problem (P) into three subproblems: PRB assignment, scheduling, and power allocation. These are solved iteratively in the Alternating MultiService Resource Allocation (AMRA) algorithm, an alternating optimization (AO) loop until convergence. We describe how to solve each subproblem in the following. QoS surrogates: At a current power iterate p̄, de(n) fine the receiver-side intra-service interference I¯i,k (t) = P (n) (n) (n) ¯(n) ℓ̸=k p̄i,ℓ gi,ℓ,k zi,ℓ for i ∈ {s, r} and Iν,u analogously for navigation. The sensing threshold and navigation information aggregate (both affine X in(n)p) are(n)
sen sen Γi,k,m (t) ≜ γi zi,k (t) I¯i,k (t) + N0 Brb , (10) n

(n) 2 2 (n) X X a(n) ν,k,u (t) 8π Brb gν,k,u (t) pν,k (t) . (11) Qu (t; p̄) =
(n) c20 I¯ν,u (t) + N0 Brb k∈Sν (u) n Stage 1: PRBX Assignment: With {a, p} fixed, we solve (n) (n) (P1): max xi (t) R̂i (t) (12) x

n,t,i (n)

(n)

s.t. (1), (9a), xi (t) ≥ zi,k (t), ∀i, k, n, t, (12a) (n) where the per-service PRB benefit is R̂c (t) =
P (n) (n) (n) = k,uwu ac,k,u (t)Brb log2 1 + SINRc,k,u (t) , R̂i (t) P (n) (n) (n) µi k,m∈Mi,kηi,k,m p̄i,k (t), ∀i ∈ {s, r}, R̂ν (t) = P (n) (n) µν u,k∈Sν (u)βu,k (t)p̄ν,k (t), all evaluated at p̄, with µi , µν > 0 service priority weights. The consistency constraint (n) (n) xi (t) ≥ zi,k (t) ensures the updated x does not revoke a

grant already used by a, preserving feasibility of (2) across AO iterations; a softer variant that allows revocation with a Stage-2 feasibility-restoration step accelerates convergence at the cost of additional per-iteration work and is left to future investigation. (P1) is a binary LP problem, solvable greedily or using CVX-Gurobi solver [18]. Stage 2: PRB X Scheduling: With {x, p} fixed, we solve wu Ru (13) (P2): max a

u∈Uc

s.t. (2), (9a), X (n) (n) (n) zi,k (t)ηi,k,m p̄i,k (t) ≥ Γsen i,k,m (t),

(13b)

rate is constant in a and the QoS surrogates (13b)–(13c) are P (n) (n) affine in a via zi,k (t) = u ai,k,u (t), so (P2) is a binary LP, solvable greedily or using a solver such as CVX-Gurobi [18]. Stage 3: Power Allocation via SCA: With {x, a} fixed, (n) the rate admits a difference-of-concave (DC) form ru (t) = (n) (n) (n) (n) ai,kc (u),u (t)Brb [log2 (Su (t)+Iu (t)+N0 Brb )−log2 (Iu (t)+ (n)

(n)

N0 Brb )] with Su (t) = pc,kc (u) (t)gc,kc (u),u (t). Linearizing the second (concave) term at p̄ via first-order Taylor expansion eu (p̄) ≤ Ru . Echo power yields a concave lower bound R being linear in p, the sensing constraint becomes affine, P (n) (n) (n) sen n zi,k (t)ηi,k,m pi,k (t) ≥ Γi,k,m (t). Assumption 1 (Isotropic anchor geometry). For every u ∈ Uν and t, the visible anchor geometry is approximately isotropic, i.e., Ju (t) ≈ 12 tr(Ju (t))I2 . Under Assumption 1, tr(J−1 u ) = 4/tr(Ju ), so PEBu (t) ≤ ϵmax ⇔ tr(Ju (t)) ≥ 4/ϵ2max . Lower-bounding the rangingvariance denominator at p̄ yields the affine sufficient condition P 1 = 4/ϵ2max . Hence, the convex SCA Q (t; p̄) ≥ Qmin u u t T subproblem is formulated as X eu (p̄) (P3.1): max wu R (14) p

(AMRA) (n) }, {Oi,k }, γisen , ϵmax , {wu , µi }. 1: Input: {gi,k,u 2: Init: round-robin x(0) , best-PRB a(0) , equal-power p(0) ; if (7) and (8) are violated,

run a feasibility-recovery boost (allocate additional PRBs/power to deficit services); ℓ ← 0. 3: repeat 4: Solve (P1) ⇒ x(ℓ+1) . 5: Solve (P2) at p̄ = p(ℓ) ⇒ a(ℓ+1) . 6: Iterate |∆obj| ⇒ p(ℓ+1) ; ℓ ← ℓ + 1. P (P3.1) until P < ϵSCA (ℓ) (ℓ−1) 7: until | u wu Ru − u wu Ru | < ϵAO . 8: Output: {x(ℓ) , a(ℓ) , p(ℓ) }.

(13a)

n P 1 min (13c) t Qu (t; p̄) ≥ Qu , ∀u ∈ Uν , T min 2 where Qu ≜ 4/ϵmax (justified in Stage 3). With p fixed, the

(n)

Algorithm 1 Alternating Multi-Service Resource Allocation

u∈Uc

s.t. (3), (4), and the affine QoS surrogates, which has a concave objective and affine constraints and is solved by the CVX-Mosek/Gurobi solver [18]. The joint algorithm is summarized in Alg. 1. Let Np = Sc N T denote the number of power variables. Stage 1 performs N T greedy PRB selections at O N T (Sc Uc +Ss M̄s +Sr M̄r +
Uν Ā) , where M̄s , M̄r are the average numbers of targets P per sensing/radar node and Ā ≜ |U1ν | u |Sν (u)| the average visible-anchor count P per navigation user. Stage 2 solves binary assignment at O( i Si Ui N T ), and Stage 3 solves (P3.1) via interior-point methods at O(Np3.5 ) per SCA iteration, requiring Nsca = O(1/ϵ P sca ) iterations [19]. Stage 3 dominates when Sc2 N T 2 ≫ i Ui , yielding overall complexity
O Niter Nsca (Sc N T )3.5 . (15) Although (P) is NP-hard, the decomposition is polynomial per iteration. The cubic scaling in Sc N T nevertheless renders (15) prohibitive at scale, since the interior-point solver is re-invoked at every SCA iteration of every AO cycle, motivating the lowcomplexity heuristic of the following section.

Algorithm 2 QoS-Aware Greedy Alternating Allocation (QGAA) 1: Input, Init: {x(0) , a(0) , p(0) } as in Algorithm 1. 2: repeat 3: for each t ∈ T do 4: Reserve PRBs for QoS violators (Step 1). (n) 5: For each n: assign to arg maxi Ψi (t) via (16) (Step 2). 6: Intra-service scheduling (Step 3); greedy power repair (Step 4). 7: end for P 8: until |∆ u wu Ru | < ϵQGAA . 9: Output: {x, a, p}.

IV. Q O S-AWARE G REEDY H EURISTIC We propose the QoS-Aware Greedy Alternating Allocation (QGAA) heuristic, which prioritizes sensing/navigation feasibility while opportunistically maximizing weighted cellular throughput. At each slot t, QGAA executes four steps. Step 1—QoS Reservation. For each violator of (7) and (8), candidate PRBs are ranked by marginal QoS improvement (sensing SNR gain ∆SINRsen i,k,m for i ∈ {s, r} or PEB for i = ν) and reserved greedily until reduction −∆PEB(n) u violations clear or resources are exhausted. Step 2—Greedy PRB Assignment. Each remaining PRB is (n) awarded to i⋆ = arg maxj Ψj (t), where 
(n)  maxk,u wu Brb log2 1+SINRc,k,u (t) , i = c, (n) Ψi (t) = maxk,m ∆SINRsen i ∈ {s, r}, i,k,m (t), 
 (n) i = ν. maxk,u −∆PEBu (t) , (16) Step 3—Intra-Service Scheduling. Cellular PRBs go to the user with the largest weighted-rate gain; sensing/radar PRBs to the target with the largest SNR deficit; navigation PRBs to anchors serving users with the largest positioning error. Step 4—Power Adjustment. Power is initialized uniformly, P (n′ ) (n) pi,k (t) = Pimax / n′ zi,k (t). If QoS violations persist, a finite-step water-filling-style repair is applied: at each iteration, identify the cellular PRB n⋆ with the smallest marginal cellular (n⋆ ) rate ∂R/∂pc,k and the deficit-service PRB n† with the largest (n⋆ ) QoS gain per unit power; transfer a step ∆p = ρ pc,k (ρ ∈ (0, 1]) from n⋆ to n† , subject to peak-power caps (4). The procedure terminates when all QoS constraints are met, (n⋆ ) when pc,k = 0, or after Kmax iterations. The dominant cost is computing (16) andPper-service
scheduling, yielding overall complexity O |N |T i |Si ||Ui | , linear in PRBs and slots and substantially below the MINLP, making QGAA suitable for real-time deployment as an ORAN Near-RT RIC xApp.

Runtime per realization (s)

TABLE I: Simulation Parameters General Parameters Parameter

Symbol

Value

Network area Coordination bandwidth Subcarrier spacing Time slots / slot duration Noise PSD Path-loss exp. / shadowing Receiver height Total / per-PRB power Sensing SNR threshold Navigation PEB threshold Navigation info threshold Duty cycles (c, s, ν, r) Multiplied network density

L×L B ∆f T, τ N0 2 αi , σξ,i HUE max P max , PPRB γ sen ϵmax Qmin u δi ζ

1 km× 1 km 100 MHz 30 kHz 10, 1 ms −174 dBm/Hz 2.5–3.5, 6 dB 1m 10 W, 1 W 3 (≈ 4.8 dB) 2.83 m 4/ϵ2max = 0.5 (1, 0.2, 0.1, 0.1) [1, 3]

Per-Service Parameters Service Cellular (c) Sensing (s) Radionav. (ν) Radioloca. (r)

Density ζtx /ζue

TX Height HTX (m)

Freq. (GHz)

TX Power (dBm)

60/100/km2 30/50/km2 30/50/km2 30/50/km2

25 30 50 100

2–4 3.1–3.7 2.7–5.65 2.7–5.65

46 50 60 60

V. N UMERICAL R ESULTS A. Simulation Setup Four services {c, s, ν, r} coexist in the same region. General and per-service parameters are listed in Table I; per-service frequency allocations follow FCC/NTIA assignments in the 2.7–3.7 GHz federal-band cluster [13], [14]. Specifically, the shared spectrum pool is centered around 3.5 GHz. Site-specific ray tracing. We integrate the BostonTwin1 urban digital-twin dataset with the Sionna-RT2 ray-tracing engine [12]. A fixed urban tile (BOS_G_5) supplies 3D building geometry and real-world cellular base station locations; noncellular transmitters and receivers are placed by independent homogeneous PPPs within a bounded square aligned with the BostonTwin frame. Antennas are configured via SionnaRT’s PlanarArray, and the PathSolver computes LoS, specular-reflection, and diffraction paths, yielding per-link received power, interference, and SINR from complex channel coefficients that combine large- and small-scale effects. The network layout is fixed across Monte-Carlo runs while user locations are resampled. Cellular UE weights. For long-term proportional fairness [14], UE u has weight p̃ ḡc,kc (u),u 1 w̃u = , γ eu = P , (17) log2 (1 + γ eu ) p̃ ℓ̸=kc (u)ḡc,ℓ,u + N0 Brb P (n) 1 with p̃ = Pcmax /NPRB and ḡc,k,u = NPRB n,t gc,k,u (t). T Weights are normalized to unit mean, so cell-edge UEs receive wu > 1 and strong-channel UEs wu < 1. They are computed once and held fixed during optimization, consistent with 3GPP NR Proportional Fair (PF) scheduling. Activity and procedure. Non-cellular transmitters follow predefined patterns with duty cycles (δs , δν , δr ) = (0.2, 0.1, 0.1); cellular BSs are continuously active. Each 1 https://tinyurl.com/2xjn9m43 2 https://nvlabs.github.io/sionna/rt/index.html

103 102

AMRA QGAA

101 100 1 2 3 Network density factor ζ

(a) Network region (ζ = 1).

(b) Runtime vs. network density ζ.

Fig. 2: Network deployment region (a) and complexity/runtime comparison of the proposed algorithms (b). Monte-Carlo realization samples node and user locations, computes Sionna-RT channels, initializes {x, a, p}, runs AMRA (Alg. 1), and records the weighted cellular throughput, sensing SNR margin, and navigation PEB. All metrics are averaged over 100 realizations. B. Results and Discussion Fig. 2(a) shows the BostonTwin deployment region; Fig. 2(b) reports the runtime of AMRA and QGAA versus network density factor ζ. As predicted by the complexity analysis in (15), AMRA exhibits steep cubic-like growth in ζ, whereas QGAA scales near-linearly and stays around 1 s at ζ = 1, confirming its suitability for real-time deployment as an O-RAN Near-RT RIC xApp. Throughput vs. bandwidth and power. Figs. 3a and 3b report the weighted cellular sum-rate against bandwidth and cellular transmit power. Throughput grows monotonically with both, and AMRA consistently outperforms QGAA across operating points, with the gap reflecting the cost of preserving sensing and navigation QoS. A central observation, highlighted by the dashed arrows in Fig. 3a, is the cross-bandwidth crossover: AMRA at B = 50 MHz exceeds dedicated cellular at B = 20 MHz, and AMRA at B = 100 MHz exceeds dedicated at B = 50 MHz; QGAA exhibits the same behavior. Faced with a choice between a narrow exclusive cellular allocation and a wider shared one, sharing yields strictly more cellular capacity and serves sensing, navigation, and radar, the central motivation for coordinated multi-service sharing. Moreover, Fig. 3c confirms that the weighted sum-rate increases monotonically and converges within a few outer AO iterations across bandwidth and density settings, demonstrating stability and scalability under realistic propagation. Network density and QoS sensitivity. Fig. 4 evaluates the weighted cellular sum-rate under varying network density and QoS constraints. Fig. 4a shows all schemes scaling nearlinearly with density factor ζ, with multi-service schemes tracking the dedicated baseline closely, and coexistence overhead does not compound with densification. Tightening the sensing SNR threshold γ sen (Fig. 4b) increases PRB allocation to sensing, eroding the cellular sum-rate near-linearly. In contrast, tightening the navigation PEB threshold ϵmax (Fig. 4c) induces a convex collapse driven by the non-linear cost of submeter positioning accuracy. This asymmetry persists across

Dedicated Cellular Multi-service (AMRA) Multi-service (QGAA) Init: Power Allocation Init: PRB Scheduling Init: PRB Allocation

8 6 4 2 0 20

30

50 System Bandwidth (MHz)

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(a) vs. bandwidth (Pcmax = 46 dBm, ζ = 1).

×103 10 8 6 4 Dedicated Cellular Multi-service (AMRA) Multi-service (QGAA) Init: Power Allocation Init: PRB Scheduling Init: PRB Allocation

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(b) vs. transmit power (B = 100 MHz, ζ = 1).

Weighted Cell. Sum Rate (Mbps)

×103

Weighted Cell. Sum Rate (Mbps)

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×103 15 B = 20 MHz, ζ = 1 B = 20 MHz, ζ = 2 B = 100 MHz, ζ = 1 B = 100 MHz, ζ = 2

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(c) Convergence of AMRA (Pcmax = 46 dBm).

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400

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Dedicated Cellular Multi-service (AMRA) Multi-service (QGAA) PRBs: Sensing PRBs: Radiolocation

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(b) vs. sensing SNR threshold γ sen (ζ = 1).

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Dedicated Cellular Multi-service (AMRA) Multi-service (QGAA) PRBs: Radionavigation

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Fig. 3: Weighted cellular sum-rate: dedicated cellular vs. multi-service AMRA and QGAA.

0

(c) vs. navigation PEB threshold ϵmax (ζ = 1).

Fig. 4: Weighted cellular sum-rate vs. network density and QoS thresholds (B = 100 MHz, Pcmax = 46 dBm). channel models, indicating a structural property of the QoS constraints (13b)–(13c) rather than an artifact of analytical shadowing. VI. C ONCLUSION We presented the first unified resource-allocation framework for coordinated spectrum sharing across cellular, RF sensing, radionavigation, and radiolocation services, formulated as an MINLP and decomposed into PRB assignment, scheduling, and SCA-based power allocation, complemented by a low-complexity QoS-aware greedy heuristic. Evaluations on the BostonTwin urban digital twin demonstrate substantial cellular-throughput gains while strictly satisfying sensing and navigation QoS constraints. The framework maps naturally onto an O-RAN architecture, with AMRA as a Non-RT RIC rApp issuing A1 policies to a Near-RT RIC xApp executing QGAA. Future work targets learning-based and distributed implementations, channel-uncertainty robustness, chance-constrained PEB formulations, and O-RAN testbed validation. R EFERENCES [1] M. Ghosh, “New regulatory activities for sharing in the 3.1–3.45 GHz and 7.125–8.4 GHz frequency bands,” IEEE Wireless Commun., vol. 32, no. 1, pp. 14–15, Feb. 2025. [2] FCC, “Third Report and Order,” Federal Communications Commission, Tech. Rep., Dec. 2024. [Online]. Available: https://docs.fcc.gov/public/ attachments/FCC-24-125A1.pdf [3] ITU, “Operational and technical characteristics and protection criteria of radiodetermination radars in the frequency band 2700–2900 MHz,” ITU-R, Recommendation ITU-R M.1313-1, 2000. [4] Federal Communications Commission, “Spectrum policy task force report,” Federal Communications Commission, Report ET Docket No. 02135, Nov. 2002. [5] F. Liu, Y. Cui, C. Masouros, J. Xu, T. X. Han, Y. C. Eldar, and S. Buzzi, “Integrated sensing and communications: Toward dual-functional wireless networks for 6G and beyond,” IEEE J. Sel. Areas Commun., vol. 40, no. 6, pp. 1728–1767, Jun. 2022.

[6] R. Saruthirathanaworakun, J. M. Peha, and L. M. Correia, “Opportunistic sharing between rotating radar and cellular,” IEEE J. Sel. Areas Commun., vol. 30, no. 10, pp. 1900–1910, Nov. 2012. [7] F. Wang and H. Li, “Power allocation for coexisting multicarrier radar and communication systems in cluttered environments,” IEEE Trans. Signal Process., vol. 69, pp. 1603–1613, Feb. 2021. [8] F. Dong, F. Liu, Y. Cui, W. Wang, K. Han, and Z. Wang, “Sensing as a service in 6G perceptive networks: A unified framework for ISAC resource allocation,” IEEE Trans. Wireless Commun., vol. 22, no. 5, pp. 3522–3536, May 2023. [9] H. Zhang, B. Chen, X. Liu, and C. Ren, “Joint radar sensing, location, and communication resources optimization in 6G network,” IEEE J. Sel. Areas Commun., vol. 42, no. 9, pp. 2369–2379, Sep. 2024. [10] Y. Shen and M. Z. Win, “Fundamental limits of wideband localization– Part I: A general framework,” IEEE Trans. Inf. Theory, vol. 56, no. 10, pp. 4956–4980, Oct. 2010. [11] U.S. Department of Defense, “Department of defense electromagnetic spectrum superiority strategy,” U.S. Department of Defense, Tech. Rep., Oct. 2020. [12] P. Testolina, M. Polese, J. M. Jornet, T. Melodia, and M. Zorzi, “Modeling interference for the coexistence of 6G networks and passive sensing systems,” IEEE Trans. Wireless Commun., vol. 23, no. 8, pp. 9220–9234, Aug. 2024. [13] S. Jones, R. Hinkle, F. Sanders, and B. Ramsey, “Technical characteristics of radiolocation systems operating in the 3.1-3.7 GHz band and procedures for assessing emc with fixed earth station receivers,” NTIA, Dec. 1999. [14] 3GPP, “NR; physical layer procedures for data,” 3rd Generation Partnership Project (3GPP), Tech. Speci. TS 38.214, 2023. [15] M. I. Skolnik, Radar Handbook, 3rd ed. New York, NY: McGraw-Hill, 2008. [16] M. Z. Win, A. Conti, S. Mazuelas, Y. Shen, W. M. Gifford, D. Dardari, and M. Chiani, “Network localization and navigation via cooperation,” IEEE Commun. Mag., vol. 49, no. 5, pp. 56–62, May 2011. [17] S. Martello and P. Toth, Knapsack Problems: Algorithms and Computer Implementations. John Wiley & Sons, 1990. [18] M. Grant and S. Boyd, “CVX: Matlab Software for Disciplined Convex Programming, Version 2.1,” http://cvxr.com/cvx/, Dec. 2018. [19] S. Boyd and L. Vandenberghe, Convex Optimization. Cambridge, U.K.: Cambridge Univ. Press, 2004.

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