A Computationally Efficient Joint Maximum Likelihood Estimator for Passive Localization in OFDM Distributed Antenna Systems with Pilots and Unknown Data Payloads
Communication-centric Integrated Sensing and Communications (ISAC) is a promising paradigm for sixth-generation (6G) wireless systems, enabling new sensing services by leveraging the already-deployed communication infrastructure. Communication signals typically comprise both known deterministic pilot sequences and unknown random data payloads. For localization and sensing tasks, the prevailing approach in multistatic and distributed ISAC systems relies exclusively on pilot symbols, entirely overlooking the positioning information carried by data payloads, which constitute the majority of each transmitted frame. Alternatively, Decision-Directed (DD) approaches treat data estimates as additional pilots, inherently limiting localization performance to that of the underlying communication system, while Non-Data-Aided (NDA) methods from the literature require prior knowledge of the data symbol distribution and incur a computational cost that grows with constellation size. In this paper, we derive a Joint Maximum Likelihood (JML) estimator that jointly exploits pilot and data symbols for localization without requiring data decoding, in a passive scenario where a distributed sensing receiver localizes a User Equipment (UE) by exploiting its Orthogonal Frequency-Division Multiplexing (OFDM) communication signal as a signal of opportunity. The optimal solution is derived and shown to be computationally intractable for typical 6G parameters. Two tractable approximations are then proposed, achieving localization performance superior to DD baselines at comparable computational complexity, while remaining constellation-agnostic and yielding substantially lower computational requirements than existing NDA approaches. Furthermore, the proposed estimators are shown to admit a geometric interpretation, providing insight into their intrinsic localization behavior.