# Removing False Targets for Cyclic Prefixed OFDM Sensing with Extended Ranging +
## 1 Introduction  
Integrated sensing and communications (ISAC) has attracted extensive attention in the radar and communications community [1, 2, 3, 4, 5, 6, 7, 8]. A key benefit of ISAC is that it can greatly improve cost, energy, and spectral efficiency of wireless systems that require both sensing and communications functions [9]. While there are several ways of realizing ISAC, as reviewed in [10, 11], a relatively easy way is to add a sensing receiver to an existing communication system and perform sensing by reusing the communication waveforms. We refer to this ISAC methodology as the communications-enabled sensing (CES) and focus on it in this work. Interested readers are referred to [12] for a review of CES. Orthogonal frequency-division multiplexing (OFDM) and its variants, e.g., DFT-spread OFDM (DFT-S-OFDM), have been widely studied for CES. In [13], OFDM CES is considered, with a focus on evaluating the impact of radar antenna setups on common communication metrics. Before the work of [13], OFDM radar was extensively studied without considering data communications in general [14]. The ambiguity functions of OFDM radars were intensively studied as well [15, 16, 17, 18, 19, 20]. A milestone CES method was developed in [21], referred to as the classical OFDM sensing (COS). Using a coherent synchronised transceiver, COS removes the cyclic prefix (CP) of each OFDM symbol in the echo signal. Then, it transforms the symbols into the frequency domain, where the communication data symbols modulated onto sub-carriers are removed through point-wise division (PWD). Afterwards, COS performs inverse discrete Fourier transforms (IDFTs) along the sub-carrier dimension and discrete Fourier transforms (DFTs) over the symbol dimension, resulting in a range-Doppler map (RDM). COS has been widely used in the past decade and has become a mainstream for OFDM sensing, particularly in automotive applications [7; 8; 22; 23; 24; 25; 26; 27; 28; 29; 30]. Recent OFDM sensing works, which are based on COS, mainly seek to develop new techniques for improving the RDM quality, such as noise level. The work in [23] increased the overall baseband bandwidth of the OFDM by introducing the stepped carrier techniques. This, hence, improves the range resolution. The work in [24] employed random stepped carriers and the compressed sensing methods to obtain high-resolution RDMs. The works reviewed above typically ignore the intercarrier interference (ICI). In contrast, the work in [25] considered the impact of ICI on OFDM sensing and developed a novel signalling, which repeats the same OFDM symbol over (slow-)time, to facilitate the estimation and suppression of ICI. The phase shift keying was considered in [21], and hence PWD does not have a noise enhancement issue. However, this issue can be prominent when DFT-S-OFDM is performed. This is because signals modulated onto sub-carriers in DFT-S-OFDM can be noise-like and centred around zero. To relieve noise enhancement, the work in [31] proposed to replace PWD with the point-wise product (PWP) and followed the other steps of COS. While COS and PWP-COS fully comply with the underlying communication system, their ranging capability is known to be restricted by the CP duration. Such restriction is relieved by a unified sensing framework (USF) developed in [32] (the unification is based on the feature that the sensing framework can be applied to OFDM, DFT-S-OFDM, and other OFDM-like waveforms, e.g., the orthogonal time-frequency space (OTFS), even with reduced CP (RCP). RCP-OTFS adds a single CP for the signal block that may be equivalent to multiple OFDM symbols. COS and many of its variants cannot work for RCP waveforms). USF segments a block of sensing echo signal as per sensing needs and employs virtual CPs to establish a deterministic relation between the transmitted signal and each segmentation of echo signals. A notable feature of USF is that it can sense a target with the sample delay much greater than CP length (provided there is a sufficient link budget).