EP4666486A1 - Scheduling of resources for sensing and communication systems based on cramer-rao bound for delay and doppler shift - Google Patents

Abstract

The present disclosure relates to allocating wireless time-frequency resources in an integrated sensing and communication system. In particular, a plurality of data transmissions is obtained to be allocated resources, each transmission of the data transmissions being associated with a modulation constellation. The wireless time-frequency resources are allocated to each transmission of the plurality of transmissions based on a Cramér-Rao bound for delay and/or Doppler shift for elements of the time-frequency resources, and, possibly, based on the modulation constellation. This may result in scheduling according to the modulation constellation associated with said data transmission especially if extended modulation is applied.

Description

VE4127 Scheduling of resources for Sensing and Communication Systems based on Cramer-Rao Bound for Delay and Doppler Shift The present disclosure relates generally to wireless communication and in particular to performing resource allocation in time-frequency resources of a wireless sensing and communication system. BACKGROUND The integration of sensing functionality is emerging as a desired feature for future wireless radio access technologies such as beyond fifth generation (5G), sixth generation (6G), and Institute for Electrical and Electronics Engineers, IEEE, 802.11bf. One possible approach for this goal is to utilize a communication waveform for dual functionalities of communication and radar-sensing performance. Several communication systems have been recently based on orthogonal frequency division multiplexing (OFDM). Due to OFDM’s efficient performance under frequency selective channels, robust synchronization, and MIMO support, OFDM continues to be the cornerstone of current wireless communication standards. However, OFDM is not specifically designed to meet sensing requirements of emerging applications. Therefore, further improvements are desired to meet the sensing requirements while maintaining efficient communication performance. SUMMARY Methods and techniques are described herein for facilitating a modulation order-based scheduling taking into account a Cramér-Rao Bound for delay and/or Doppler shift for sensing applications in a communication system. The invention is defined by the independent claims. Some exemplary implementations are provided by the dependent claims. For example, a method is provided for allocating wireless time-frequency resources in an integrated sensing and communication system, the method comprising: obtaining a plurality of data transmissions to be allocated resources; and allocating the wireless time-frequency resources to each transmission of the plurality of transmissions based on a Cramér-Rao bound for delay and/or Doppler shift for elements of the time-frequency resources. VE4127 These and other features and characteristics of the presently disclosed subject matter, as well as the methods of operation and functions of the related elements of structures and the combination of parts and economies of manufacture, will become more apparent upon consideration of the following description and the appended claims with reference to the accompanying drawings, all of which form a part of this specification. It is to be expressly understood, however, that the drawings are for the purpose of illustration and description only and are not intended as a definition of the limits of the disclosed subject matter. As used in the specification and the claims, the singular form of “a,” “an,” and “the” include plural referents unless the context clearly dictates otherwise. BRIEF DESCRIPTION OF DRAWINGS An understanding of the nature and advantages of various embodiments may be realized by reference to the following figures. FIG.1 is a block diagram illustrating a communication and/or sensing system with a transmitter and a receiver. FIG.2 is a schematic drawing illustrating a time-frequency domain of the communication and/or sensing system. FIG.3 is a block diagram illustrating exemplary devices and signals exchanged between them in a communication and sensing system. FIG.4 is a schematic drawing illustrating a 4-QAM constellation diagram. FIG.5 is a schematic drawing illustrating a 16-QAM constellation diagram. FIG.6 is a schematic drawing illustrating a Cramér-Rao Bound calculated for a time- frequency domain specifically for delay, for Doppler shift, and for both delay and Doppler shift. FIG.7 is a block diagram illustrating an exemplary scheduling apparatus structure. FIG.8 is a block diagram illustrating an exemplary functional structure of a memory module of the scheduling apparatus. FIG.9 is a flow diagram showing an exemplary method for scheduling taking into account the Cramér-Rao Bound. VE4127 FIG.10 is a schematic drawing illustrating an extended 4-QAM constellation diagram. FIG.11 is a schematic drawing illustrating an extended 16-QAM constellation diagram. FIG.12 is a flow diagram illustrating a method for scheduling based on the Cramér-Rao Bound and a modulation order. FIG.13 is a schematic drawing illustrating an equal distribution of data transmissions (users) onto the time-frequency resources. FIG.14 is a schematic drawing illustrating of scheduling of data transmissions (users) onto the time-frequency resources based on the delay CRB. FIG.15 is a schematic drawing illustrating of scheduling of data transmissions (users) onto the time-frequency resources based on the Doppler CRB. FIG.16 is a schematic drawing illustrating of scheduling of data transmissions (users) onto the time-frequency resources based on the delay and Doppler CRB. Like reference numbers and symbols in the various figures indicate like elements, in accordance with certain example implementations. DETAILED DESCRIPTION For purposes of the description hereinafter, the terms “end,” “upper,” “lower,” “right,” “left,” “vertical,” “horizontal,” “top,” “bottom,” “lateral,” “longitudinal,” and derivatives thereof shall relate to the disclosed subject matter as it is oriented in the drawing figures. However, it is to be understood that the disclosed subject matter may assume various alternative variations and step sequences, except where expressly specified to the contrary. It is also to be understood that the specific devices and processes illustrated in the attached drawings, and described in the following specification, are simply exemplary embodiments or aspects of the disclosed subject matter. Hence, specific dimensions and other physical characteristics related to the embodiments or aspects disclosed herein are not to be considered as limiting unless otherwise indicated. No aspect, component, element, structure, act, step, function, instruction, and/or the like used herein should be construed as critical or essential unless explicitly described as such. Also, as used herein, the articles “a” and “an” are intended to include one or more items and may be used interchangeably with “one or more” and “at least one.” Furthermore, as used herein, the term “set” is intended to include one or more items (e.g., related items, unrelated items, a VE4127 combination of related and unrelated items, and/or the like) and may be used interchangeably with “one or more” or “at least one.” Where only one item is intended, the term “one” or similar language is used. Also, as used herein, the terms “has,” “have,” “having,” or the like are intended to be open-ended terms. Further, the phrase “based on” is intended to mean “based at least partially on” unless explicitly stated otherwise. Communication and sensing system For radar-sensing applications, parameters of delay, Doppler shift, and angle have been taken into consideration. The angle parameter (angle of arrival and/or angle of departure) depends on the size and design of antenna array. On the other hand, estimation accuracy of the delay and Doppler shift parameters depends on the time and frequency design of the waveform. Therefore, if a single antenna is considered, the waveform design goal for dual-functional radar-communications (DFRC) is to optimize the time and frequency shape of the waveform. In literature, Cramér-Rao bound (CRB) has been considered for improving the estimation accuracy of the delay and Doppler shift parameters. Some techniques have been developed to improve the CRB of OFDM waveform for dual- functional radar-communications. In particular, The CRB has been used to optimize the subcarriers power levels in the time and frequency domain. For instance, a radar-optimal waveform design may be provided to minimize the CRB on delay-Doppler estimation, subject to an integrated side-lobe level (ISL) constraint in the delay-Doppler ambiguity domain. Then, the problem of DFRC trade-off waveform design may be investigated to optimize the communications rate under radar similarity constraint. The CRB optimization may be performed by optimizing the power levels of the subcarriers with channel state information at the transceiver and a feedforwarding signaling to a receiver. In some works, the minimization of CRB is obtained by filling the empty subcarriers within an OFDM frame with optimized samples while reallocating a proportion of a communication subcarriers’ power, which essentially controls the fairness between the two functionalities. Both communication and filled radar subcarriers are used for radar-sensing processing. In some other works, the CRB minimization is obtained by exploiting a constellation extension of quadrature amplitude modulation (QAM) to achieve a better estimation accuracy of delay and Doppler parameters without requiring the feedforwarding signaling and radar subcarrier reservation. Thus, it may provide a spectrally efficient and communication along with some CRB optimization for conventional OFDM systems. However, these approaches are mainly aimed at a general and static system design. VE4127 Fig.1 illustrates an exemplary communication system CS in which Tx represents a transmitter and Rx represents a receiver. The transmitter Tx is capable of transmitting a signal to the receiver Rx over an interface Intf. The interface Intf may be, for instance, a wireless interface. The interface may be specified by means of resources, which can be used for the transmission and reception by the transmitter Tx and the receiver Rx. Such resources may be defined in one or more (or all) of the time domain, frequency domain, code domain, and space domain. It is noted that in general, the “transmitter” and “receiver” may be also both integrated in the same device. In other words, the devices Tx and Rx in Fig.1 may respectively also include the functionality of the Rx and Tx. The present disclosure is not limited to any particular transmitter Tx, receiver Rx and/or interface Intf implementation. However, it may be applied readily to some existing communication systems as well as to the extensions of such systems, or to new communication systems. Exemplary existing communication systems may be, for instance the 5G New Radio (NR) in its current or future releases, and/or the IEEE 802.11 based systems such as the recently studied IEEE 802.11be or the like. Moreover, the transmitter and/or the receiver may support sensing. For example, the interface Intf may be a common communication and sensing interface. In joint communication and sensing system, the communication signals are also used for the sensing. Fig.2 illustrates a time and frequency domain 200 of the waveform such as a waveform at an interface Intf of an Integrated Sensing and Communication (ISAC) transceiver. The term “transceiver” herein refers to an apparatus that has a transmitting and/or receiving capability. For example, transmitter Tx and receiver Rx mentioned above may be referred to as transceivers. In addition, transmitter Tx may also have receiving capability and receiver Rx may also have receiving capability. The time and frequency domain 200 spans in a frequency domain 201 and in a time domain 202. In this in the ISAC system there are ^ subcarriers in the frequency domain 201 and ^ symbols (forming a frame) in the time domain 202 where ^ = 1,2, … , ^ and ^ = 1,2, … , ^. An ^-th subcarrier of ^-th symbol defines a resource element in which a modulated data symbol 203 is carried. Waveform (in the time domain 202) of such time-frequency domain 200 is obtained by inversely transforming the N subcarriers of one time domain symbol and doing this for all the time domain symbols of the frame. In some systems, as a waveform, cyclic prefix orthogonal frequency division (CP-OFDM) has been employed, but other waveforms can be also used. Therefore, ^ and ^ may represent one OFDM subcarrier in the frequency domain and CP-OFDM symbol in the time domain, respectively. VE4127 The time-frequency domain 200 with the size of ^ × ^ resource elements may be filled with modulated data symbols (such as 203). The modulated data symbols may be modulated with a modulation such as Quadrature Amplitude Modulation, QAM, scheme, or another modulation. An exemplary system model including a plurality of devices that may implement communication and/or sensing capabilities is shown in Fig.3. The system model includes an ISAC transceiver 101 (e.g. here shown with a single antenna), transmitted communication signals 102, a target 105 for sensing, a signal 103 reflected from the target, and a communication user 104 (e.g. here shown with a single antenna). The ISAC transceiver 101 broadcasts a signal to communication users 1 to K (among them User 1, 104) and receives the reflected signal 103 from the target 105 to estimate a range and/or a velocity of the target 105. There may be more targets in addition to the target 105 in the system model. One target 105 is referred to herein for the simplicity of explanation. For the communication, ^ users which may employ modulations with mutually different modulation order are considered, and this is represented in Fig.3 as User k, ^ = 1,2, … ^. As the modulation, QAM is described herein. However, the present disclosure is not limited to using the QAM, and a different modulation scheme can also be employed by the users. The reason of exemplarily selecting QAM modulation is that it has been widely used in many wireless standards like fourth generation (4G), 5G, and Wireless Local Area Network (WLAN) family standards (IEEE 802.11 standard family). The order of the QAM is referred to as ^. In an adaptive modulation and coding scheme, a modulation order is assigned to users dynamically according to their current channel quality. If they have a good channel quality, a higher modulation order is selected for their data transmission resulting in a higher data rate. If on the other hand they have a bad channel quality, a lower modulation order is selected for their data transmission resulting in a lower data rate, but to a higher error resilience. Constellation diagrams of a 4-QAM (D=4) and a 16-QAM (D=16) are illustrated in Figs.4 and 5. In particular, Fig. 4 shows a 4-QAM constellation diagram 300 and a (modulation) data symbol 300 of the 4-QAM. Fig. 5 shows a 16-QAM constellation diagram 350 and a (modulation) data symbol 304 of the 16-QAM. As can be seen, constellation diagram 300 of the 4-QAM consists of four constellation points whereas constellation diagram 350 of the 16- QAM consists of sixteen constellation 4-QAM and 16-QAM are merely exemplary, modulations of other orders may be used (e.g.32-QAM, 64-QAM, 128-QAM, or the like) or modulations of other types may be used (e.g. Quadrature Phase Shift Keying, QPSK such as 8-PSK, 16-PSK, or the like) alternatively or in addition. VE4127 The in-phase and quadrature coordinates of the data symbols (illustrated by the constellation points) are represented on the horizontal and vertical axis on the constellation diagram, respectively. Constellation points L of a ^-QAM are defined as ^ = {±(2^ + 1) ± (2^ + 1)^} with ^ = {0, 1, ... , √^/2 − 1}. The data symbols of ^-QAM constellation have the average power of ^_^ and a normalization factor is calculated as _^(2 (D − 1) /3). The normalization factor is used to divide ^_^. It is noted that the constellation points are associated with respective e.g. binary data symbol values. The binary data symbol values (not shown in Figs.4 and 5) of a ^-QAM constellation have the length of √D bits. For DFRC systems, it is desirable to further improve the OFDM to meet sensing requirements for the determined delay and Doppler accuracies. For this purpose, different power enhancement methods of the subcarriers have been developed to minimize the CRB. In the present disclosure, a modulation order-based scheduling is provided in relation with a CRB reduction. Conventionally, a user scheduling is performed to maximize a capacity by exploiting a knowledge of Channel State Information (CSI) of users at the transmitter. The CSI is typically fed back to the transmitter Tx by a receiver Rx by way of side information (signaling). The approaches described herein do not require availability of CSIs for the users. The scheduling may operate based on knowledge of modulation order of users at the transmitter, which is usually available without additional signaling. In particular, in some embodiments, a scheduling device (e.g. ISAC transceiver 101) schedules the users with different modulation orders to reduce the Cramér-Rao Bound (CRB) for a better sensing estimation accuracy. The subcarriers in the time-frequency domain 200 do not contribute equally to CRB minimization and taking into account a varying modulation order of the subcarriers may help optimizing the CRB further. Moreover, such scheduling may be advantageously implemented for some further CRB minimization such as employing waveform design with a constellation extension. The CRB minimization depends on power levels of the subcarriers in the time and frequency domain. Since different ^-QAM modulations have different power levels, scheduling these modulated data symbols into a different resources in the time and frequency domain of the waveform can change CRB value. The subcarriers in the time and frequency domain of the waveform do not equally contribute to the CRB minimization. This is illustrated in Fig.6. In particular, Fig.6 shows CRB calculated for the time-frequency domain resource elements (in which the respective data symbols may be carried). The effect of each subcarrier on a delay CRB is denoted 401. The effect of each subcarrier on a Doppler CRB is denoted 402. The effect of each subcarrier on both a delay and Doppler CRB is denoted 403. In the present disclosure, these effects are exploited for user scheduling. VE4127 In particular, according to an embodiment, a device is provided for allocating wireless time- frequency resources in an integrated sensing and communication system. An example of such device 700 is illustrated in Fig.7. The device comprises processing circuitry 720. The device may be a scheduling device that schedules multiple users and/or multiple data transmissions of one or more users. Thus, the scheduling device may be for example a base station such as a Node B (eNB in 4G, gNB in 5G, or the like) or an Access Point (AP) in a WLAN, or a similar communication infrastructure device. The scheduling functionality may be implemented in a user equipment (UE) or STA, so that a UE or a STA may be the scheduling device. The present disclosure is not limited to any particular standardized device 700 and may also be implemented in proprietary communication and sensing systems. The processing circuitry 720 is configured to obtain a plurality of data transmissions to be allocated resources. As mentioned above, the data transmissions may be data transmissions of one or more users. A data transmission here is a certain sequence of bits that are to be transmitted or received wirelessly by the device 700. The actual transmission or reception of the physical signals (waveforms) is perform by a wireless transceiver 730, which may be also comprised by the device 700. Each transmission of the data transmissions is associated with a modulation constellation. When referring to modulation constellation herein, included is modulation order and/or modulation type. In one exemplary implementation, each transmission of the data transmissions is associated with a modulation order, wherein the modulation type remains the same (e.g. QAM). In another exemplary implementation, the modulation type may vary, too: for example, QAM and/or QPSK or the like; with or without extension may be used. It is noted that the data transmissions may correspond to respective user transmissions, in systems or system configurations in which a user has the same modulation constellation for all his/her transmissions. The processing circuitry 720 is further configured to allocate the wireless time-frequency resources to each transmission of the plurality of transmissions based on a Cramér-Rao bound for delay and/or Doppler shift for elements of the time-frequency resources. In some embodiments, the allocation is also performed based on the modulation constellation associated with said data transmission. By considering the CRB for delay and/or shift in scheduling the data transmissions, sensing performance and thus overall performance if the joint sensing and communication system may be improved. VE4127 As mentioned above, the device 700 may further comprise a transceiver configured to transmit or receive the data transmissions in the allocated wireless time-frequency resources. The transceiver may be controlled by the processing circuitry 720 to transmit or receive the data transmissions. As is illustrated in Fig.7, the device 700 may further comprise a bus 701 over which the processing circuitry 720 may communicate with the transceiver 730 and possible other components. The possible other components may include a memory 710. The memory may store program code, which when executed on the processing circuitry 720, configures the processing circuitry as mentioned above. Fig.8 shows a functional structure of the memory 710. In particular, the memory 710 may comprise a CRB estimation module that includes code used to provide the CRB and an allocation module 780 including code used to allocate the resources based on the CRB and a modulation order. The processing circuitry 720 may communicate with the memory over the bus 701. It is noted that Fig.7 is simplified. The processing circuitry may include one or more processors and/or programmable hardware or application specific hardware which may be integrated on one chip or separated. The memory may be integrated on a chip together with the processing circuitry 720 or with one or more of its portions; or the memory 710 may be integrated separately from the processing circuitry 720. The memory 710 may be a volatile memory or a non-volatile memory. The device 700 may further comprise a user interface 740 enabling a user to enter some parameters and/or to obtain state of the device 700. However, such user interface is not necessary for operation of the device 700. It is noted that the device 700 is only exemplary. The present disclosure is not limited to any particular device structure. Correspondingly, methods are provided that include steps described herein as performed by some particular modules of the device 700. Fig.9 illustrates a flow diagram 500 of a method for waveform design for a joint communication and sensing system. The processing circuitry 720 may be configured to perform these steps. Accordingly, the allocating of resources mentioned above comprises a step 501 of determining a plurality, S, of allocation patterns of the plurality of data transmissions in the wireless time- frequency resources. An allocation pattern may specify which data transmission are located in (assign to) which resources. The resources may be specified by way of resource elements or by way of other resource units comprising a plurality of resource elements in the time- frequency grid. The allocation pattern may be referred to as a scheduling case, representing a possible scheduling outcome. In other words, S allocation patterns may correspond to S possible outcomes of resource allocation for the obtained data transmissions. The obtained transmissions may be K different transmissions of respective K different users as is indicated in Fig.9, step 501. However, as mentioned above, in general, the data transmissions may be VE4127 or include plural transmissions of a same user. The S allocation patterns may include all possible allocation patterns. However, this may be practically computationally complex. Thus, the S allocation patterns may be a predetermined subset of all possible allocation patterns. The allocating of resources mentioned above further comprises step 502 of calculating the Cramér-Rao bound for delay and/or Doppler shift for each allocation pattern of the S allocation patterns. An index of an allocation pattern among the S allocation patterns is denoted as s and numbered from 0 to S-1. The subcarrier (more precisely resource element) power levels for the ^-th scheduling case in the time and frequency domain is denoted as ^^{(^)}. The allocating of resources mentioned above further comprises step 503 of allocating the wireless time-frequency resources according to that allocation pattern which has the Cramér- Rao bound for delay and/or Doppler shift lowest among the S allocation patterns. Thus, the CRB optimization may be used to or contribute to perform scheduling of resources in a joint wireless sensing and communication. More specifically, in some exemplary implementations, an allocation pattern specifies power for respective elements of the time-frequency resources resulting from the modulation constellation. For example, power differences only due to modulation constellation differences (e.g. difference in modulation order) may be considered. As mentioned above, data symbols may have different power levels due to different modulation orders. This example may consider that all K users (data transmissions) have same average power. Therefore, there would be no power difference apart from the difference due to the modulation constellation. As deduced from the CRB calculation, the waveform design with minimum CRB can be achieved with optimizing the power matrix ^. Although increasing the power levels for the resource elements in ^ decrease the CRB, the effects of the resource elements in the minimization is not same. Therefore, it may be advantageous to distribute the power according to an impact of the respective resource elements on the CRB minimization. On the other hand, embodiments of the present disclosure envisage to schedule the K users or data transmissions for a better CRB minimization, i.e. to determine location of the resources allocates to each of the K users or data transmissions within the time-frequency grid according to the CRB. Accordingly, even if all K users had the same average power, different scheduling cases may lead to different CRB values. Thus, scheduling based on modulation constellation can contribute to reducing the CRB. The reason is the data symbols of e.g. a QAM modulation have different power levels so that changing their location in the time-frequency domain may affects the CRB minimization. VE4127 However, the present disclosure is not limited to considering power differences only due to modulation order or type for the CRB determination. In an exemplary implementation, an allocation pattern specifies power for respective elements of the time-frequency resources resulting from the modulation constellation and a preconfigured power factor associated with the data transmission. In other words, the data transmissions (or users) can have different average power levels. As mentioned with reference to Fig. 9, step 501 determines the total number of scheduling cases (^) for ^ users in the time and frequency domain. In some implementations, the scheduling only changes the locations of the users in the time and frequency domain. In other words, the S scheduling cases (allocation patterns) differ from each other only by allocating to a user (data transmission) resource elements in different locations within the time-frequency resource grid. In other implementations, the S scheduling cases also differ by further parameters, such as (average) power and/or antenna direction or the like. The S scheduling cases may be generated according to a predefined algorithm. It is noted that the predefined algorithm may also determine the number S of the scheduling cases. Then, the CRBs of delay, Doppler, or joint delay and Doppler is calculated for each scheduling case of the S scheduling cases in step 502. Afterwards, the best scheduling case among the ^ scheduling cases is selected in step 503, taking into account CBR. Step 503 may select the scheduling case with the lowest CBR. However, the present disclosure is not limited thereto. In general, the best scheduling case may be determined by minimizing a cost function in which the CRB is included and which includes one or more further parameters (e.g. priorities of the users or data transmissions, interference, etc.). It is noted that the above mentioned approach of testing different allocation patterns and selecting the best one taking into account its CRB may be time consuming in case all possible allocation patterns are tested. Thus, a limited number S of the allocation patterns may be tested, smaller than the number of all possible allocation patters. In some embodiments, such testing may be disposed of and the best allocation patterns may be found in accordance with a predefined approach taking into account the modulation order. A waveform design with constellation extension may enhance the power levels of outer data symbols of a ^-QAM constellation to further delay and/or Doppler CRB. The waveform design with constellation extension for 4-QAM and 16-QAM is represented in Figs.10 and 11. In particular, Fig.10 shows a 4-QAM constellation diagram 601 and therein a data symbol 603 of the 4-QAM, as well as a power enhanced data symbol 605 of the enhanced 4-QAM. Fig.11 shows a 16-QAM constellation diagram 602, and therein a data symbol 604 of 16-QAM, as well as a power enhanced data symbol 606 of the enhanced 16-QAM. In an extended QAM modulation scheme, the power levels of (only) outer data symbols of ^- QAM are enhanced up to a maximum power limit ^_^^^. This facilitates minimizing the CRBs. As can be inferred from Figs. 10 and 11, a probability (frequency of occurrence) of a data symbol for the power enhancement in a D-QAM decreases with the increase in modulation order D. For instance, the power levels of all data symbols of the 4-QAM can be enhanced, because they all correspond to outer constellation points. On the other hand, the power levels of only 12 data symbols out of all 16 data symbols can be enhanced up to ^_^^^. This is because out of the 16 constellation points, in 16-QAM, only 12 are outer constellation points. In general, the probability of a data symbol for the power enhancement in a QAM modulation with order D can be formulated as (4_√^ − 4)/^. Therefore, a CRB can be minimized better with low modulation orders, if there is no total power limitation. If there is a total power limitation, this may not apply. The power enhancement (or extension of a constellation) of the subcarriers with low order modulations may require more extra power compared to higher modulation orders. Therefore, the number of empowered subcarriers can be lower if there is a power limitation. For instance, the power level of the outer data symbols on a low and a high modulation order are 1 and 1.5, and maximum power and power limitations are 2 and 4, respectively. In this example, the maximum power limitation for different modulation may differ, because the power level of outer data symbols in constellations can be different even if they have the same average power. If modulation order increases, the power levels of the outer data symbols thus become larger compared to the power levels of the outer data symbols with low modulation order while they still have a same average power. In this case, the power level of 4 (4*1) subcarriers can be increased for low modulation order but 8 (8*0.5) subcarriers for high modulation order. Therefore, the number of empower subcarriers can be more for high order modulations. This example is further detailed below. In the constellation extension method, the power levels of the outer data symbols in the constellation are increased to the maximum power level ^_^^^. as shown in Figs.10 and 11. Therefore, extra power is used for this extension. The of the outer data symbols in two different constellations can be determined. For simplicity, the power levels of the outer points are taken as 1 and 1.5 above, for low and high order modulations, respectively. In the constellation extension approach, the power levels of the outer data symbols are increased to the maximum power level ^_^^^.. Assume that ^_^^^. = 2. Therefore, 1 power unit is needed to increase the power level 1 to ^_^^^. = 2, and 0.5 power unit is needed to increase the power level 1.5 to ^_^^^. = 2. Here, it is emphasized that there are different power increments for the constellation extension of different constellations. Therefore, if there is a total power limitation, the total number of subcarriers that apply the constellation extension differ. Assuming that the power limitation is 4 so that this power can be used for constellation extension, since 1 and 0.5 power units are necessary for an outer data symbols of low and high modulation orders, the constellation extension with power limitation 4 can be applied for 4 (4*1=4) and (8*0.5=4) subcarriers, respectively. As inferred from this example, the total number of subcarriers with constellation extension for higher modulation order can be larger than lower modulation order. On the other hand, note that if there is no power limitation, the total number of subcarriers with constellation extension for lower modulation order is larger than higher modulation order. Therefore, the CRBs can be minimized better with high modulation orders if there is a total power limitation. Note that if the total transmit power is enough to enhance all possible (outer) data symbols of a ^-QAM in the time-frequency domain, the CRBs is minimized better with low modulation orders. The minimization performance thus changes according to the modulation order ^ when using the extended modulation. For instance, while power levels of all data symbols of a 4-QAM can be enhanced, the power levels of only 12 data symbols out of 16 data symbols can be enhanced. Therefore, the ratio of suitable data symbols for the power enhancement to all data symbols decreases with larger modulation order ^. For this reason, the location of the subcarriers in the time and frequency domain may be relevant for a better CRB minimization. Thus, the channel qualities of K users (in general, K data transmissions) are expected to be in the order of: 1. ^^^^ > 2. ^^^^ > … > ^. ^^^^. This may be due to the different distances of the K users to an ISAC transceiver 101 as illustrated in Fig.3. For this reason, the modulation order of these users may be ordered as ^_^ > ^_^ > .. > ^_^, where ^_^ represents the modulation order of ^-the user. For instance, if there are three communication users in the system, they may have the 64-QAM, 16-QAM, and 4-QAM for first user, second user, and third user, respectively. In general, it is assumed that the K users have K different modulation orders. The higher the quality, the higher the modulation order. It is noted that the may be impacted by other factors than the above mentioned distance from the transceiver 101. To improve accuracies of range and velocity estimation, CRB has been widely taken into consideration. This parameter determines the accuracy level of range and velocity estimation. VE4127 If the CRB is high, a worse accuracy performance is expected. Therefore, it is advantageous to decrease the CRB parameter for a better radar-sensing performance. This parameter depends on the power profile of the time-frequency domain. Thus, the power levels of subcarriers in the time-frequency domain may be optimized for an optimum CRB reduction. The waveform design to increase the radar performance by minimizing the CRB of delay and/or Doppler profits from a proper power allocation. Power levels of respective data symbols (resource elements) in the time-frequency domain are represented by matrix ^, and the vector form of ^ is denoted as ^ ≜vec (^). Then, the CRBs of unbiased estimates ^̂ and ^̂ for delay and Doppler estimation respectively in a single target case can be calculated as: 1 (^^{^} ^)( ^^{^}^_^^) ^^^(^̂) ≥ ^_^ = ^{^ ^} ^, 2^_^ ( ^ ^_^^)( ^ ^_^^) − ( ^^{^}^_^^^) ^^^(^̂ ^, where ^_^ ≜ 2^∆^(^_^ ^^_^), ^_^ ≜ 2^^_^^_^(^_^ ^^_^), ^_^ ≜ (^_^ ^^_^)^^ ^_^ − ^_^^_^ ^{^}, ^_^ ≜ (^_^ ^^_^)^^ ^_^ − ^_^^_^ ^{^}, ^_^^ ≜ (^_^ ^^_^)^^ ^_^ − ^_^^_^ ^{^}. Here, ^_^ is the signal-to- (SNR) at a radar receiver 101, ∆^ is a subcarrier spacing, ^_^ is a carrier frequency, ^_^ is a CP-OFDM symbol duration (or in general a duration of a time- frequency symbol), and ^_^ = [0, 1, ... , ^ − 1]. Symbols (. )^ and (. )^ denote transposition and Hermitian transposition, respectively. Symbols ⊙ and ⊗ denote the Hadamard and tensor product, respectively. ^_^ is one vector with the size of M. As seen from above equations, the CRBs on ^, ^_^, ∆^, ^_^, and ^_^. Since the parameters of ^_^, ∆^, ^_^, and ^_^ are system parameters, in a target delay and Doppler estimation, only ^ is changed for the CRB minimization in the waveform design. P is a matrix with the size of NxM. VE4127 Therefore, each element in the matrix corresponds to a power level of a respective resource element (subcarrier of a time-domain symbol) in the time-frequency domain. According to the above CRB formulas, the effect of each subcarrier on delay CRB, Doppler CRB, and joint delay and Doppler CRB are shown in the above mentioned Fig.4. The power increment effect of the subcarrier in the time-frequency domain for delay CRB (401), for Doppler CRB (402), and for joint delay and Doppler CRBs (403) shows that each subcarrier has a different contribution on CRB minimization. For instance, edge subcarriers are more effective for the delay CRB minimization, edge OFDM symbols are more effective for the Doppler minimization, and edge subcarriers and edge OFDM symbols are more effective for joint delay and Doppler CRBs minimization. For the joint CRB optimization, ^^_^ + (1 − ^)^_^ is minimized, where ^ denotes a predetermined weighting factor for delay and Doppler estimation. Therefore, the weighting matrix according to their effect on CRB minimization can be generated as ^ with the size of ^ × ^. Therefore, the (n, m)-th element in ^ denotes a weighting factor of n-the subcarrier of m-the OFDM symbol on CRB minimization. The CRB weight factor matrices of delay, Doppler, and joint delay and Doppler are denoted by ^_^, ^_^, and ^_^^, respectively. The matrix ^ ∈ ℝ^{^×^} of the weight factors is obtained based on the CRB minimization of each subcarrier as follows: Firstly, the system parameters of ^_^, ∆^, ^_^, ^_^, N, M, ^_^^^ and ^ are determined. If the system parameters are constant for a different frame generation, same ^ matrix can be used to select the subcarrier indices for CRB minimization. For a fair evaluation, a unit power level is assigned to all subcarriers in the beginning as ^^{^} = ^_^×^. Then, the power level of the n-th subcarrier of the m-th OFDM symbol is increased to ^_^^^ as ^^{^} (^, ^) = ^_^^^ . Next, the ^^{^} matrix is vectorized to ^ ≜ vec(^^{^}). Afterwards, according to the minimization problem, the weight factor for the n-th subcarrier of the m-th OFDM symbol is found as ^(^, ^) = ^ ^_^ + (1 − ^ ) ^_^ with ^. Note that only one element with ^_^^^ is available in ^, and other elements have unit power level for each iteration. After finding the weight factors for each subcarrier indices in the frame, the matrix ^ is formed. Since the matrix ^ indicates the performance of CRB minimization for the subcarrier indices, the indices with lower values in ^ are more efficient for the minimization problem. For the matrices of ^_^, ^_^, and ^_^^, the value ^ is taken as 1, 0, and 0 < ^ < 1, respectively. Since the information of an employed order for the K communication users 104 is available at an ISAC transceiver 101 and since each subcarrier with a modulation order in the time-frequency domain may have a different impact on the CRB performance, a user scheduling based CRB reduction can be performed. An exemplary scheduling process is VE4127 summarized in Fig. 12. Firstly, the weight matrix ^ of CRB minimization is generated. This matrix can be generated by considering only the delay CRB minimization, only the Doppler CRB minimization, and a joint delay and Doppler CRB minimization as ^_^, ^_^, and ^_^^, respectively in step 801. For the calculation of these matrices, the formulas of ^_^, ^_^, and ^^_^ + (1 − ^)^_^ are used respectively. There may be different users a same modulation order. For the purposes of this exemplary scheduling process, they are considered as one user. As the invention makes resource scheduling according to the modulation order (or in general type), sharing resources of a modulation order among multiple users has no further effect on this process. The mapping of the data transmissions (or users) with the same modulation may be performed according to any known allocation / scheduling approach. The subcarrier indices according to ^_^, ^_^, and ^_^^ are represented as ^_^, ^_^, and ^_^^ in step 802. For this, the elements of ^_^, ^_^, and ^_^^ are ordered and the indices of the ordered elements are represented by the vectors of ^_^, ^_^, and ^_^^. The order of the elements can be, e.g., from a largest to a smallest or from a smallest to a largest element. Next, these vectors are divided into ^ subvectors in step 803. Afterwards, ^_^,^, ^_^,^, and ^_^^,^ denote the subcarrier indices for the k-the user for delay CRB minimization, Doppler CRB minimization, and joint delay and Doppler CRB minimization, respectively in step 804. Note that the modulation order of users is ordered from largest to smallest as mentioned above and correspondingly to ordering of the users from the user with highest quality (User 1) to the user with lowest quality (User K). Therefore, if there are three users in the communication and sensing network, the modulation order of first, second, and third user can be 64-QAM, 16-QAM, and QPSK, respectively. In other words, ^ denotes a different modulation order and when ^ increases the modulation order ^ decreases. After the scheduling is completed, the waveform design with constellation extension is applied for all subcarriers in 805. To understand this scheduling mechanism, a simplified example for delay CRB minimization is provided. For Doppler CRB minimization and joint delay and Doppler CRB minimization, the processes are similar. Assume the ^_^ matrix as 0.5 0.4 0.5 ^_^ = ^ 0.3 0.2 0.3 ^. 0.5 0.4 0.5 Then, ^_^ is converted into ^_^ in descending order as ^_{^ =} ⁽ _{1,1 1,3} ^{3,1 3,3 2,1 2,3 1,2 3,2} _2,2 ⁾^ VE4127 where the first and second parts of the element denote vertical and horizontal indices of the element within the matrix. The ordering can be also in ascending order, the present disclosure is not limited in this respect. In the case of ^ = 2 (2 different modulation orders corresponding to 2 different data transmissions or users), the subgrouping may be performed as follows: ^_^,^ = ⁽1,1 1,3 3,1 3,3 2,1^{)^}, and ^_^,^ = ⁽2,3 1,2 3,2 2,2^{)^}. As seen from the ^_^,^ and ^_^,^, as the matrix has 9 elements the sharing of elements between the users is unequal in this example. It is noted that the elements may generally be shared equally or unequally between the users. This may depend also on the amount of data to be scheduled for different users. Afterwards, the subcarrier indices according to ^_^,^ are assigned to second user, and the subcarrier indices according to ^_^,^ are assigned to first user. First and second users may use the modulation order of 16-QAM and 4-QAM, respectively. Thus, the allocating comprises obtaining 801 the Cramér-Rao bound for delay and/or Doppler shift for resource elements of the time-frequency resources. This is performed based on the power profile of the resource elements of the time-frequency resources. The allocation process further comprises obtaining a first data transmission and a second data transmission of said plurality of data transmissions, wherein the first data transmission is associated with a modulation constellation having an order higher than an order of a modulation associated with the second data transmission. Then, elements of the time-frequency resources are allocated to the first data transmission and to the second data transmission, wherein elements of the time-frequency resources allocated to the second data transmission have the Cramér-Rao bound higher than elements allocated to the first data transmission. In general, the allocating may comprise the obtaining of the Cramér-Rao bound for delay and/or Doppler shift for elements of the time-frequency resources and obtaining ordered data transmissions including ordering the plurality of data transmissions according to a modulation order of the modulation constellations associated with the respective data transmissions. The allocating may further comprise obtaining ordered resource elements including ordering the elements of the time-frequency resources according to the obtained Cramér-Rao bound; and mapping the ordered data transmissions to the ordered resource elements so that the data transmissions with highest modulation order assigned to resource elements with highest Cramér-Rao bound. VE4127 In some exemplary implementations, said modulation constellation is a Quadrature Amplitude Modulation, QAM, constellation; wherein the modulation constellations of at least two data transmissions amount the plurality of data transmissions differ in order. As mentioned above, the QAM constellation may be a QAM with enhanced power in which the outer constellation points lay on a circle or an ellipse. If the users are scheduled as described above, the waveform design with constellation extension may be improved. The user scheduling result examples for delay, Doppler, and joint delay and Doppler CRB minimization are illustrated in Figs.13 to 16, under an assumption that the total transmit power is sufficient to empower all suitable subcarriers or there is not a total transmit power limitation. Consider the information of a used modulation order of communication users 104 is available at the ISAC transceiver 101. If the channel state information (CSI) is also available at the ISAC transmitter 101 a channel-based scheduling of the communication users may be performed to maximize the capacity. However, if only information of the used modulation order of communication users 104 is available, the channel-based scheduling may be difficult. Therefore, the communication users 104 would be scheduled in the time-frequency domain with uniform resource allocation as illustrated in Fig.13. Fig.13 shows a frequency domain 701, a time domain 702, a first group 703 of resources for user 1 in the time-frequency domain, the second group 704 of resources for user 2 in the time-frequency domain, and the ^-th group 705 of resources for user K in the time-frequency domain. Although a uniform horizontal grouping is done in Figure 7, a different grouping like vertical or random can be also done. Fig. 14 shows a frequency domain 901 and a time domain 902 with resources allocated to users 1, 2, …, K based on the delay CRB. It further illustrates a first group 903 of resources for user K in the time-frequency domain, a second group 904 of resources for user 2 in the time-frequency domain, and a third group 905 of resources for user 1 in the time-frequency domain. Since edge subcarriers (subcarriers at the edge of the time-frequency resource grid) contribute more to delay CRB minimization (see also Fig.6) and the power-enhancement ratio of the subcarriers is high for lower D values, the subcarrier grouping of users are scheduled from edge subcarriers to inner subcarriers with the order of ^, … , 2, 1 as seen from Fig.14. In particular, user K has resources 903 allocated on the top of the grid and on the bottom of the grid, i.e. at the edges of the frequency domain. User 1 on the other hand, has resources 905 allocated in the inner part of the frequency in this specific example in the middle of the frequency domain. The remaining users (User 2 and further users up to K-1, if any) have resources scheduled between the resources of User 1 and resources of User K. VE4127 Correspondingly, an embodiment of the present disclosure is an allocation pattern for K data transmissions (or users) that differ in modulation order. The allocation pattern allocates the data transmissions according to their modulation order. In particular, the allocation pattern allocates resources at the edges of the frequency domain grid (highest and lowest frequency of the grid) to data transmissions with the lowest modulation order (among the data transmissions to be scheduled). The remaining users are allocated resources away from the edges of the frequency domain towards the centre of the frequency domain in the sequence of their modulation order. Such allocation pattern may reduce the CRB of the delay and thus improve radar performance especially in terms of range accuracy. The scheduler may use this allocation pattern for allocating resources for the K data transmissions. It is noted that a further allocation optimization may take place within the data of the k-th data transmission (user), based on further criteria. The waveform design with power extension modulation can reduce delay CRB further by enhancing the power levels of utilizing more data symbols in the edge subcarriers. Fig. 15 shows a frequency domain 1001 and a time domain 1002-1102 with resources allocated to users 1, 2, …, K based on the Doppler CRB.. It further illustrates the first group 1003 of resources for user K in the time-frequency domain, the second group 1004 of resources for user 2 in the time-frequency domain, and the third group 1005 of resources for user 1 in the time-frequency domain. Since edge symbols (time-domain symbols at the edge of the time-frequency resource grid) contribute more to Doppler shift CRB minimization (see also Fig.6) and the power-enhancement ratio of the subcarriers is high for lower D values, the subcarrier grouping of users are scheduled from edge symbols to inner symbols with the order of ^, … , 2, 1 as seen from Fig.15. In particular, user K has resources 1003 allocated on the left hand side of the grid and on the right hand side of the grid, i.e. at the edges of the time domain. User 1 on the other hand, has resources 1005 allocated in the inner part of the time domain; in this specific example in the middle of the time domain. The remaining users (User 2 and further users up to K-1, if any) have resources scheduled between the resources of User 1 and resources of User K. A corresponding allocation pattern allocates the data transmissions according to their modulation order. In particular, the allocation pattern allocates resources at the edges of the time domain grid (first and last symbols of the frame) to data transmissions with the lowest modulation order (among the data transmissions to be scheduled). The remaining users are allocated resources away from the edges of time domain towards the centre of the time domain in the sequence of their modulation order. Such allocation pattern may reduce the CRB of the Doppler and thus improve radar performance especially in terms of velocity accuracy. VE4127 In summary, since edge OFDM symbols contribute more to Doppler CRB minimization and the power-enhancement ratio of the subcarriers is high for lower D values, the subcarrier groupings of users are scheduled from the edge of the OFDM symbols to inner OFDM symbols with the order of ^, … , 2, 1 as seen in Fig. 15. In this way, the waveform design with modulation extension method can reduce the Doppler CRB further. Fig.16 shows a frequency domain 1101 and a time domain 1102. It further illustrates the first group 1103 of resources for user K in the time-frequency domain, the second group 1104 of resources for user 2 in the time-frequency domain, and the third group 1105 of resources for user 1 in the time-frequency domain. Since edge OFDM symbols and edge subcarriers contribute more to joint delay and Doppler CRB reduction and the power-enhancement ratio of the subcarriers is high for lower D values, the subcarrier grouping of users are scheduled from edge OFDM symbols and edge subcarriers towards inner OFDM symbols and inner subcarriers with the order of ^, … , 2, 1 as seen from Fig.16. In this way, the waveform design with extension method can reduce joint delay and Doppler CRB further by enhancing the power levels of utilizing more data symbols in the edge OFDM symbols and subcarriers. The corresponding allocation patterns allocated users with lowest modulation order the resources in the corners of the time-frequency domain grid and allocates concentrically further users with growing modulation order towards the centre of the resource grid. It is noted that if the total power limitation is not sufficient to enhance the power levels of all possible subcarriers, the user scheduling can be in the order of 1, 2, … , ^ instead of ^, … , 2, 1. The above described embodiments and exemplary implementations do not require any change in wireless standards. Therefore, it can be readily applied directly to any wireless standards such as 4G, 5G, and IEEE 802.11 or beyond. It may improve the CRB minimization of the waveform design especially with constellation extension. The above described embodiments and exemplary implementations may be particularly suitable for vehicular communication where a vehicular system communicates and makes radar-sensing simultaneously with a single waveform such as OFDM. The estimation accuracy of radar-sensing may be improved in WiFi-sensing in the above described manners. Moreover, the present disclosure can be utilized for any transmitter that communicates and makes radar- sensing simultaneously with a single waveform such as OFDM or other orthogonal or non- orthogonal time-frequency resource grid. OFDM is widely used in many wireless standards, the present disclosure can be used in these standards without requiring any modification. VE4127 Implementations in software and hardware It is noted that although embodiments and examples of the present disclosure were provided in terms of a method above, the corresponding devices providing the functionality described by the methods are also provided. Moreover, it is noted that any of the steps described above may be included as code instructions in a program, which may be executed by one or more processors. The methodologies described herein may be implemented by various means depending upon the application. For example, these methodologies may be implemented in hardware, operation system, firmware, software, or any combination of two or all of them. For a hardware implementation, any processing circuitry may be used, which may include one or more processors. For example, the hardware may include one or more of application specific integrated circuits (ASICs), digital signal processors (DSPs), digital signal processing devices (DSPDs), programmable logic devices (PLDs), field programmable gate arrays (FPGAs), processors, controllers, any electronic devices, or other electronic circuitry units or elements designed to perform the functions described above. If implemented as program code, the functions performed by the transmitting apparatus (device) may be stored as one or more instructions or code on a non-transitory computer readable storage medium. The computer-readable media includes physical computer storage media, which may be any available medium that can be accessed by the computer, or, in general by the processing circuitry. Such computer-readable media may comprise RAM, ROM, EEPROM, optical disk storage, magnetic disk storage, semiconductor storage, or other storage devices. Some particular and non-limiting examples include compact disc (CD), CD- ROM, laser disc, optical disc, digital versatile disc (DVD), Blu-ray (BD) disc or the like. Combinations of different storage media are also possible – in other words, distributed and heterogeneous storage may be employed. The above examples are not to limited the present disclosure. There are many modifications and configurations, which may be used in addition or alternatively. This present disclosure can be used in any kind of device that is receiving signals over a wireless channel. The embodiments and exemplary implementations mentioned above show some non-limiting examples. It is understood that various may be made without departing from the claimed subject matter. For example, modifications may be made to adapt the examples to new systems and scenarios without departing from the central concept described herein. VE4127 Selected embodiments and examples Summarizing, embodiments of the present disclosure relate to allocating wireless time- frequency resources in an integrated sensing and communication system. In particular, a plurality of data transmissions is obtained to be allocated resources, each transmission of the data transmissions being associated with a modulation constellation. The wireless time- frequency resources are allocated to each transmission of the plurality of transmissions based on a Cramér-Rao bound for delay and/or Doppler shift for elements of the time-frequency resources, and, possibly, based on the modulation constellation. This may result in scheduling according to the modulation constellation associated with said data transmission especially if extended modulation is applied. According to a first aspect, a method is provided for allocating wireless time-frequency resources in an integrated sensing and communication system, the method comprising: obtaining a plurality of data transmissions to be allocated resources; and allocating the wireless time-frequency resources to each transmission of the plurality of transmissions based on a Cramér-Rao bound for delay and/or Doppler shift for elements of the time-frequency resources. According to a second aspect, further to the first aspect, each transmission of the data transmissions being associated with a modulation constellation; and the allocating the wireless time-frequency resources to each transmission of the plurality of transmissions is based on the modulation constellation associated with said data transmission. According to a third aspect, further to the first or the second aspect, the allocating comprises: determining a plurality, S, of allocation patterns of the plurality of data transmissions in the wireless time-frequency resources; calculating the Cramér-Rao bound for delay and/or Doppler shift for each allocation pattern of the S allocation patterns; and allocating the wireless time-frequency resources according to that allocation pattern which has the Cramér-Rao bound for delay and/or Doppler shift lowest among the S allocation patterns. According to a fourth aspect, further to the third aspect, each allocation pattern specifies power for respective elements of the time-frequency resources resulting from the modulation constellation. According to a fifth aspect, further to the third aspect, each allocation pattern specifies power for respective elements of the time-frequency resources resulting from the modulation constellation and a preconfigured power factor associated with the data transmission. VE4127 According to a sixth aspect, further to any of the first to fifth aspect, the allocating comprises: obtaining the Cramér-Rao bound for delay and/or Doppler shift for elements of the time- frequency resources; obtain a first data transmission and a second data transmission of said plurality of data transmissions, wherein the first data transmission is associated with a modulation constellation having an order higher than an order of a modulation associated with the second data transmission; allocate elements of the time-frequency resources to the first data transmission and to the second data transmission, wherein elements of the time- frequency resources allocated to the second data transmission have the Cramér-Rao bound higher than elements allocated to the first data transmission. According to a seventh aspect, further to any of the first to fifth aspect, the allocating comprises: obtaining the Cramér-Rao bound for delay and/or Doppler shift for elements of the time- frequency resources; obtaining ordered data transmissions including ordering the plurality of data transmissions according to a modulation order of the modulation constellations associated with the respective data transmissions; obtaining ordered resource elements including ordering the elements of the time-frequency resources according to the obtained Cramér-Rao bound; and mapping the ordered data transmissions to the ordered resource elements so that the data transmissions with highest modulation order are assigned to resource elements with highest Cramér-Rao bound. According to an eighth aspect, further to any of the first to seventh aspect, the Cramér-Rao bound ^_^ for delay ^̂ and/or the Cramér-Rao bound ^_^ for Doppler shift ^̂ is calculated as follows: ^^^( ^, 1 (^^{^} ^)( ^^{^}^_^^) ^^^(^̂ ) ≥ ^_^ = ^ ^_^ ^ ^_^ − ( ^ ^_^ ^)^, 2^ ^^{^ ^ ^} _^ wherein ^_^ ≜ (^_^ ^^_^)^^ ^_^ − ^_^^_^ ^{^}, ^_^ ≜ (^_^ ^^_^)^^ ^_^ − ^_^^_^ ^{^}, VE4127 ^_^^ ≜ ⁽^_^ ^^_^ ⁾^^ ^_^ − ^_^^_^ ^{^}, and ^ ≜vec (^); ^ is a power matrix with a size N×M; N is a number of subcarriers in the time- frequency resources; M is a number of symbols in the time-frequency resources of one physical layer frame; ^_^ is the signal-to-noise ratio, SNR, at the radar receiver; ∆^ is the subcarrier spacing; ^_^ is the carrier frequency, ^_^ is the symbol duration; ^_^ = ^[0, 1, ... , ^ − 1^]; (. )^ and (. )^ denote transposition and Hermitian transposition, respectively; ⊙ and ⊗ denote the Hadamard and tensor product, respectively; ^_^ is one vector with the M. According to a ninth aspect, further to any of the first to eight aspect, said modulation constellation is a Quadrature Amplitude Modulation, QAM, constellation; wherein the modulation constellations of at least two data transmissions amount the plurality of data transmissions differ in order. According to a tenth aspect, further to any of the first to ninth aspect, the QAM constellation is a QAM with enhanced power in which the outer constellation points lay on a circle or an ellipse. According to an eleventh aspect, further to any of the first to tenth aspect, the plurality of data transmissions include data transmissions by mutually different users. According to a twelfth aspect, a device is provide for allocating wireless time-frequency resources in an integrated sensing and communication system, the device comprising: processing circuitry configured to: obtain a plurality of data transmissions to be allocated resources; and allocate the wireless time-frequency resources to each transmission of the plurality of transmissions based on a Cramér-Rao bound for delay and/or Doppler shift for elements of the time-frequency resources. According to a thirteenth aspect, further to the twelfth aspect, each transmission of the data transmissions being associated with a modulation constellation; and the allocating the wireless time-frequency resources to each transmission of the plurality of transmissions is based on the modulation constellation associated with said data transmission. According to a fourteenth aspect, further to the twelfth or thirteenth aspect, the device is further comprising a transceiver configured to transmit or receive the data transmissions in the allocated wireless time-frequency resources. According to a fifteenth aspect, further to any the twelfth to fourteenth aspect, the allocating comprises: determining a plurality, S, of allocation patterns of the plurality of data transmissions in the wireless time-frequency resources; calculating the Cramér-Rao bound for delay and/or Doppler shift for each allocation pattern of the S allocation patterns; and allocating the wireless VE4127 time-frequency resources according to that allocation pattern which has the Cramér-Rao bound for delay and/or Doppler shift lowest among the S allocation patterns. According to a sixteenth aspect, further to the fifteenth aspect, each allocation pattern specifies power for respective elements of the time-frequency resources resulting from the modulation constellation. According to a seventeenth aspect, further to the fifteenth aspect, each allocation pattern specifies power for respective elements of the time-frequency resources resulting from the modulation constellation and a preconfigured power factor associated with the data transmission. According to a eigteenth aspect, further to any of the twelfth to seventeenth aspect, the allocating comprises: obtaining the Cramér-Rao bound for delay and/or Doppler shift for elements of the time-frequency resources; obtain a first transmission and a second data transmission of said plurality of data transmissions, wherein the first data transmission is associated with a modulation constellation having an order higher than an order of a modulation associated with the second data transmission; allocate elements of the time- frequency resources to the first data transmission and to the second data transmission, wherein elements of the time-frequency resources allocated to the second data transmission have the Cramér-Rao bound higher than elements allocated to the first data transmission. According to a nineteenth aspect, further to any of the twelfth to eighteenth aspect, the allocating comprises: obtaining the Cramér-Rao bound for delay and/or Doppler shift for elements of the time-frequency resources; obtaining ordered data transmissions including ordering the plurality of data transmissions according to a modulation order of the modulation constellations associated with the respective data transmissions; obtaining ordered resource elements including ordering the elements of the time-frequency resources according to the obtained Cramér-Rao bound; and mapping the ordered data transmissions to the ordered resource elements so that the data transmissions with highest modulation order are assigned to resource elements with highest Cramér-Rao bound. According to a twentieth aspect, the Cramér- Rao bound ^_^ for delay ^̂ shift ^̂ is calculated as follows: 1 (^^{^} ^)( ^^{^}^_^^) ^^^(^̂) ≥ ^_^ = ^ ^{^} _^ )( ^ ^_^^) − ( ^ ^_^^^)^, 2^ ( ^ ^ ^ ^{^ ^} VE4127 1 (^^{^} ^)( ^^{^}^ ^) ^^^(^̂ ) ≥ ^ _{^ ^} = , 2^_^ ( ^^{^}^_^^)( ^^{^}^_^^) − ( ^^{^}^_^^^)^ wherein ^_^ ≜ 2^∆^(^_^ ^^_^), ^_^ ≜ 2^^_^^_^(^_^ ^^_^), ^_^ ≜ (^_^ ^^_^)^^ ^_^ − ^_^^_^ ^{^}, ^_^ ≜ (^_^ ^^_^)^^ ^_^ − ^_^^_^ ^{^}, ^_^^ and ^ ≜vec (^); ^ is a power matrix of subcarriers in the time- frequency resources; M is a number of symbols in the time-frequency resources of one physical layer frame; ^_^ is the signal-to-noise ratio, SNR, at the radar receiver; ∆^ is the subcarrier spacing; ^_^ is the carrier frequency, ^_^ is the symbol ^_^ = [0, 1, ... , ^ − 1]; (. )^ and (. )^ denote transposition and Hermitian transposition, respectively; ⊙ and ⊗ denote the Hadamard and tensor product, respectively; ^_^ is one vector with the size M. According to a twenty-first aspect, further to any of the twelfth to twentieth aspect, said modulation constellation is a Quadrature Amplitude Modulation, QAM, constellation; wherein the modulation constellations of at least two data transmissions amount the plurality of data transmissions differ in order. According to a twenty-second aspect, further to any of the twelfth to twenty-first aspect, the QAM constellation is a QAM with enhanced power in which the outer constellation points lay on a circle or an ellipse. According to a twenty-third aspect, further to any of the twelfth to twenty-second aspect, the plurality of data transmissions include data transmissions by mutually different users.

Claims

CLAIMS 1. A method for allocating wireless time-frequency resources in an integrated sensing and communication system, the method comprising: obtaining a plurality of data transmissions to be allocated resources; and allocating the wireless time-frequency resources to each transmission of the plurality of transmissions based on a Cramér-Rao bound for delay and/or Doppler shift for elements of the time-frequency resources. 2. The method according to claim 1, wherein each transmission of the data transmissions being associated with a modulation constellation; and the allocating the wireless time-frequency resources to each transmission of the plurality of transmissions is based on the modulation constellation associated with said data transmission. 3. The method according to claim 1 or 2, wherein the allocating comprises: determining a plurality, S, of allocation patterns of the plurality of data transmissions in the wireless time-frequency resources; calculating the Cramér-Rao bound for delay and/or Doppler shift for each allocation pattern of the S allocation patterns; and allocating the wireless time-frequency resources according to that allocation pattern which has the Cramér-Rao bound for delay and/or Doppler shift lowest among the S allocation patterns. 4. The method according to claim 3, each allocation pattern specifies power for respective elements of the time-frequency resources resulting from the modulation constellation. 5. The method according to claim 3, wherein each allocation pattern specifies power for respective elements of the time-frequency resources resulting from the modulation constellation and a preconfigured power factor associated with the data transmission. 6. The method according to any of claims 1 to 5, wherein the allocating comprises: obtaining the Cramér-Rao bound for delay and/or Doppler shift for elements of the time-frequency resources; obtain a first data transmission and a second data transmission of said plurality of data transmissions, wherein the first data transmission is associated with a modulation constellation having an order higher than an order of a modulation associated with the second data transmission; allocate elements of the time-frequency resources to the first data transmission and to the second data transmission, wherein elements of the time-frequency resources allocated to the second data transmission have the Cramér-Rao bound higher than elements allocated to the first data transmission. 7. The method according to any of claims 1 to 6, wherein the allocating comprises: obtaining the Cramér-Rao bound for delay and/or Doppler shift for elements of the time-frequency resources; obtaining ordered data transmissions including ordering the plurality of data transmissions according to a modulation order of the modulation constellations associated with the respective data transmissions; obtaining ordered resource elements including ordering the elements of the time- frequency resources according to the Cramér-Rao bound; and mapping the ordered data transmissions to the ordered resource elements so that the data transmissions with highest modulation order are assigned to resource elements with highest Cramér-Rao bound. VE4127 8. The method according to any of claims 1 to 7, wherein the Cramér-Rao bound ^_^ for delay ^̂ and/or the Cramér-Rao bound ^_^ for Doppler shift ^̂ is calculated as follows: 1 (^^{^} ^)( ^^{^}^_^^) ^^^(^̂) ≥ ^_^ = ^ _{^ ^} ( ^ ^_^^^)^, 2^ ( ^^{^}^ ^)( ^^{^}^ ^) − ^{^} 1 (^^{^} ^)( ^^{^}^_^^) ^^^(^̂ ) ≥ ^_^ = ^ ^{^} _^ ^^{^}^_^^) − ( ^^{^}^_^^^)^, 2^ ( ^ ^ ^)( wherein ^_^ ≜ 2^∆^(^_^ ^^_^), ^_^ ^_^ ≜ (^_^ ^^_^)^^ ^_^ − ^_^^_^ ^{^}, ^_^^ ≜ ⁽^_^ ^^_^ ⁾^^ ^_^ − ^_^^_^ ^{^}, and ^ ≜vec (^); ^ is a power matrix with a size N×M; N is a number of subcarriers in the time-frequency resources; M is a number of symbols in the time-frequency resources of one physical layer frame; ^_^ is the signal-to-noise ratio, SNR, at the radar receiver; ∆^ is the subcarrier spacing; ^_^ is the carrier frequency, ^_^ is the symbol duration; ^_^ = ^[0, 1, ... , ^ − 1^]; (. )^ and (. )^ denote transposition and Hermitian transposition, respectively; ⊙ and ⊗ denote the Hadamard and tensor product, respectively; ^_^ is one vector with the size M. 9. The method according to any of claims 1 to 8, wherein said modulation constellation is a Quadrature Amplitude Modulation, QAM, constellation; wherein the modulation constellations of at least two data transmissions amount the plurality of data transmissions differ in order. VE4127 10. The method according to any of claims 1 to 9, wherein the QAM constellation is a QAM with enhanced power in which the outer constellation points lay on a circle or an ellipse. 11. The method according to any of claims 1 to 10, wherein the plurality of data transmissions include data transmissions by mutually different users. 12. A device for allocating wireless time-frequency resources in an integrated sensing and communication system, the device comprising: processing circuitry configured to: obtain a plurality of data transmissions to be allocated resources; and allocate the wireless time-frequency resources to each transmission of the plurality of transmissions based on a Cramér-Rao bound for delay and/or Doppler shift for elements of the time-frequency resources. 13. The method according to claim 12, wherein each transmission of the data transmissions being associated with a modulation constellation; and the allocating the wireless time-frequency resources to each transmission of the plurality of transmissions is based on the modulation constellation associated with said data transmission. 14. The device according to claim 12 or 13, further comprising a transceiver configured to transmit or receive the data transmissions in the allocated wireless time-frequency resources. 15. The device according to any of claim 12 to 14, wherein the allocating comprises: VE4127 determining a plurality, S, of allocation patterns of the plurality of data transmissions in the wireless time-frequency resources; calculating the Cramér-Rao bound for delay and/or Doppler shift for each allocation pattern of the S allocation patterns; and allocating the wireless time-frequency resources according to that allocation pattern which has the Cramér-Rao bound for delay and/or Doppler shift lowest among the S allocation patterns. 16. The device according to claim 15, wherein each allocation pattern specifies power for respective elements of the time-frequency resources resulting from the modulation constellation. 17. The device according to claim 15, wherein each allocation pattern specifies power for respective elements of the time-frequency resources resulting from the modulation constellation and a preconfigured power factor associated with the data transmission. 18. The device according to any of claims 12 to 17, wherein the allocating comprises: obtaining the Cramér-Rao bound for delay and/or Doppler shift for elements of the time-frequency resources; obtain a first transmission and a second data transmission of said plurality of data transmissions, wherein the first data transmission is associated with a modulation constellation having an order higher than an order of a modulation associated with the second data transmission; allocate elements of the time-frequency resources to the first data transmission and to the second data transmission, of the time-frequency resources allocated to the second data transmission have the Cramér-Rao bound higher than elements allocated to the first data transmission. VE4127 19. The device according to any of claims 12 to 18, wherein the allocating comprises: obtaining the Cramér-Rao bound for delay and/or Doppler shift for elements of the time-frequency resources; obtaining ordered data transmissions including ordering the plurality of data transmissions according to a modulation order of the modulation constellations associated with the respective data transmissions; obtaining ordered resource elements including ordering the elements of the time- frequency resources according to the obtained Cramér-Rao bound; and mapping the ordered data transmissions to the ordered resource elements so that the data transmissions with highest modulation order are assigned to resource elements with highest Cramér-Rao bound. 20. The device according to any of claims 12 to 19, wherein the Cramér-Rao bound ^_^ for delay ^̂ and/or the Cramér-Rao bound ^_^ for Doppler shift ^̂ is calculated as follows: ^^^ ^, 1 (^^{^} ^)( ^^{^}^_^^) ^^^(^̂ ) ≥ ^_^ = ^ ^{^} _^^)( ^ ^_^^) − ( ^ ^_^^^)^, 2^ ( ^ ^ ^{^ ^} wherein ^ ^ _^^ − ^_^ ≜ (^_{^ ^^} − ^_^^_^ ^{^}, ^_^^ ≜ (^_^ ^^_^)^^ ^_^ − ^_^^_^ ^{^}, and VE4127 ^ ≜vec (^); ^ is a power matrix with a size N×M; N is a number of subcarriers in the time-frequency resources; M is a number of symbols in the time-frequency resources of one physical layer frame; ^_^ is the signal-to-noise ratio, SNR, at the radar receiver; ∆^ is the subcarrier spacing; ^_^ is the carrier frequency, ^_^ is the symbol duration; ^_^ = [0, 1, ... , ^ − 1]; (. )^ and (. )^ denote transposition and Hermitian transposition, respectively; ⊙ and ⊗ denote the Hadamard and tensor product, respectively; ^_^ is one vector with the size M. 21. The device according to any of claims 12 to 20, wherein said modulation constellation is a Quadrature Amplitude Modulation, QAM, constellation; wherein the modulation constellations of at least two data transmissions amount the plurality of data transmissions differ in order. 22. The device according to any of claims 12 to 21, wherein the QAM constellation is a QAM with enhanced power in which the outer constellation points lay on a circle or an ellipse. 23. The device according to any of claims 12 to 22, wherein the plurality of data transmissions include data transmissions by mutually different users.