EP4681357A1 - Method of generating a voxelated environment model for signal processing in wireless communication, methods of receiver-side or transmitter-side processing wireless signals using said voxelated environment model, and receiver or transmitter implementing the methods - Google Patents

Abstract

A method of generating a voxelated environment model for signal processing in wireless communication comprising: - receiving information about spatial locations of UEs and APs, about a frequency or frequency band used in a current communication, about spatial dimensions of voxels within the voxelated environment, and receiving a puncturing threshold, - modelling all theoretically possible geometric paths and associated properties between each UE and each AP, considering all the possible voxels, - determining properties of communication channels corresponding to respective modelled geometric paths, - identifying unavailable paths, - identifying unrealistic paths, and - generating a voxelated environment model, from which the unavailable paths and the unrealistic paths are removed in accordance with the received puncturing threshold. Further, random blockages may be introduced into the environment model. The voxelated environment, or data derived therefrom, are used in methods of joint communication and environment perception and/or in pre-processing signals prior to transmitting.

Description

METHOD OF GENERATING A VOXELATED ENVIRONMENT MODEL FOR

SIGNAL PROCESSING IN WIRELESS COMMUNICATION, METHODS OF RECEIVER-SIDE OR TRANSMITTER-SIDE PROCESSING WIRELESS SIGNALS

USING SAID VOXELATED ENVIRONMENT MODEL, AND RECEIVER OR TRANSMITTER IMPLEMENTING THE METHODS

FIELD OF THE INVENTION

The invention relates to the field of wireless communication, in particular to wireless communication that employs a spatial representation of an environment for optimising operating parameters in transmitters and/or receivers.

NOTATIONS

Scalar values are denoted herein by lowercase letters in italics, as in x, while complex vectors and matrices are denoted by boldface lowercase and uppercase letters, as in x and X, respectively. (^.)^T and (•)* denote the transposition and complex conjugation operators respectively, and diag(-) denotes the diagonalization operator. | • | denotes the absolute value operator whereas || |p denotes the f-th norm. E_x(x) and Var_x(x) respectively denote the expectation and variance operator of x with respect to the distribution of x given by Px(x). R and C denote the real and complex number fields respectively, and N\n, v) and CN\iz, v) denotes the real and complex Gaussian distributions with mean // and variance v.

Throughout this specification the term environment sensing may be used for the various expressions widely used for capturing information about an environment for creating a three-dimensional representation thereof.

BACKGROUND

Spatial representations of environments are widely used in the field of robotic vision, localizing and mapping, as well as in computer graphics and medical imaging. One known technique involves discretely approximating a true environment by a voxelated occupancy grid. Typically, voxels are regular cubes arranged in a 3D space covering the environment, which are assigned information about the space they occupy. The resulting discreteness of the voxelated space is well suited for 3D modelling where, depending on the size of the unit voxel, objects in the region of interest may be represented by rough estimates or more accurate shapes.

Figure 1 a) shows an exemplary environment that is represented, in voxelated representations having different resolutions, through use of voxels of different sizes in figures 1 b) and 1 c). In figures 1 b) and c) 3D voxelated occupancy grids are shown, where the total region of interest (ROI) is defined as a cuboidal space of dimensions Lx x L_y x z_z, each denoting the dimensional lengths of the x, y, z-axes in meters, respectively. The entire ROI is subdivided into a grid consisting of

Nv = N_x • N_y • N_z voxels, where Nx = — Ly, N_y = — Ly , and N_z = — Ly denote the number of voxels, or partitions, per x, y, z -axes, respectively, and Lv is the edge length of a voxel cube in meters, corresponding to the image resolution. If represented as a tensor of three dimensions (Nx x N_y x Nz), the voxelated occupancy grid directly represents a discretized model of the ROI, as shown in Fig. 1 b) and c). The elements of the three-dimensional tensor indicate the occupancy of the voxels, and thus, whether that portion of the space is empty or filled with a given material.

In addition to the estimation accuracy flexibility provided by voxelated grids, one of the biggest advantages of the grid-based models is the simplicity of the data representation, especially as opposed to 3D vertex-based or point cloud-based methods, which makes voxelated grids even more favourable from a machinelearning point of view.

Recent developments in communication technology have identified modelling the space between a transmitter and a receiver by a voxelated environment as beneficial for joint communication and sensing (JCAS), sometimes also referred to as integrated sensing and communication, or ISAC. Throughout this specification, the terms JCAS and ISAC are used interchangeably. JCAS is a technique in wireless communications with the objective of retrieving information about the environment from the signal scattering which is present in the effective channel state information (CSI), e.g., due to objects in the environment, blockage, user activity, etc., while simultaneously achieving data communication. To this end, the electromagnetic scattering behaviour of objects in the true environment may be added to the 3D geometric information as provided by the classic voxelated occupancy grid, for tailoring the communication channel modelling method that is utilized in a wireless communication scenario. For considering the scattering behaviour, each voxel is assigned a voxel occupancy coefficient Vk e {0, 1} with k e {1, ..., Nv], where Vk = 0 indicates that the fc-th voxel is empty, i.e., the corresponding environment is free-space, and Vk = 1 indicates that the A- -th voxel is occupied by a scatterer object, e.g., the table, chair or the object on the wall, as illustrated in Fig. 1 . Note that the binary voxel occupancy coefficients may be extended to complex voxel scattering coefficients, i.e., Vk = 0k-e~^ju>k e C, to also capture the effect incurred to the reflected electromagnetic waves by the occupied voxels. The constants /& and ^ depend not only on the material itself, but also on the frequency and the angle of incidence of propagating signals, and capture the effect of the material occupying a given voxel onto the electromagnetic wave reflected or refracted by it. In other words, the values of the voxel scattering coefficients are expected to be highly dependent on the electromagnetic characteristics of the scatterer object and the impinging wave, which may be empirically measured and modelled as a function of the properties such as frequency and material.

Figure 2 a) and b) shows a general concept of line-of-sight (LOS) paths and non- line-of-sight (NLOS) paths in a voxelated space, where all paths are available and the reflection angles are within a range that actually reflects impinging electromagnetic waves. In figure 2 a) the LOS path is the direct path between the user equipment (UE) and the access point (AP), indicated by the solid line, while the two occupied voxels in the ROI reflect signals emitted by the UE towards the AP. The dashed lines represent the NLOS UE-to-voxel path, and the dotted lines represent the NLOS voxel-to-AP path. In figure 2 b) one of the voxels that was filled is now empty, which will obviously have an effect on the scattering coefficients of that voxel. The dashed line from the empty voxel to the AP represents the path that was present in figure 2 a) and is not to be taken as an existing path. An exemplary regular voxelated 3D space with some scatterer objects accommodating a single access point (AP), a single reconfigurable intelligent surface (RIS), and multiple single-antenna user equipment (UEs) is discussed by X. Tong, Z. Zhang, J. Wang, C. Huang and M. Debbah in “Joint Multi-User Communication and Sensing Exploiting Both Signal and Environment Sparsity,” IEEE Journal of Selected Topics in Signal Processing, vol. 15, no. 6, pp. 1409- 1422, Nov. 2021 . The multiple UEs are communicating to the AP via sparse code multiple access (SCMA) over multiple frequency subcarriers and over multiple transmission instances, via LOS paths and NLOS paths from the UEs, to the scatterers, to the RIS, then finally to the AP.

Figure 3 shows a schematic representation of the 3D space considered in the known system and method, including the RIS. Here, the signal reflected off the RIS towards the AP is shown in a dash-dotted line, to highlight its specific origin.

According to the known system model and assumptions, the signals received at the AP would not only carry the UEs’ payload, or data, but also contain the scattered path information which can be used to retrieve, or perceive, the environment. To aid the estimation, UEs are assumed to transmit a known length of pilot symbols at the beginning of the transmission interval, i.e., a known preamble. The known method aims to return the estimates of the transmitted SCMA codes of the UEs, i.e., user detection, or identification, and a binary voxel occupancy grid which corresponds to the estimation of the environment, e.g., 0 for a voxel representing empty space and 1 for a voxel representing an occupied space.

The known system may be represented mathematically by the following model

Y = (H + PRQVB) [X_PX] + W where Y is the received signal matrix over all receive antennas and APs across all symbol instances, H is the UE-to-AP LOS channel matrix, P is the RIS-to-AP NLOS channel matrix, R is the RIS reflection coefficient matrix, Q is the voxel-to-RIS NLOS channel matrix, B is the UE-to-voxel NLOS channel matrix, V is the voxel occupancy matrix, X_P is the pilot symbol matrix, X is the data symbol matrix, and W is the AWGN noise matrix. Since the matrices P, R, Q, and B are known, the model can be simplified to

Y = (H + AVB) [X_PX] + W where A = PRQ is the effective voxel-to-AP NLOS channel matrix.

From this, the main joint communication and sensing problem is formulated, i.e., to estimate the environment matrix V and data symbol matrix X, with known channel matrices H, A, B, and known pilot matrix X_p.

To do so the prior art method uses three modules:

• an environment estimation module, using a linear generalized approximate message passing (GAMP) algorithm which uses the known channels, with given data symbols X, either pilots or estimated symbols from a previous iteration, for estimating the environment V, on the model

Y = (H + AVB) [X] + W

• an effective channel reconstruction module which, by integrating known channels and the estimated environment and using V estimated by the GAMP algorithm, combines the information with known H, A, B to calculate the effective total channel

H = H + AVB

• a data signal estimation module which, using a linear SOMA message passing algorithm (MPA) and the estimated effective channel, estimates the unknown data symbols X,

Y = HX + W

These three modules are iterated in a sliding window fashion on the time domain as illustrated in Figure 4, such that first, the environment estimation is carried out using the known pilot symbols, but for the data signal estimation, the window slides for estimating the unknown data symbols, and so on. However, like other known method of JCAS in voxelated environments, the prior art method discussed further above relies on the idealised assumptions that all paths between all transmit and receive antennas are fully available, i.e., no paths are blocked, that the channel gains for UEs-to-AP LOS paths are known, that the channel gains for the UEs-to-voxels, voxels-to-RIS, RIS-to-AP NLOS paths are known, that the RIS reflection coefficients are known, that the voxelated environment model is binary, i.e., only discrete occupancy values 0 or 1 are possible, that all scattered paths have realistic reflection angles, that an SCMA communication scheme is used, and that only a single AP is present. It is noted that throughout this specification the terms voxelated environment, voxelated space, 3D space, 3D grid and similar expression may be used interchangeably unless a specific use is apparent from the context, and may also be represented by the abbreviation VE.

Further to the simplifications of the known model, the energy loss at reflection scattering that depends on the material and surface structure of the scatterer object, the frequency-dependent scattering behaviour, as well as the relative distances between voxels and devices and the resulting effect on the channel gains are not considered.

These assumptions pose severe limitations to applying the known method to actual 3D real-world environments, giving rise to the need for a method of generating an improved voxelated environment model for signal processing in wireless communication, methods of transmitting or receiving using said improved voxelated environment model, and a transmitter and a receiver implementing the methods.

SUMMARY OF THE INVENTION

This need is addressed by the methods of claim 1 , 7 and 8, the computer program product of claim 10, the wireless communication apparatus of claim 12 and the communication system of claim 14. A corresponding computer-readable storage medium is presented in claim 11.

Prior to describing the various aspects of the invention, the concept of unavailable paths and unrealistic paths in the voxelated environment will be elucidated. Figure 5 a) and b) show exemplary voxelated spaces where some paths may be rendered infeasible or unavailable due to various physical phenomena. In both, figure 5 a) and b), the direct solid line from user equipment UE to the access point AP represents a LOS path, which is available. It is obvious that, if an occupied voxel lies directly in line with the path between the UE and the AP (not shown in the figure), the corresponding path will be unavailable. If the scattering angle between the incident and the reflected path is too large and exceeds a critical angle, e.g., an angle close to 180°, the corresponding NLOS path will be unrealistic and, in effect, be unavailable, as shown in figure 5 a). The dashed line from voxel to the AP represents the reflected voxel-to-AP NLOS path that has an unrealistic reflection angle, i.e., is not available. The determination of the critical angle is dependent on the electromagnetic properties of the RF wave and the environment, e.g., on the operating frequency, and hence the present invention proposes a simplified model to approximately incorporate such phenomena into the channel matrices of the voxelated grid environment model. Unavailability of a path may also be caused by a skewed surface, as shown in figure 5 b), where the signal is reflected away from the AP. Like in figure 5 a), the theoretically possible NLOS path reflected from the empty voxel in figure 2 b) will be unavailable due to the object in the voxel reflecting the incident wave away.

Further prior to describing the various aspects of the invention, a general underlying channel model will be described. It is assumed that the ROI comprises Nu single-antenna UEs, and NA multi-antenna APs equipped with NR receive antennas each. As illustrated in Fig. 5, the effective channels between the UEs and APs contain two distinct types of components, the LOS components, which is the direct path between the UEs and APs, and the NLOS components, which encompass the paths reflected at occupied voxels corresponding to parts of objects in the environment, i.e., paths scattered by voxels representing scatterer objects, as described further above. For reasons of simplicity it is further assumed that the frequency band is sufficiently high that the power of paths reflected more than once is negligible such that NLOS components may be decomposed into two sub-paths, the UE-to-voxel sub-path and the voxel-to-AP sub-path, which together with the voxel scattering coefficient comprises the aggregate NLOS channel. It is noted that considering NLOS paths having more than one reflexion is also conceivable.

In light of the above, the effective channel between the Nu single-antenna UEs and the ensemble of NANR receive antennas of all APs (i.e., for all NR antennas per each of the NA APS), is given by where G G is the effective channel matrix, H G A G Z^NANRXNV, and B G c^WyX7Vu are the constituting channel matrices for the UE-to-AP LOS path, voxel-to-AP NLOS sub-path, and UE-to-voxel NLOS sub-path, respectively, and v G c^Ni^,xl is the vector containing all scattering coefficients of the voxelated grid. The elements of the channel matrices H, A, and B are assumed to follow a zeromean complex Normal distribution with variances a#, erf , and crj, respectively.

It is noted that the channel model presented above can be straightforwardly extended to a multi-carrier system, yielding with f denoting a specific frequency in the set 7 of all subcarrier frequencies.

It is important to notice that the channel model in the equation shown above assumes that all paths between UEs, APs, and voxels are fully available, like in the known system discussed above in the background section. However, in reality many paths may be rendered unavailable due to various physical phenomena, e.g., blockage by air-borne particles, absorption, path loss, or by the finite resolution of the voxelated model itself. Also, as described above, if the angle between the incident and reflected path is too large and exceeds the critical angle, the corresponding NLOS path will not be available, as shown in Fig. 5 a). Likewise, if an occupied voxel is directly in line with the LOS path, the corresponding path will not be available. The determination of the critical angle is dependent on the electromagnetic properties of the RF wave and the environment, e.g., on the operating frequency, and hence a simplified model is proposed to approximately incorporate such phenomena into the channel matrices of the voxelated grid environment model.

Realistically modelling all paths may be computationally prohibitive, Thus, the present invention suggests eliminating unrealistic and unavailable paths, and further suggests considering the statistical feasibility of paths, for improving the voxelated grid model.

Since the geometric positions of all the voxels, and the UEs and the APs are assumed to be known relative to each other, in the uniform voxelated grid, it is possible to straightforwardly calculate the trigonometrical distances of all the paths. With the knowledge of these distances and the operation frequency, the channel loss of the paths is obtained, using, e.g., the Friis transmission formula, which gives the path loss coefficient as a function of distance and frequency. It is further possible to calculate angles of reflexion for all voxels in paths between a UE and an AP. This information may already be used for eliminating unrealistic or unavailable paths.

To this end, the physical phenomena occurring at the reflection of propagating waves are considered, in particular, the fact that for any given frequency: i) a critical angle 0* exists such that, as illustrated in Fig. 5 a), if the incidence angle 0> 0*, the wave is absorbed rather than reflected, and consequently the corresponding voxel-to-AP NLOS sub-path is not available, and

II) the curvature of the surface exposed to the impinging wave may be such that no signal is reflected towards an AP, as illustrated in Fig. 5 b).

As mentioned before, the complexity of modelling such phenomena at each voxel may be far too complex to carry out, especially if the resolution of the voxelated ROI is high, i.e., the individual voxels are small. Thus, a statistical approach for considering the angle between the impinging and reflected waves at each voxel, hereafter referred to as the scattering angle, and consequently, the availability of each voxel-to-AP NLOS sub-path is proposed, which significantly reduces the computational complexity.

In light of the above, the present invention proposes the following stochasticgeometric model for integrating the aforementioned phenomena into the channel matrices of the voxelated grid environment model.

Note that it is assumed that the multiple antennas of the respective APs are fully located within a single voxel, such that their angles-of-arrival (AoA) are assumed to be identical, while still having different channel path coefficients. Given the known 3D coordinates of the UE, AP and the considered voxel as respectively, the scattering angle 6 of the path at the respective voxel may be computed as where the arccos( ) operator denotes the inverse cosine trigonometric function.

The empirical probability distribution functions (PDFs) of the scattering angles 6 can be obtained by evaluating the foregoing equation for all possible combinations of admissible locations of UE, AP and voxel within the ROI, respectively given by cu, CA and cv, and exemplary PDFs for an environment voxelated at various resolutions are shown in figure 6. Admissible locations refers to all possible locations within the confines of the grid, i.e., excluding positions off-grid, outside the ROI, and excluding two or more UEs or APs being located in the same voxel.

It is visible in figure 6 that for a sufficiently large Nv the distribution of scattering angles 0can be well modelled by a mixture of two beta distributions, namely, fx(x) = yP(a\, bi) + (l-y)'(ci2, b2), with support * G [0; 180°] and where y is a weighing factor and the quantities ai, 02, by b2 are shape parameters optimised to match the empirical data obtained by evaluating the foregoing equation, with cu, CA and crtaken randomly within the voxelated grid. Utilizing this empirical stochastic-geometric approach, the voxelated environment models obtained so far can be improved by the incorporation of random blockages of NLOS sub-paths, in proportion to the complement cumulative distribution of the approximated beta mixture PDF, and in accordance with the scattering angles at each voxel, as a function of a selected critical angle. The selection of a critical angle may consider the frequency or frequency band used in the corresponding communication and/or a fixed minimum and/or maximum value.

As mentioned before, the scattering angle 0 at all voxels is calculated for all pairs of UEs and APs. A scattered path is determined to be unavailable if 180°], and the corresponding paths are removed from the NLOS channel matrices A and B, respectively.

The effect of the critical angle 6_Cht on the severity of puncturing in the channel matrices is illustrated in figure 7, where the result is obtained by numerical evaluations with random numbers and positions of UEs and APs for various voxelated grid resolutions, with the average channel puncturing rate normalized by the total number of path vertices (NA + NR). AS expected, the puncturing rate shows a smooth increase between e_crit = 180° with no puncturing, and with full puncturing. This inherently includes the blocked LOS case, since the blockages may be regarded as a case with 0= 180°. As mentioned above, the true critical angle is dependent on the elaborate electromagnetic properties of the environment, but its determination is out of scope of this invention. However, a very interesting behaviour is observed where the severity of puncturing becomes effectively invariant to the resolution of the voxelated environment model, i.e., the size of the voxels, converging to the same relationship at a sufficiently high resolution.

As illustrated in figure 7, the convergent curve may be very closely approximated by a scaled Gaussian curve, where a heuristic search yields the optimal parameterization of X(-9.8, 54²) with a scaling factor Drawing from the above, an efficient model of the puncturing behaviour is proposed by introducing the feasibility coefficient ^G [0, 1] which follows a Bernoulli distribution with probability p? obtained by evaluating the scaled Gaussian distribution ®^crit- Then, independent and identically distributed (i.i.d.) feasibility coefficients are multiplied to each element of the channel matrices, and capture the behaviour of the infeasible paths being unavailable and punctured.

The benefits of the improved environment model will be shown in the following for two exemplary ISAC methods. Here, an uplink communication scenario between the group of Nu UEs and a total of NA APS, under the models described above, is considered, with the NA APS connected to a central processing unit (CPU) via error- free fronthaul links of unlimited throughput, such that the received signals at all NANR receive antennas are aggregated without loss of information or delay.

The aggregated received signal matrix Y, over Nr discrete transmission instances (symbol slots) is given by where is the effective channel matrix as described above,

X G <C^NU^XNT i_s the transmit signal matrix collecting the symbols from all M/ UEs, each drawn from the constellation Nof cardinality N_x, and W G £^NAHR*N_T j_S the receiver-side additive white Gaussian noise (AWGN) matrix with independent and identically distributed (i.i.d.) elements drawn from CA/"(0, No), where No is the noise variance.

The transmit signal X comprises of a pilot block X and a data block such that where Np and ND denote the number of symbol slots allocated to the pilot and data sequences, respectively, with NT=NP+ND, and where the pilot symbol matrix Xp is assumed to be perfectly known at the CPU.

In view of the equations provided above, the goal of the exemplary ISAC schemes discussed hereafter can be concisely stated. The communication objective of the CPU is to estimate the unknown data symbol matrix Xp, under the knowledge of only the pilot symbols in Xp, after the estimation of the channel matrix G. In turn, the sensing objective is to extract the voxelated model of the environment as the vector of occupancy coefficients v, from said channel matrix G.

By combining the previously presented channel decomposition model for G, the received signal model for Y and the transmit signal model for X, the overall system model becomes where the unknown variables of interest are the environment, i.e., the voxel coefficients vector v and the data symbol matrix Xo.

In the following description it is assumed that the LOS channel H, and the UE-to- voxel and voxel-to-AP sub-path of components A and B in the foregoing equation for Y are known, which still leaves an atypical relationship between the two variables diag(v) and Xo. In particular, the latter unknowns are related, under the foregoing equation for Y, by an asymmetric bilinear system, requiring sophisticated computation schemes to be either decoupled or jointly estimated.

The exemplary ISAC methods for the joint estimation problem of the asymmetric bilinear system expressed by the foregoing equation for Y discussed below leverage the well-known Gaussian belief propagation (GaBP) message passing (MP) framework. Both exemplary ISAC methods benefit from the improved modelling of the VE proposed herein. It is noted that other ISAC methods may likewise benefit from the improved modelling of the VE.

The first proposed method, dubbed Alternating Linear ISAC (AL-ISAC), incorporates two separate linear estimation processes for each of the unknown variables v and Xz>, estimating these unknown variables in an alternate fashion via a feedback chain between the two processes. Both estimation processes are based on equation (6) and can respectively described as: - an iterative first linear GaBP MP process for estimating the environment vector v, given the transmit signal matrix X, and conversely, and

- an iterative second linear GaBP MP process for estimating the transmit signal matrix X, given the environment vector v.

The two linear GaBP processes and the constituting MP rules are derived hereinafter, before the construction of the full AL-ISAC process encompassing the two derived processes is described.

The iterative first linear GaBP MP process for the environment vector v operates on only one unknown variable, so that in order to estimate v, the entire transmit signal matrix X must be assumed known, in addition to the known channel matrices H, A, and B. Assuming knowledge of X, the system described by the foregoing equation for Y may be reformulated as where, since the channel matrix A _anc| the matrix products a_re known, the described system is linear on v, to which a corresponding factor graph as shown in figure 8 may be obtained.

Each element y_m,t of the receive signal of Y, with m e {1, ..., NANR} and t e {1, ..., NT} corresponds to the factor nodes, represented by the squares in the figure, and each element vk of the unknown environment variable v, with k e {1, ..., Nv} corresponds to the variable nodes, represented by the circles in the figure. In turn, each (m,f)-th factor node on the factor graph has a corresponding soft-replica of each variable node element vk, denoted by v_k.mit, with the corresponding mean-squared-error (MSE) given by Utilizing soft-replicas and their MSEs, the factor nodes perform soft interference cancellation (IC) on the received signal y™,tfor each variable vk, yielding the IC symbol scalar Gaussian approximation (SGA) where x_n,t and w_m,t are the (n,t)-th and (m,t)-th elements of X and W, respectively, with n G {1, ..., Nu}, and where the auxiliary variable Ck,t = Xu=i ^bk,u^xu,t represents the aggregated incident signal at the fc-th voxel from all UEs.

Next, by leveraging the central limit theorem (CLT), the sum of difference and noise terms are approximated as a complex Gaussian scalar, such that the PDF of the interference-cancelled symbols y^m.t ^can be modelled as with the corresponding variance v^._{m t} given by

The conditional variances for all vk are computed by all factor nodes, and the message is sent to the corresponding variable nodes. Consequently, the fc-th variable node obtains the NANRNT conditional variances from all factor nodes, from which the extrinsic belief /£ is computed. In GaBP, self-interference is suppressed by excluding the conditional PDF of yk-_m,t ^a* the fc-th variable node to yield tfi.m.t with the PDF where the extrinsic mean ^and variance is respectively given by

Finally, by following the Bayes rule, the updated posterior may be obtained by combining the PDF of the extrinsic belief and the prior distribution of vk, from which the updated soft-replica is obtained as where the normalizing factor in the denominator is the integrated updated posterior over the complex field.

Similarly, the updated error variance of the soft-replica is obtained by evaluating

Given the information of the voxel coefficient distributions, i.e., binary coefficients with a discrete prior given by a Bernoulli distribution with occupancy probability

E_v P_Vk(v_fc = 1), the soft-replica and its MSE can be efficiently obtained in closed form, respectively, given by

The updated soft-replica and the MSE of each variable node are then transmitted back to all factor nodes for the next iteration of the GaBP MP computation process.

After a given number of GaBP iterations to refine the soft-estimates, a belief consensus is taken at each variable node across the soft-replicas to obtain a single estimate v by with consensus mean jl_k and variance ip_k expressed as which is consequently used to yield the final estimate by

Equations (8) to (20) fully describe the first linear GaBP MP process for estimating the voxel environment v, i.e. the voxel coefficients, which is summarized as follows, with reference to the steps of the method 500 shown in figure 9.

Inputs to the first process are the received signal matrix Y, the channel matrices H, A, and B, the transmit signal matrix X, the noise variance No, and the prior distribution of the environment voxels P_V/c(v_fc).

The first iterative process begins with an initialisation, since the soft-replicas of Vk-.m,t and the corresponding MSEs from earlier iterat ions are not yet available. After computing, in step 502, a first signal matrix C as per C which describes the effective signals as modified by the channel between the UE and a voxel, in step 504, the soft-replica at all variables is initialised as E_Vk[v_k]Yk, m, t, and in step 506 the MSEs at all variable nodes ^are initialized wk, m, t as per equation (8). The initialisation is executed vfc.

The following steps are iterated until a termination criterion is met. In step 510 the soft-IC is performed on the received signal using equation (9), yielding In step 512 the corresponding conditional variance _t\s determined as per equation (11). In step 514 the extrinsic mean and variance ip_k.._m>t is determined as per equation (13). In step 516 the new soft-replica v_km,_t and the are computed as per equations (14) and (15), respectively, and in step 518 the soft-replica v_k.mit and the MSE ip_{k.m t} are updated via damping, e.g., as discussed by P. Som, T. Datta, A. Chockalingam and B. S. Rajan, in “Improved large-MIMO detection based on damped belief propagation,” IEEE Inf. Theory Workshop on Inf. Theory, 2010, pp. 1-5. The damping factor may be selected from an interval rjE [0, 1] and serves for preventing early convergence to a local optimum. It is to be noted that each of steps 510 through 518 is carried out Vfc, m, t. In step 520 a check is performed to find out if a termination criterion is met. In the negative case, “no”-branch of step 520, steps 510 through 518 are repeated, using the respective most recent values of the soft-replicas and the MSEs as input. In the positive case, “yes”-branch of step 520, the consensus mean p._k and variance V_k are computed vfc as per equation (19) in step 522, and in step 524 the final soft- estimate v is computed as per equation (20). The termination criterion for the iteration loop may comprise a predetermined maximum number of iterations, or a predetermined convergence threshold which may be evaluated in terms of the soft- replica MSE. Note that the steps following meeting the termination criterion are carried out Vfc.

It is important to note that the signal matrix X is assumed given - i.e., X is not estimated by the process - and therefore is kept constant throughout the iterations, as seen by the precomputation of the effective signals ck,t.

The complementary second linear GaBP MP process dedicated to the estimation of the transmit signal matrix X for a given v will be now described.

In order to derive the second linear GaBP MP process for estimating the signal matrix X for a given v, the overall system model derived further above and represented by equation (6) is first reduced to the aggregated received signal matrix Y initially presented in equation (4), with the effective channel

G = H+A diag(v)B. The corresponding factor graph is illustrated in Fig. 10, where each element x_n,t of the unknown signal matrix X with n e{l, ..., Nu }, is a variable node, represented by the circles. Note that in this case, since the variable X is two-dimensional, the linear system results in a factor graph that is separated into “pages”, such that the variable nodes and factor nodes having different time indices t e{l, NT } are independent and that the messages are only exchanged by nodes with the same time index t. Other than this separation of factor graphs, the derivation of the MP rules is similar to that of the linear GaBP MP process for the environment vector v presented further above.

The soft-replica of the transmit signal matrix element x_n,tto the (m,r)-th factor node is denoted by x_m,t._n,t, with the corresponding MSE given by

The soft-replica and the MSE are used in the soft-IC of the received signals for xn,t, following with the conditional PDF described by and the conditional variance v£_t;znjt is given by

The conditional PDFs are combined with self-interference cancellation at the variable nodes to yield the extrinsic beliefs following with the extrinsic mean Hn.t-.m.t and variance ypn,t-.m,t respectively given by

In turn, since the symbols have a uniformly discrete prior from the symbol constellation x, with the symbol probability PxQr) = 1/| xl, their soft-replicas and MSEs are obtained by

For the particular case of M-ary quadrature amplitude modulation (M-QAM) with M= 4, the soft-replica and MSE computations reduce to efficient closed-form expressions given by

(29) where E_x = E_x [|x|²] denotes the average symbol power of the constellation X, and tanh(-) denotes the trigonometric hyperbolic tangent function.

Finally, the consensus PDF, which is taken after the iterations is given by with the consensus mean and variance expressed as yielding the soft estimate Equations (21) to (33) fully describe the second linear GaBP MP process for estimating the transmit signal matrix X given the environment vector v, which is summarized below, with reference to the steps of the method 600 shown in figure 11 .

Inputs to the second process are the received signal matrix Y, the channel matrices H, A, and B, the environment vector v, the noise variance Afa, and the prior distribution of the transmit symbols .

Like the first computation process, the second computation process begins with an initialisation, in which the effective channel matrix G= H + A diag(v) B is computed in step 602, followed by initialising the soft-replica at all variable nodes in step 604 as x_n,t-.m,t = ^Ex_nt[^xn,t]. and by initialising, in step 606, the MSE at all variable nodes P^er equation (21). The initialisation is executed Vm,n, t.

The following steps are iterated until a termination criterion is met. In step 610 the received signal yn.t-m.t after soft-IC is computed as per equation (22), and the corresponding conditional variance _t is computed in step 612, using equation (24). Next, in step 614 the extrinsic mean and variance are computed as per equation (26), which permits computing, in step 616, the new soft-replica x_nit.mit and the corresponding MSE ipn,t-.m,t as per equations (27) and (28), respectively. Now the soft-replica x_nit.mit and the MSE can be updated via damping in step 618, similar to the updating process in method 500 discussed further above. Here too, damping serves for preventing early convergence to a local optimum. It is to be noted that each of steps 610 through 618 is carried out Ym,n, t. In step 620 a check is performed to find out if a termination criterion is met. In the negative case, “no”-branch of step 620, steps 610 through 618 are repeated, using the respective most recent values of the soft-replicas and the MSEs as input. In the positive case, “yes”-branch of step 620, the consensus mean are computed V/c as per equation (32) in step 622, and in step

624 the final soft-estimate x_{n t} is computed as per equation (33). The final soft- estimate x_nt is then projected, in step 626, to the symbol constellation X, and the projected _t is output, in step 628, as final hard estimate. The termination criterion for the iteration loop may comprise a predetermined maximum number of iterations, or a predetermined convergence threshold which may be evaluated in terms of the soft-replica MSE.

The two previously described processes now need to be combined for completing the proposed AL-ISAC process, which estimates both unknown variables.

Each of the two estimation processes presented before is adapted to estimate only one of the two variables v or X, assuming in each case availability of full information on the respective other variable. However, the very inherent problem of ISAC in the overall system model derived further above is that neither of the variables are fully known such that the linear processes may not be directly applied for estimation.

To address the problem, the proposed AL-ISAC process successively invokes the two linear GaBP MP processes for estimating the two sets of variables. This requires separating the received signal is into blocks corresponding to the pilot phase and the data phase, as

First, using only the pilot phase of the system as represented by equation (34a), the first linear GaBP MP process for estimating the voxel environment v is invoked for estimating the initial environment vector v_init with the pilot block Xpas known input signal matrix. Next, using only the data phase of the system as represented by equation (34b), the second linear GaBP MP process for estimating the transmit signal matrix X is invoked for estimating the unknown data block £ using the initial environment estimate v_init as the known input environment vector. Finally, the environment vector is obtained by invoking the first linear GaBP MP process for estimating the voxel environment v again, but with the initial environment estimate Vj_nit as the initialization value of the soft-replicas at all factor nodes, and [XPXZ?] as the known input signal matrix. A schematic block chart showing the alternating nature of the exemplary AL-ISAC process is illustrated in figure 12.

Despite having a potential complexity advantage, especially for scenarios with large numbers of UEs, as will be shown further down, the alternating approach of the AL-ISAC process has the drawback of causing a heavy dependence on the length of the pilot sequence Xp, which, as will likewise be shown further below, affects the performance of both environment and data signal estimation, in addition to the obvious trade-off concerning the total communication throughput.

The second one of the two alternative exemplary estimation processes, dubbed Bilinear ISAC (Bi-ISAC), aims to circumvent this deficiency. This alternative process simultaneously estimates both unknown v and Xp in parallel, using a single bilinear estimation module, more specifically a bilinear MP, which incorporates the uncertainty of both estimates at each iteration. The bilinear MP requires only a single estimation module to acquire both variables, as illustrated in the exemplary block chart of figure 13.

The unique asymmetric bilinear relationship of v and Xz>, as per the system equation reformulated for the AL-ISAC method discussed further above, prevents the application of known bilinear estimators, such as the bilinear generalized approximate message passing (BiGAMP) or the parametric BiGAMP. The BiGAMP operates only on symmetric systems described by equations in the form for the joint estimation of the unknowns V and X, whereas the parametric BiGAMP only works on systems with the structure to jointly estimate v_k and X with known Ak.

In contrast to these two examples, the aforementioned unique asymmetric system discussed herein is described in neither of the aforementioned forms, nor can it be transformed to fit general bilinear forms. This mandates that new, purpose-built bilinear Gaussian belief propagation (BiGaBP) MP rules be derived for its solution.

In the second exemplary method discussed herein the BiGaBP message passing is performed on a tripartite factor graph as illustrated in Fig. 14. Here, the factor nodes, represented as square nodes, are the received symbols and the two sets of variable nodes, represented as circular nodes, correspond to the environment vector v and the signal matrix X, respectively. An important distinction is made between the two types of variable nodes: a data variable node receives messages only from NANR factor nodes corresponding to the same time instance t, while an environment variable node receives messages from all NANRNT factor nodes.

Figure 14 shows the higher complexity of the factor graph compared to those of the linear GaBP processes shown in figures 8 and 10. The higher complexity is due to the asymmetric and embedded system structure of the equation for the initial system model presented further above in relation to both variables together, as opposed to the lower complexity equations for linear system structures where one variable is considered at a time. Other than that, the messages transferred over the graph edges carry the same information items as in the linear GaBP processes presented further above, i.e., the soft-replicas, MSEs, and conditional PDFs of the variables of interest. However, since neither of the latter is known, except as soft- replicas, the corresponding calculation of the messages must incorporate the uncertainties in both variables, in the form of the respective MSEs.

In light of the above, similar to the derivation in the section dealing with the AL- ISAC process, the exchanged messages are constructed on the basis of soft- replicas of the variables. Since the entries in X corresponding to t e {1, 7V_P} are pilot symbols XP, the corresponding soft-replicas are set to their known pilot value, i.e., x_n)t.m>t = (xp'ln tWt e {1, with the corresponding MSE values set to 0. The remaining soft-replicas and MSEs for t e {N_p + 1, ••• 7V_r} are as given in the equations for the AL-ISAC process.

In hand of the soft-replicas and their MSEs, the factor nodes perform soft-IC for each variable v_k and x_n>t by where the soft-IC for the data variables given in equation (35b) is only performed for unknown variable nodes with indices t e {N_p + 1, ••• N_T}. Following the soft-IC, the respective conditional PDFs are with the respective conditional variances given by where the expectation E_v = E_{Vk} [| v_k | ^z] has been introduced for convenience of notation. In turn, all variable nodes compute the interference-cancelled extrinsic belief PDFs given by with the respective extrinsic means and variances given by

Using equations (41a) through (42b), the updated soft-replicas and the MSEs can be obtained through the same equations as in the linear GaBP process, namely equations (14) and (15) for v_k, and equations (27) and (28) for x_{n t}, with the postconvergence consensus as in equations (19) and (20) for v_k.mit, and equations (32) and (33) for x_{n t;m t}, respectively.

A complete description of the exemplary Bi-ISAC process for estimating the EV v and the transmit data signal matrix X_D is summarized as follows, with reference to the steps of the method 700 shown in figure 15.

Inputs to the iterative process are the received signal matrix Y, the channel matrices H, A, and B, the pilot matrix Xp, the noise variance No, and the prior distributions of the environment P_Vfc(v_k) and of the transmit symbols Outputs of the process are the estimated environment vector v and the estimated transmit signal matrix X. Once again, the iterative process begins with an initialisation in step 702. Here, for the data variable nodes corresponding to the pilot block, i.e., for t e {1, ..., Np}, the soft-replicas are initialised as pilot signals: x_n>t.m>t = Ym, n. The corresponding ^are initialised to 0 Vm,n. For the data variable nodes corresponding to the data block, i.e., for r e { Afc+l, ..., NT}, the soft replicas are initialised as Vm, n, and the corresponding ^are initialised via equation (21 ) Vm, n. Finally, for the environment variable nodes, i.e., for the environment soft replicas are initialised as v The corresponding ^are initialised via equation (8).

The core of the method comprises repeating, for all m, n, k, t, the following steps until a termination criterion is met:

710: Compute soft-IC signals y_k.mit and y using equation (35).

712: Compute conditional variances using equation (38).

714: Compute extrinsic mean $._{m t}. and variance using equation (41 ).

716: Compute extrinsic mean ^ancl variance using equation (42).

718: Compute new soft-replicas v_fc;rn,_t and x_{njt;zn t} using equations (14) and (27).

720: Compute new MSEs using equations (15) and (28).

722: Update all soft-replicas and MSEs via damping.

724: Termination criterion met?

The method further comprises, after the termination criterion is met and for all n, k, t

726: Compute consensus PDFs with p._k, using equation (32), and i/^and using equation (19).

728: Compute the final soft-estimates v_k using equations (20) and (33). 730: Output v_k as the final estimate Vfc. 732: Project the final soft estimate _t to the symbol constellation X

734: Output the projected x_n>t as final estimate

Notably in MP-type processes, removing a signal path from a communication environment is analogous to removing an edge from the factor graph representation of the system. This means that fewer messages are passed between the fixed and variable nodes. While fewer messages may result in a decrease in the accuracy of the estimation, the computational load can be significantly reduced. By accordingly selecting a puncturing threshold the amount of paths removed, i.e., edges removed from the factor graph representation of the system, can be controlled in accordance with the respective requirements of the use case. This may also be referred as a controllable “aggressiveness” of the puncturing of the channel matrices.

Thus, in accordance with a first aspect of the invention a method of generating a voxelated environment model for signal processing in wireless communication in a region of interest (ROI) is presented. The ROI comprises NA > 1 access points (AP) and Nu > 1 UEs (UE). Each of the NA APS (AP) has NR > 1 antennas and all APs (AP) serving the ROI are communicatively connected to a central processing unit (CPU). The VE comprises voxels arranged in a three-dimensional grid.

The method comprises receiving, at the CPU, information about spatial dimensions of voxels within the voxelated environment (VE), about spatial locations of UEs and APs within voxels of the VE, and receiving a puncturing threshold. The spatial locations of UEs and APs may be obtained, e.g., from prior executions of a JCAS method, geo-location information imparted by UEs and/or APs, dead-reckoning considering the movement of an apparatus executing the method, or a combination thereof. The spatial locations are then mapped into the 3D voxel grid of the VE.

The puncturing threshold may comprise a threshold value for the attenuation along a total path length, a critical angle for scattering at a voxel’s surface, information about frequency-dependent attenuation over path length or frequency-dependent critical scattering angles, a value for the maximum number of reflexions along a path, a maximum value or range for a permitted phase shift at reflexion, a maximum value or range for a change in the polarisation at reflexion, and the like, up to which the path is still considered available or realistic. The puncturing threshold may further comprise a probability threshold relating to the probability of a voxel being occupied or empty. The puncturing threshold may be considered a selection input determining how realistic the environment is modelled.

The method further comprises modelling all theoretically possible geometric paths between each UE and each AP, considering all the voxels in the VE of the region of interest (ROI). Modelling all theoretically possible geometric paths only requires the knowledge of the locations of all APs and UEs within the VE, and will yield all paths irrespective of whether or not a voxel in the VE is filled or empty. At this stage, the voxels’ real or assumed properties are not known and of no importance; the theoretically possible geometric paths may be determined simply by considering reflexions off of one or more surfaces of the voxels’ respective parallelepiped.

In a next step, properties of the communication channels corresponding to the respective modelled possible geometric paths are determined. Properties associated with the communication channels comprise at least the total path length, which will correspond to the geometric path’s length, and may further comprise information about lengths of path segments, angles of reflexion between path segments reflected off of a surface of a voxel’s parallelepiped, also referred to herein as scattering angles, parameters relating to the reflexion, such as frequency-dependent attenuation, phase shift, change of polarisation, and the like, that may occur on reflexion. These properties may further comprise, inter alia, frequency-dependent attenuation in accordance with the total channel length.

Once the properties of the communication channels are determined, unavailable paths and/or unrealistic paths are determined and are removed from the totality of the theoretically possible paths. A corresponding VE model is generated that only contains the remaining available and realistic signal paths. The removal of the unavailable and/or the unrealistic paths may be controlled in accordance with the received puncturing threshold. The VE model, a prior distribution of the environment voxels and their respective occupancy parameters derived from the VE model, feasibility coefficient matrices for the respective channel matrices of all available and/or realistic signal paths derived from the VE model, and/or channel matrices punctured in accordance with the feasibility coefficient matrices are then provided to a process of receiving and processing wirelessly transmitted signals in a communication environment represented by the VE, or to a processes of pre-processing signals to be wirelessly transmitted into the communication environment represented by the VE. The feasibility coefficient matrices may hold binary values 0 or 1 , which result in the channel coefficients associated with a feasibility coefficient 0 to be removed, or punctured. It may, however, also be possible to use non-integer feasibility coefficients, and to use thresholds for puncturing.

Determining unavailable and/or unrealistic paths may comprise identifying all geometric paths having more than a predetermined number of reflexions between the UE and the AP, identifying all geometric paths having a total path length or path attenuation exceeding a predetermined value, and/or identifying all geometric paths having at least one reflexion whose scattering angle exceeds a predetermined critical scattering angle 0*. When determining the scattering angles, a reflexion on a surface of a voxel’s parallelepiped may be assumed for simplicity. The information provided in the puncturing threshold may be used, inter alia, for controlling the angle of reflexion that is assumed to still provide a useful signal at the respective receiving node.

When the critical scattering angle 0* is frequency-dependent embodiments of the method may further comprise receiving information about the relation between frequencies and corresponding critical scattering angles 0*, and receiving information about a frequency or frequency band used in a current communication between a UE and an AP. The received information is considered for determining unavailable and/or unrealistic paths.

In one or more embodiments of the method determining unavailable and/or unrealistic paths may further comprise computing, for all antennas of all APs and for each voxel of the VE or for each voxel of the VE that contributes to an available or realistic path, a probability that a signal from a UE is scattered off that voxel towards the respective AP. The puncturing threshold may comprise a predetermined probability threshold value, and a probability below the threshold value indicates that the path is unavailable or unrealistic and is to be removed. The probability may be expressed by a probability density function (PDF) of the scattering angles, e.g., by evaluating equation (3) for all possible combinations of admissible locations of UE, AP and voxel within the ROI, respectively given by cu, CA and cv.

The probability may further be refined based on previous or current received signals and/or previous executions of the method, yielding a most likely state of voxel occupancy, which can be translated into a yet more accurate voxelated environment model.

Identifying unavailable and/or unrealistic paths may further comprise incorporating random blockages of NLOS sub-paths as a function of a selected critical scattering angle 3*, in proportion to the complement cumulative distribution of the probabilities that a signal from a UE is scattered off of that voxel towards a respective AP, and in accordance with the scattering angles at each voxel of the VE. When the critical scattering angle 3* is frequency-dependent, introducing random blockages may also consider the respective frequency or frequency-band used for a transmission from a UE.

The elimination of unavailable and unrealistic paths from the VE proposed herein results in a reduced number of calculations to be performed, or a reduced number of messages to be passed, in a message passing algorithm used for estimating the channel, determining a representation of the environment or recovering received signals. However, the reduction also reduces the accuracy of the channel model and the representation of the environment, and may have an influence on the speed or quality of the signal recovery.

As indicated further above, the method in accordance with the first aspect of the invention can be used in receivers of a communication system configured for performing JCAS. Thus, in accordance with a second aspect of the present invention a method of processing wireless communication signals for use in joint communication and environment perception in a region of interest (ROI) is presented. The ROI comprises NA > 1 access points (AP) and Nu> 1 UEs (UE). Each of the NA APS (AP) has NR > 1 antennas and all APs (AP) serving the ROI are communicatively connected to a central processing unit (CPU). The ROI is represented by a voxelated environment (VE) comprising voxels arranged in a three-dimensional grid. The method comprises receiving, at the CPU, wireless signals received at one or more antennas of one or more APs serving the ROI, and generating, using the method in accordance with the first aspect of the invention presented hereinbefore, a VE model, a prior distribution of the environment voxels and their respective occupancy parameters based on such VE model, feasibility coefficient matrices for respective channel matrices of all available and/or realistic signal paths based on such VE model and/or channel matrices punctured in accordance with the feasibility coefficient matrices. Alternatively, such environment information may be received. The generated or received environment information is then provided as input to a JCAS process in a receiver associated with the ROI. It is noted that the receiver may be collocated with the CPU, e.g., when the communication system is configured for centralised signal reception for the ROI. Exemplary JCAS processes to which the environment information can be provided include the AL-ISAC process and the Bi-ISAC process, although other JCAS processes may also benefit from the environment information.

The method in accordance with the first aspect of the invention may also be used in transmitters of a communication system. Thus, in accordance with a third aspect of the present invention a method of transmitter-side processing wireless communication signals is presented. The transmitter is communicatively connected to a central processing unit (CPU), which CPU is communicatively connected to NA > 1 access points (AP) serving a region of interest (ROI). The ROI is represented by a voxelated environment (VE) comprising voxels arranged in a three-dimensional grid. The method comprises receiving, from the CPU and determined in accordance with the method in accordance with the first aspect of the invention, a VE model of the ROI. Alternatively, a prior distribution of the environment voxels and their respective occupancy parameters based on such VE model, or at least one feasibility coefficient matrix based on such VE model for a corresponding respective channel matrix of a signal path between the transmitter () and a user equipment (UE) located within the ROI may be received. In a further step, at least one channel matrix of a signal path between the transmitter and a UE, punctured in accordance with the received environment information is determined, or at least one such punctured channel matrix is received from the CPU. The at least one punctured channel matrix is then provided to an equaliser process and/or or to a precoder process in the transmitter as an input, for preequalising and/or precoding, respectively, signals to be transmitted. The preequalized and/or pre-coded signals may then be transmitted into the ROI, after any optional further processing.

In the following section the robustness of the exemplary methods discussed further above under various degrees of puncturing and elimination of unrealistic paths is analysed, incidentally also revealing advantages of each method relative to the other.

For the sensing function in particular, it is noted that metrics used for radar-based ISAC cannot be used directly due to the unique voxelated occupancy grid-based approach exploited herein. It is, therefore, useful to instead introduce a new metric, referred to as the voxel-occupancy-error-rate (VOER), which measures the rate of false-positive (FP) and false-negative (FN) elements, defined as the incorrect estimation of an occupied voxel element in presence of an empty ground-truth, and the incorrect estimation of an empty voxel element in the presence of an occupied ground-truth, respectively. Mathematically, the VOER is defined as where v is the ground truth and v is the voxel coefficient estimate vector, respectively, while ||-||₀ denotes the -norm of a vector.

Note that for the trivial all-empty (or “blind”) estimator, which returns v = 0_NyX1, the VOER reduces to which is the average sparsity of the environment. This figure can, therefore, be used as an absolute reference of performance, in the sense VOER « V0ER_ernpty indicating a good sensing performance for a considered ISAC method. Finally, instead of the SER often used in related literature, here the communication performance of the exemplary ISAC methods in terms of the more descriptive BER is evaluated, which is defined as BER = ^\B_e]/B, where Be denotes the number of erroneously detected data bits of XD, and #is the total number of bits conveyed in XD.

In the first evaluation, the effect of varying the amount of pilot symbols - as captured by the parameter p - onto the performances of the methods proposed herein is studied. The results on the sensing performance, shown in Fig. 16 (a), indicate that, with the same values of p, the Bi-ISAC method outperforms the AL- ISAC method over the entire SNR range. In other words, for a given SNR the Bi- ISAC method requires a much lower number of pilots to achieve the same VOER performance as the AL-ISAC method.

The effect of the pilot ratio on the communications performance in terms of BER is evaluated in Fig. 16 (b). It can be seen that tor small pilot ratios, i.e., p< 0.2, the two methods proposed herein achieve a similar performance, but that for larger pilot ratios, i.e., p> 0.3, the AL-ISAC scheme outperforms the Bi-ISAC scheme in moderate SNR cases, i.e., 5dB. This result, which may appear to be counterintuitive, is actually expected and explained by the fact that linear MP modules of the AL-ISAC scheme are constructed on the assumption of perfect symbol knowledge, i.e., 0 uncertainty for the symbol estimates, which assumption is increasingly met with large pilot ratios.

Ultimately, however, at significantly high SNRs, e.g., SNR > 15dB, the Bi-ISAC scheme is again shown to outperform the AL-ISAC scheme, which is a direct consequence of the error-floor behaviour exhibited by the AL-ISAC scheme.

Fig. 17 elucidates the effect of random channel blockages. In particular, the figure compares the VOER and BER performances of the two proposed ISAC methods with respect to the critical angle 0*, which determines the channel blockage rate following the stochastic-geometric empirical model derived further above (see figure 6). The environment sensing performance illustrated in Fig. 17 (a) exhibits a similar behaviour with respect to the effect of p, with the Bi-ISAC scheme achieving a superior performance for all cases. In addition, the curves of the Bi-ISAC scheme show a slower increase in gradient compared to those of the AL-ISAC scheme, which indicates the higher robustness of the Bi-ISAC scheme to path blockages.

The superior robustness of the Bi-ISAC scheme at short pilot lengths and against random channel blockages can be accredited to the increased number of edges in the full factor graph arising from the bilinear representation of the system, which can be seen by comparing figure 8 and figure 10 of the linear case against figure 14 of the bilinear case. Each factor node of the bilinear factor graph is connected to a significantly larger number of variable nodes compared to the factor nodes of the linear factor graphs, which implies more remaining edges for stable message passing even when a large number of edges are removed, as is proposed by the present invention. Message passing over the pruned graph is only feasible when there is sufficient pilot data still connected to the main graph, therefore making the Bi-ISAC scheme more dependent on the pilot ratio for stability.

As for the communications performances, compared in Fig. 17 (b), it is found that the behaviour of both schemes differs with the pilot ratio. For low pilot ratios, the AL-ISAC scheme is shown to slightly outperform the Bi-ISAC scheme, with similar robustness to the path blockages, whereas for high pilot ratios, the Bi-ISAC scheme exhibits a significantly superior performance over the AL-ISAC scheme. This inspires to adjust the pilot ratio in dependence of the puncturing, which itself depends on the environment.

Thus, in embodiments of the method in accordance with the third aspect of the invention, a puncturing coefficient or threshold determined for a communication connection between an AP and a UE in the ROI is provided as input to transmitters of one or more APs carrying a corresponding communication connection. As has been shown above, the puncturing coefficient or threshold carries information about a critical angle, which critical angle, together with the pilot ratio, has an impact on the VOER and BER performance of the receivers. The transmitter adapts the pilot ratio for the respective communication connection in accordance with the received puncturing coefficient or threshold.

The methods presented hereinbefore may be represented by computer program instructions of a computer program product. Accordingly, in accordance with a third aspect of the invention, a computer program product comprises computer program instructions, which, when executed by a processor of or functionally coupled with a receiver, cause the processor or control the receiver to carry out a method in accordance with the first and/or second aspect of the present invention.

The computer program instructions may be retrievably stored or transmitted on a computer-readable medium or data carrier. The medium or the data carrier may by physically embodied, e.g., in the form of a hard disk, solid state disk, flash memory device or the like. However, the medium or the data carrier may also comprise a modulated electro-magnetic, electrical, or optical signal that is received by the computer by means of a corresponding receiver, and that is transferred to and stored in a memory of the computer.

In accordance with a fourth aspect of the present invention a wireless communication apparatus configured for processing wireless communication signals for transmitting and/or upon receiving comprises at least one antenna, circuitry for processing radio frequency signals, a microprocessor, volatile and nonvolatile memory, which elements or components are connected via one or more data and/or signal lines or buses. The non-volatile memory stores computer program instructions which, when executed by the microprocessor, configure elements or components of the wireless communication apparatus to implement or carry out the method in accordance with the first, the second and/or the third aspect of the present invention.

In one or more embodiments the wireless communication apparatus comprises a receiver co-located to a transmitter.

In one or more embodiments the circuitry of the wireless communication apparatus for processing radio frequency signals comprises a low noise amplifier and/or a mixer configured for providing a representation of a received signal at an intermediate frequency. The mixer preferably uses a same oscillator signal as a transmitter co-located with a receiver. The latter may enable using signals transmitted by the entity comprising the receiver, which are reflected off objects, for environment perception.

Two or more communication apparatus according to the fourth aspect of the invention may form a system permitting communication and estimation of NLOS channels in accordance with the methods presented hereinbefore. The signals used in the system preferably have at least one pilot signal.

The present invention advantageously permits more realistically and accurately modelling a voxelated environment model that considers path blockage, scattering, non-ideal geometry-based behaviour, unrealistic reflection angles, energy loss at scattering, other frequency-dependent behaviour, and channel path losses based solely on geometry, for use in communication systems. Not only enables this a much improved and more accurate channel estimation, it also reduces the computational effort, since unavailable and/or unrealistic paths are removed from the process, i.e., are not considered. The statistical approach, in which it is tried to accommodate the fact that there statistically may be a scatter at any voxel, may further improve the model, yielding a most likely state of a voxel. The improved channel estimation contributes to an improved and faster symbol detection and, inter alia, may open the path to a lighter forward error correction, which may translate into a higher spectral efficiency.

Unlike prior VE models, the method in accordance with the invention further takes the behaviour at scattering into account. Generally, it can be assumed that there is scattering of the incident signal wave at the positions of at least some voxels. The prior art assumes that the scattering occurs without energy loss and occurs equally in all directions. Contrary to that, the method in accordance with the invention captures the actual physical behaviour of the electromagnetic wave at scattering. This permits modelling of scattered paths based on geometry and frequency, and further permits modelling of energy-loss at scattering. With these two pieces of information, the unrealistic scattered paths may be punctured based on physical electromagnetic wave theories, i.e., Mie’s or Rayleigh’s scattering formula, Maxwell equations, and the scattering coefficients of the voxels can be extended from the binary 0-or-1 , which is found in prior art methods, to a more realistic continuous value between 0 and 1 , or even complex values.

Finally, the method in accordance with the invention permits adjusting how strongly the method removes the unrealistic, i.e., blocked paths, and scattering, by adjusting the “puncturing threshold” input to the method. This adds margin intervals for the blocked paths and scattering angle calculations, to provide a more lenient puncturing.

The methods presented herein are applicable to any scenario where a voxelated grid model is to be used to model the environment, namely the scenarios that may be considered in the joint communication and sensing settings. In particular, the present invention can be used in indoor scenarios with stationary APs, communicating and detecting an environment by mobile vehicles communicating to roadside units (RSUs) while achieving vehicular/pedestrian detection, by multiple vehicles cooperatively sensing an environment and road conditions without RSUs, by multiple connected UEs (Bluetooth, Wi-Fi, loT, etc.) for passively sensing an environment (i.e., without the use of sensing specific signals), and the like. The use-cases and benefits of the methods of communication and environment sensing functionalities presented herein involve and can be achieved within, respectively, the same wireless interface.

BRIEF DESCRIPTION OF THE DRAWING

The figures in the attached drawing are used for detailing aspects of the present invention. In the figures

Fig. 1 shows an exemplary environment with objects in a region of interest, and voxelated representations thereof,

Fig. 2 shows a representation of the general concept of LOS and NLOS paths in a voxelated space,

Fig. 3 shows a schematic representation of the 3D space considered in a known system and method, Fig. 4 shows process modules of a prior art JCAS method that are iterated in a sliding window fashion,

Fig. 5 shows a schematic representation of unavailable and unrealistic communication paths in the voxelated space,

Fig. 6 shows empirical beta mixture modelling of scattering angle distributions,

Fig. 7 shows the effect of the critical angle G_crn on the severity of puncturing on the channel matrices for different voxelated grid resolutions

Fig. 8 shows the factor graph of the linear system formulated for the estimation of the voxel coefficients v,

Fig. 9 shows an exemplary flow diagram of methods steps invoked for the estimation of the voxel coefficients v,

Fig. 10 shows the factor graph of the linear system formulated for the estimation of the signal matrix X,

Fig. 11 shows an exemplary flow diagram of methods steps invoked for the estimation of the signal matrix X,

Fig. 12 shows a schematic flow diagram of the exemplary AL-ISAC method,

Fig. 13 shows a schematic diagram of the exemplary Bi-ISAC method,

Fig. 14 shows the tripartite factor graph of the bilinear system,

Fig. 15 shows an exemplary flow diagram of the exemplary Bi-ISAC method,

Fig. 16 shows the VOER and BER performance of the exemplary AL-ISAC and Bi-ISAC methods at varying SNR values, as a function of the pilot length ratio p,

Fig. 17 shows the VOER and BER performance of the exemplary AL-ISAC and Bi-ISAC methods at varying pilot length ratios p as a function of the critical angle 0*,

Fig. 18 shows a schematic overview of the inputs and outputs to the method in accordance with the first aspect of the invention,

Fig. 19 shows an exemplary block diagram of a wireless communication apparatus in accordance with the fourth aspect of the invention,

Fig. 20 shows an exemplary schematic flow diagram of the method in accordance with the first aspect of the invention,

Fig. 21 shows an exemplary schematic flow diagram of the method in accordance with the second aspect of the invention, and Fig. 22 shows an exemplary schematic flow diagram of the method in accordance with the third aspect of the invention.

DETAILED DESCRIPTION OF EMBODIMENTS

Figures 1 to 17 have been described further above and will not be discussed again.

Figure 18 shows a schematic overview of the inputs and outputs to the method in accordance with the first aspect of the invention. Inputs to the method are physical parameters, e.g., the spatial positions of the UEs and the APs, and configurable parameters, e.g., the voxel unit size and the puncturing threshold. The output is a voxelated environment model that comprises the scatterer voxels and the realistically available channel paths.

Figure 19 shows an exemplary block diagram of a wireless communication apparatus 400 in accordance with the fourth aspect of the invention. The wireless communication apparatus 400 comprises at least one antenna 402, circuitry 404 for processing radio frequency signals, a microprocessor 412, a volatile memory 414, and a non-volatile memory 416. The aforementioned elements are communicatively connected via at least one signal or data connection or bus 418. The non-volatile memory 416 stores computer program instructions which, when executed by the microprocessor 412, cause the wireless communication apparatus 400 to implement or execute embodiments of the method according to the first or the second aspect of the present invention.

Figure 20 shows an exemplary schematic flow diagram of the method 100 in accordance with the first aspect of the invention. In step 110 information about spatial dimensions of voxels within the VE, about spatial locations of UEs and APs within voxels of the VE, and a puncturing threshold are received. In step 120 all theoretically possible geometric paths between each UE and each AP are modelled, considering all voxels in the VE of the ROI. In step 130 properties of communication channels corresponding to the respective modelled geometric paths are determined. In step 140 unavailable and/or unrealistic paths are determined. In step 160 a VE model is generated, from which the unavailable and/or unrealistic paths are removed in accordance with the received puncturing threshold. In step 170 the VE model, a prior distribution of the environment voxels and their respective occupancy parameters derived from the VE model, feasibility coefficient matrices for the respective channel matrices of all available and/or realistic signal paths derived from the VE model, and/or channel matrices punctured in accordance with the feasibility coefficient matrices are output.

Figure 21 shows an exemplary schematic flow diagram of the method 200 in accordance with the second aspect of the invention. In step 210 wireless signals received at one or more antennas of one or more APs serving the ROI are received at the CPU. In step 220 a VE model, a prior distribution of the environment voxels and their respective occupancy parameters based on such VE model, feasibility coefficient matrices for respective channel matrices of all available and/or realistic signal paths based on such VE model and/or channel matrices punctured in accordance with the feasibility coefficient matrices is generated in accordance with the method 100 in accordance with the first aspect of the invention, or such environment information is received. In step 230 the environment information and, optionally, the received wireless signals are provided as input to a JCAS process in a receiver associated with the ROI.

Figure 22 shows an exemplary schematic flow diagram of the method 300 in accordance with the third aspect of the invention. In step 310 a VE model of the ROI, or a prior distribution of the environment voxels and their respective occupancy parameters based on such VE model, or at least one feasibility coefficient matrix based on such VE model for a corresponding respective channel matrix of a signal path between the transmitter and a user equipment (UE) located within the ROI, determined in accordance with the method 100 in accordance with the first aspect of the invention, is received from the CPU. In step 320 at least one channel matrix of a signal path between the transmitter and a UE, punctured in accordance with the received environment information is determined, or at least one such punctured channel matrix is received from the CPU. In step 330 the at least one punctured channel matrix is provided as input to an equaliser process and/or or to a precoder process in the transmitter, for pre-equalising and/or precoding, respectively, signals to be transmitted. Finally, in step 340, the signals are transmitted into the ROI.

Claims

1 . A method (100) of generating a voxelated environment model for signal processing in wireless communication in a region of interest (ROI) comprising NA > 1 access points (AP) and Nu > 1 UEs (UE), each of the NA APs (AP) having NR > 1 antennas and all APs (AP) serving the ROI being communicatively connected to a central processing unit (CPU), the VE comprising voxels arranged in a three-dimensional grid, the method comprising:

- receiving (110), at the CPU, information about spatial dimensions of voxels within the voxelated environment (VE), about spatial locations of user equipment (UE) and access points (AP) within voxels of the VE, and a puncturing threshold,

- modelling (120) all theoretically possible geometric paths between each UE and each AP, considering all voxels in the VE of the region of interest (ROI),

- determining (130) properties of communication channels corresponding to the respective modelled geometric paths,

- determining (140) unavailable and/or unrealistic paths,

- generating (160) a VE model from which the unavailable and/or unrealistic paths are removed in accordance with the received puncturing threshold, and

- providing (170) the VE model, a prior distribution of the environment voxels and their respective occupancy parameters derived from the VE model, feasibility coefficient matrices for the respective channel matrices of all available and/or realistic signal paths derived from the VE model, and/or channel matrices punctured in accordance with the feasibility coefficient matrices, to a process of receiving and processing wirelessly transmitted signals in a communication environment represented by the VE, or to a processes of pre-processing signals to be wirelessly transmitted into the communication environment represented by the VE.

2. The method of claim 1 , wherein determining (140) unavailable and/or unrealistic paths comprises identifying all geometric paths having more than a predetermined number of reflexions between the UE and the AP, identifying all geometric paths having a total path length or path attenuation exceeding a predetermined value, and/or identifying all geometric paths having at least one reflexion whose scattering angle exceeds a predetermined critical scattering angle (3*).

3. The method of claim 2, further comprising, when the critical angle (6*) is frequency-dependent:

- receiving, at the CPU, information about the relation between frequencies and corresponding critical scattering angles (0*),

- receiving, at the CPU, information about a frequency or frequency band used in a current communication between a UE and an AP, and

- considering the respective critical scattering angles (0*) for determining (140) unavailable and/or unrealistic paths.

4. The method of one of the preceding claims, wherein determining (140) unavailable and/or unrealistic paths comprises computing, for all antennas of all APs and for each voxel of the VE or for each voxel of the VE that contributes to an available or realistic path, a probability that a signal from a UE is scattered off that voxel towards the respective AP, and correspondingly removing unavailable and/or unrealistic paths in accordance with the received puncturing threshold.

5. The method of claim 4, wherein computing the probability comprises evaluating, for all theoretically possible geometric paths between admissible locations of APs, UEs and voxels within the ROI, scattering angles at each voxel.

6. The method of claim 4 or 5, wherein determining (140) unavailable paths further comprises incorporating random blockages of NLOS sub-paths as a function of a predetermined critical scattering angle (0*), in proportion to a complement cumulative distribution of the probabilities that a signal from a UE is scattered off that voxel towards the respective AP, and in accordance with the scattering angle at each voxel of the VE or at each voxel of the VE that contributes to an available or realistic path.

7. A method (200) processing wireless communication signals for use in joint communication and environment perception (JCAS) in a region of interest (ROI) comprising NA > 1 access points (AP) and Nu > 1 UEs (UE), each of the NA APS having NR > 1 antennas and all APs serving the ROI being communicatively connected to a central processing unit (CPU), the ROI being represented by a voxelated environment (VE) comprising voxels arranged in a three-dimensional grid, the method comprising:

- receiving (210), at the CPU, wireless signals received at one or more antennas of one or more APs serving the ROI,

- generating (220), in accordance with the method of one or more of claims 1 to 6, a VE model, a prior distribution of the environment voxels and their respective occupancy parameters based on such VE model, feasibility coefficient matrices for respective channel matrices of all available and/or realistic signal paths based on such VE model and/or channel matrices punctured in accordance with the feasibility coefficient matrices, or receiving such environment information, and

- providing (230) the environment information and, optionally, the received wireless signals as input to a JCAS process in a receiver associated with the ROI.

8. A method (300) of transmitter-side processing wireless communication signals comprising, at a transmitter communicatively connected to a central processing unit (CPU), which CPU is communicatively connected to NA > 1 access points (AP) serving a region of interest (ROI), the ROI being represented by a voxelated environment (VE) comprising voxels arranged in a three-dimensional grid:

- receiving (310), from the CPU and determined in accordance with the method (100) in accordance with one or more of claims 1 to 6, a VE model of the ROI, or receiving a prior distribution of the environment voxels and their respective occupancy parameters based on such VE model, or receiving at least one feasibility coefficient matrix based on such VE model for a corresponding respective channel matrix of a signal path between the transmitter and a user equipment (UE) located within the ROI,

- determining (320) at least one channel matrix of a signal path between the transmitter and a UE, punctured in accordance with the received environment information, or receiving at least one such punctured channel matrix from the CPU,

- providing (330) the at least one punctured channel matrix as input to an equaliser process and/or or to a precoder process in the transmitter, for preequalising and/or precoding, respectively, signals to be transmitted, and

- transmitting (340) the signals into the ROI.

9. The method of claim 8, further comprising providing a puncturing coefficient determined for a communication connection between an AP and a UE in the ROI as input to transmitters of one or more APs carrying a corresponding communication connection, and adapting the pilot ratio for the respective communication connection in accordance with the puncturing coefficient.

10. A computer program product comprising computer program instructions, which, when executed by a processor of or functionally coupled with a central processing unit (CPU), a receiver or a transmitter, cause the processor or control the CPU, the receiver or the transmitter to carry out the methods of one or more of claims 1 to 6, 7 or 8 to 9, respectively.

11 . Computer readable medium or data carrier retrievably transmitting or storing the computer program product of claim 10.

12. A wireless communication apparatus (400) configured for processing wireless communication signals for transmitting and/or upon receiving, the apparatus comprising at least one antenna (402), circuitry (404) for processing radio frequency signals, a microprocessor (412), volatile (414) and non-volatile (416) memory, connected via one or more data and/or signal lines or buses (418), wherein the non-volatile memory stores computer program instructions which, when executed by the microprocessor, configure components of the wireless communication apparatus to implement or carry out the method of any one of claims 1 to 9.

13. The wireless communication apparatus (400) of claim 12, wherein the circuitry for processing radio frequency signals comprises a low noise amplifier and/or a mixer configured for providing a representation of a received signal at an intermediate frequency, preferably using a same oscillator signal as a co-located transmitter.

14. A communication system comprising two or more communication apparatus according to any one of claims 12 or 13.