System and methods for multiplexing with modulation on zeros

Abstract

A first aspect of the present disclosure is related to a device for providing a communication signal, configured to: - provide a base signal, wherein the base signal is based on modulation on zeros, MOZ, wherein a zero-vector is chosen from a zero-constellation vector-set, to encode data into a data zero-vector, and in particular a guard zero-vector, to provide control information or to shape properties of the base signal.

Description

[0001] System and Methods for Multiplexing with Modulation on Zeros

[0002] Technical Field

[0003] This disclosure is related to devices for transmitting, receiving, and sensing signals in relation to Modulation on Zeros

[0004] Background

[0005] Modulation On Zeros (MOZ) is a recently developed communication technique (US 10,797,926 B2) used to modulate data by manipulating the positions of zeros of a polynomial of a base signal. Unlike traditional modulation schemes that map information to modulated IQ samples in time or frequency domain, MOZ maps information to zeros in a complex plane, which define a polynomial, and transforms them back to the polynomial coefficients which are the modulated IQ-samples in time domain. This method can provide advantages in certain communication environments, particularly in multipath- rich and / or high mobility scenarios. Further developments of this communication scheme are presented in the following.

[0006] Summary

[0007] An object of the present disclosure is to improve a communication based on Modulation on Zeros.

[0008] This object is solved by the disclosed embodiments, which are defined in particular by the subject matter of the independent claims. The dependent claims provide information for further embodiments. Various aspects and embodiments of these aspects are also disclosed in the summary and description below, which provide additional features and advantages.

[0009] In this disclosure, embodiments for a signaling scheme between host and target are presented, which use a recently disclosed non-coherent modulation scheme called Modulation on Zeros. MOZ is used here in combination with a spatial-temporal (ST) pulsed-beam-sweeping technique. The host and target can be vehicles or a mobile transceivers in general. The invention allows a reliable transmission of data from hosts to targets, in a given observable region, and at the same time the sensing of the 2D / 3D MIMO channel at the hosts (mono-static radar where host transmitter and host receiver are co-located), i.e. sensing the channel in time by its paths delays, gains and phases and in space by its paths directions.

[0010] In a modification of the target receiver, a sensing of the 2D / 3D MIMO channel is also possible at the target. In a further modification, a third party could also sense the 2D / 3D MIMO channel between the transmit host and target by receiving the reflection from the target as well. This passively receiving third party can identify a position of a target if it knows the position of a transmitting host (bi-static radar) and is properly synchronized with the transmitting host.

[0011] Some of the disclosed embodiments based on the MOZ signaling scheme allow for a fast beam-sweeping of a given spatial-domain with higher accuracy in speed and position estimations of the targets, by utilizing shorter pulsed- radar signals with an Interference Suppression technique for signals of adjacent beams. The transmitted signals are hereby spread over a spatial- temporal-domain, given by the triple (Q, R, T). The observable Spatial-Domain O = Q A R, is defined for two dimensions in an azimuth plane by the angle <p in an angular area Q, which defines a direction of a target from a hosts driving direction, and by a distance d in the range region R. The temporal-domain T is separated in consecutive time-slots T n, in which a complete signal is transmitted in one direction.

[0012] In a more particular case of MOZ called Modulation on Conjugate-reciprocal Zeros (MOCZ), improved radar properties and non-coherent data transmission can be achieved, since the signals can be kept extremely short in time, allowing an increased communication-radar performance.

[0013] A first aspect of the present disclosure is related to a device for providing a communication signal, configured to:

[0014] - provide a base signal, wherein the base signal is based on modulation on zeros, MOZ, wherein a zero-vector is chosen from a zero-constellation vector- set, to encode data into a data zero-vector, and in particular a guard zero- vector, to provide control information or to shape properties of the base signal.

[0015] A base signal can be sequence of complex-numbers, e.g. representing the IQ samples of a time-discrete baseband signal. In particular a base signal can be a finite sequence of complex-numbers.

[0016] For a base signal based on modulation on zeros (MOZ) the sequence of complex-numbers are the coefficients of a polynomial determined by its roots / zeros given by a zero-vector and a scaling factor. For a base signal x based on MOZ of order K the polynomial X(z) has K zeros a_1 , a_2, . . . , a_K, defined as the coefficient of the zero-vector a, and K +1 polynomial coefficients x_0, x_1 . . . , x_K, defined as the coefficient of the base signal x. As an example for K = 2 consider x_2*zA2 +x 1*z+x_0 = x_2*(z-a_1 )*(z-a_2 ) = X(z), where the complex-numbers x_0 , x_1 and x_2 are the coefficients of the polynomial X(z) and the coefficients of the zero-vector a = (a_1 , a_2 ) are its zeros / roots and x_2 its complex-valued scaling factor.

[0017] A zero-vector defining the zeros of a base signal based on MOZ is separated in a data-zero-vector and a guard-zero-vector. The data-zero vector carries the information / message / payload of the base signal and the guard-zero-vector shapes and / or controls the base signal.

[0018] A zero-constellation vector-set can be a set of zero vectors, wherein some zeros can be related to data zeros and others can be related to guard zeros.

[0019] By using a zero vector from a pre-defined zero-constellation vector set guard zeros and data can be comprised such that certain conditions such as stability and hardware effects, etc. can be met. An embodiment of the first aspect is related to a device for providing a communication signal, configured to:

[0020] - provide the MOZ base signal is based on a guard zero-vector that comprises one or more guard-zeros, wherein, in particular, the one or more guard zeros are characterized by one or more of the following characteristics in a complex plane:

[0021] - being placed on / near the unit-circle;

[0022] - being located as a contiguous block such that its phases are near a given phase;

[0023] - being placed at "1".

[0024] By providing the above-named characteristics, a MOZ signal can be equipped with one or more pre-defined characteristics, such as a DC-value (in case a zero is placed at 1).

[0025] An embodiment of the first aspect is related to a device for providing a communication signal, configured to:

[0026] - provide a MOZ base signal of order K that comprises a zero-vector with K zeros; wherein a phase distance for each zero to its two next-neighbor zeros is 2TT / K in the complex plane.

[0027] This distribution of zeros with the complex plane can increase numerical stability and / or robustness, e.g. against noise.

[0028] A second aspect of the present disclosure is related to a device for providing a communication signal, configured to:

[0029] - obtain and / or determine multiple MOZ base signals;

[0030] - provide a further signal based on one or more convolutions and / or correlations between individual linear transformations of the multiple MOZ base signals.

[0031] The device can also be configured to provide a plurality of further signals, wherein each of these further signals is based on respectively determined multiple MOZ base signals.

[0032] A convolution can be performed before a correlation and / or vice versa.

[0033] In both cases (correlation, convolution) zeros of the processed MOZ base signals are joint. This can be used, e.g. for joining information. In case the MOZ base signals are based on the same information this increases redundancy.

[0034] An embodiment of the second aspect is related to a device for providing a communication signal, wherein the multiple MOZ base signals comprise individual zero-constellation vector-sets of pre-defined size.

[0035] Different MOZ signals can have different signal lengths. Thereby, short MOZ signals can be joint with longer MOZ signals.

[0036] An embodiment of the second aspect is related to a device for providing a communication signal, wherein one or more of the linear transformations are a composition of multiple linear transformations.

[0037] Thereby, different MOZ signals can be constructed based on simpler, shorter MOZ signals.

[0038] An embodiment of the second aspect is related to a device for providing a communication signal, wherein one or more of the linear transformations are a deterministic or random filter g combined with an expander E.

[0039] This can increase numerical stability and / or robustness, e.g. against noise.

[0040] An embodiment of the second aspect is related to a device for providing a communication signal, wherein one or more of the linear transformations are based on a deterministic and / or random time-frequency transformation.

[0041] Thereby, robustness and signal flexibility can be increased.

[0042] An embodiment of the second aspect is related to a device for providing a communication signal, wherein a linear transformation is a mapping D_£ based on a weighted repetition of a vector.

[0043] Thereby, stability, robustness, and redundancy can be increased.

[0044] An embodiment of the second aspect is related to a device for providing a communication signal, wherein a linear transformation is comprised in a sum of time-frequency transformation of weighted repetitions applied on one or more MOZ base signals.

[0045] Thereby, stability, robustness, and redundancy can be increased.

[0046] An embodiment of the second aspect is related to a device for providing a communication signal, configured to:

[0047] - provide a MOZ signal with a fingerprinting that encodes additional pre- determined information. Thereby, different information can be added to a MOZ signal, e.g. hardware characteristics of the device.

[0048] A third aspect of the present disclosure is related to a device for providing a communication signal, configured to:

[0049] - obtain and / or determine a base signal;

[0050] - add to the obtained and / or determined base signal an additional MOZ base signal by a third party or by itself, wherein the adding is based on a convolution and / or a correlation of the base signal with the MOZ base signal.

[0051] This allows, e.g., a fingerprinting by a MOZ base signal of any obtained signal.

[0052] In case the device is a relaying device, it is configured to receive a base signal from another party and add information either from a third party and / or from itself to the received base signal as a fingerprint.

[0053] An embodiment of the second aspect is related to a device for providing a communication signal, wherein the obtained and / or determined signal is a MOZ base signal using a zero-constellation-vector set which has no common zero to the zero- constellation-vector-set used by the added MOZ signal.

[0054] Thereby, it can be assured that no information collide in case the received signal is a MOZ signal as well.

[0055] An embodiment of the second aspect is related to a device for providing a communication signal, wherein the convolution and / or correlation is based on a baseband and / or a passband. Performing the processing in the base band may require a digital signal processing of the provided signal.

[0056] Performing the processing in the passband allows an analog processing of the provided signal.

[0057] A fourth aspect of the present disclosure is related to a device for providing a communication signal, configured to:

[0058] - provide a MOZ base signal; wherein the zeros of the MOZ base signal are based on at least two different zero-constellation vector-sets for encoding different control and / or data payloads.

[0059] With one zero-constellation vector-set determines control data and the other zero-constellation vector-sets determines payload data.

[0060] A fifth aspect of the present disclosure is related to a receiver for obtaining a communication signal, configured to:

[0061] - obtain information on one or more used zero-constellation-vector-sets, each comprising a data zero-constellation-vector-set and a control zero- constellation-vector-set;

[0062] - obtain a MOZ signal comprising a zero-constellation-vector that comprises a data zero-constellation-vector and a control zero-constellation-vector;

[0063] - extract data from the obtained MOZ signal based the data zero-constellation- vector, on the control zero-constellation-vector, and on the data zero- constellation-vector-sets and the control zero-constellation-vector-sets.

[0064] By knowing the control information, the payload data can be decoded more efficiently and / or reliably. An embodiment of the fifth aspect is related to a device for obtaining a communication signal, configured to:

[0065] - obtain a MOZ base signal comprising data zeros and control zeros; - determine a control MOZ-base signal based on known control zeros of the control zero-constellation vector sets;

[0066] - convolve and / or correlate the obtained MOZ base signal with the determined control MOZ-base signal to determine a data signal from the MOZ base signal.

[0067] If the control information that is comprised in the received MOZ base signal does not match the know control information, the signal is suppressed.

[0068] Otherwise, the data zeros of the received MOZ base signal can be decoded more reliable.

[0069] A sixth aspect of the present disclosure is related to a device for integrated communication and sensing, configured to:

[0070] - provide a first signal comprising communication data, wherein the first signal is based on a MOZ;

[0071] - obtain a second signal which is based on a reflection of the first signal;

[0072] - correlate a third signal, based on characteristics of the first signal, with the second signal;

[0073] - determine a time-based, a position-based, phase-based, and / or Doppler- based parameter based on a similarity measure, for example correlation.

[0074] In this case the transmitter of the MOZ signal also receives a radar-like reflection signal based on the transmitted MOZ signal.

[0075] A seventh aspect of the present disclosure is related to a device for communicating a signal, configured to:

[0076] - provide a first signal based on a MOZ and based on a first spatial and / or temporal characteristic; - provide a second signal based on a MOZ and on a second spatial and / or temporal characteristic;

[0077] - identify a reflection based on the first signal and a reflection based on the second signal, wherein the identification is based on one or more correlations.

[0078] Brief description of the figures

[0079] Further advantages and features result from the following embodiments, some of which refer to the figures. The figures do not always show the embodiments to scale. The dimensions of the various features may be enlarged or reduced, in particular for clarity of description. For this purpose the figures are at least partially schematized.

[0080] Fig. 1 illustrates a configuration of data zeros and guard zeros according to embodiments of the present disclosure.

[0081] Fig. 2 illustrates a MOZ signal with piggybacking of new information by a sensor B to signal of sensor A with BMOCZ schemes according to embodiments of the present disclosure.

[0082] Fig. 3 illustrates a zero-constellation vector set according to embodiments of the present disclosure.

[0083] Fig. 4 illustrates a binary MOCZ in the z-domain according to embodiments of the present disclosure.

[0084] Fig. 5 illustrates transmission of ISAC signals between different vehicles according to embodiments of the present disclosure.

[0085] Fig. 6 illustrates radar detection with beam sweeping according to prior art. Fig. 7 illustrates a configuration of a pulsed-radar method with angular scanning / beam-sweeping according to prior art.

[0086] Fig. 8 illustrates a configuration of a pulsed-radar beam sweeping method according to embodiments of the present disclosure.

[0087] Fig. 9 illustrates a beam-forming set-up according to embodiments of the present disclosure.

[0088] Fig. 10 illustrates an observable region from a perspective of a host vehicle according to embodiments of the present disclosure.

[0089] Fig. 11 illustrates a beam interference of a received signal at a host vehicle according to embodiments of the present disclosure.

[0090] Fig. 12 illustrates an ISAC situation with two host vehicles according to embodiments of the present disclosure.

[0091] Fig. 13 illustrates a channel delay propagation according to embodiments of the present disclosure.

[0092] Fig. 14 illustrates an external fingerprinting by a relay-cube at the center of a street junction according to embodiments of the present disclosure.

[0093] In the following description reference is made to the accompanying figures which form part of the disclosure, and which illustrate specific aspects in which the present disclosure can be understood. Identical reference signs refer to identical or at least functionally or structurally similar features.

[0094] In general, a disclosure of a described method also applies to a corresponding device (or apparatus) for carrying out the method or a corresponding system comprising one or more devices and vice versa. For example, if a specific method step is described, a corresponding device may include a feature to perform the described method step, even if that feature is not explicitly described or represented in the figure. On the other hand, if, for example, a specific device is described on the basis of functional units, a corresponding method may include one or more steps to perform the described functionality, even if such steps are not explicitly described or represented in the figures. Similarly, a system can be provided with corresponding device features or with features to perform a particular method step. The features of the various exemplary aspects and embodiments described above or below may be combined unless expressly stated otherwise.

[0095] Since all disclosed aspects or embodiments are based on MOZ, features or functions described in context of one aspect / embodiment / figure can be used for another aspect / embodiment.

[0096] Detailed description

[0097] As used herein the term “and / or” includes any and all combinations of one or more of the associated listed items and may be abbreviated as 7”.

[0098] Although some aspects have been described in the context of an apparatus, it is clear that these aspects also represent a description of the corresponding method, where a block or device corresponds to a method step or a feature of a method step. Analogously, aspects described in the context of a method step also represent a description of a corresponding block or item or feature of a corresponding apparatus.

[0099] Notation

[0100] We write vectors as bold small roman or Greek letter, as for example x or a and their elements as small kursiv roman orgreek letters, such as x resepctivel a. Matrices are bold capital Roman letter, as for example A. Indices with small letter are running indices. Indices with capital roman letter are acronyms, for example KDis the number of data-zeros. Calligraphic capital letters are sets, as for example Z or Q. The set can have infinite or finite elements. Capital letters denote usually non-negative integers, such as M. The set of all non-negative integers is denoted by N. The notation X(z) refers to a polynomial over the complex plane C. The space CNis with scalar multiplication • and addition + an TV-dimensional vector space over the complex-plane. The notation \z\ for some z e C is the absolute value and given by the conjugation of a a complex number z = a + tb, where a, b & R are real-valued numbers and i denotes the imaginary number. The set are the first M non-negative integers. We define for some positive number a > the floor by and the ceil by > a},

[0101] 1 Modulation On Zeros Using Guard Zeros

[0102] An embodiment of this disclosure is to:

[0103] • provide a base signal, wherein the base signal is based on modulation on zeros, MOZ, wherein a zero-vector is chosen from a zero-constellation vector-set, to encode data into a data zero-vector, and in particular a guard zero-vector, to provide control information or to shape properties of the base signal.

[0104] A base signal based on Modulation On Zeros (MOZ) of order K, or for short a MOZ base signal of order K, is determined by a complex-number XK and a complex-vector ( , , , ) called a zero-vector, where the elements ai, . . . , aKdefine the K zeros, also known as roots, of the complex-valued polynomial X(z) = XK n(-z> ak)- In the following we will refer by zeros to complex numbers which are the roots of some polynomial. By the Fundamental Theorem of Algebra, the zeros mathematically generate by the Vieta Formula, for k = 1, 2, . . . ,K, (1) the co efficients aQ, ai, . . . , aK, where we set a0see for example Section 3.2 in [ ]. By calculating the energy of these coefficients 2 we cannormalize the coefficients in energy and introduce a global phase <f> > 0, with the imaginary number z = y setting (2) which defines the coeffic ients of the polynomial k ok>alsoknown as the z- transform of the base signal x = (x0, xi, . . . , XK)- The polynomial coefficient-vector x defines the time-discrete baseband signal and is called here a MOZ symbol of order K normalized in energy, see also Algorithm 1 for a specific construction.

[0105] In one embodiment, the phase 0 G [0, 2TT) of XK can be freely chosen at the transmitter or in another embodiment to be always set to 0, such that xKis a real-valued and positive number. The phase of a complex number z = Re^ is defined as its argument or angle (in radian) <f> := arg z.

[0106] Since it holds =el(<H-27r) we can restrict without loss of generality the phase to [0, 2TT), which achieves a bijective mapping from C to [0, 00) x [0, 2zr). We will measure the phase distance of two phases by:

[0107] (3) where Arg (z) G [— TT, TT) is the (bijective) principal value of the (set-valued) argument func- tion arg(z) Of a complex number z G C (see h / Argument_ (complex_analysis), such that z =

[0108] For communicating data, for example a message or payload, via a signal based on MOZ a transmitter and a receiver scheme has to be defined. The schemes define the encoding / de- coding, multiplexing / demultiplexing and modulation / demodulation of a digital message to and from a (radio) signal, transmitted or received by some antenna-device. The transmitter and receiver agree on a fixed-pattern of zeros, given by a fixed set of complex vectors, which form a zero-constellation-vector-set Z.

[0109] In one embodiment the zero-constellation-vector-set } is given by a Cartesian product disjoint data-zero-sets (4) each with Mkpossible zeros and a guard zero-vector aGG CKGof KG zeros. The zeros in ZDii, . . . , ZDJKDare all distinct and the elements of aGare chosen from some guard-area g G C. We call the Cartesian product ZDof the data zero-sets ZD)i, . . . , ZD>Kothe data zeroconstellation-vector-set. Hence, one can encode B = '£lklog Mkbits into a zero-vector a G Z of K = KD+ KG zeros. In one embodiment, the cardinality of each data-zero-set is equal to M = Mk, allowing to encode B = KDlog M bits. This is called a M-ary MOZ scheme of order K.

[0110] Let us define for some positive integer M the set . The transmitter scheme comprises a mapping of a data / message sequence m to a zero-vector a = («D, aG) = («b • • ■ , € CKof length K -.= K& + KQ where

[0111] Here, aGis a vector of guard zeros, independent of the message m, and aD(m) is a vector of data zeros defined by the message m = , m^) G M component-wise as oik = = 1, . . . , KD- Hence, the data-zero-constellation-vector-set ZDhas cardinality nfii W

[0112] Based on the composed zero-vector a = (aD, aG) G CKa MOZ symbol of order K is then generated by Vieta’s-Formula (1). As explained below, guard-zeros defined by aGcan also be added later by filtering (convolution). However, to ensure numerical stability in (1) it can be relevant to include the guard zeros aGalready at this point.

[0113] An embodiment of this disclosure is a device according to one of the two preceding claims, wherein a MOZ of order K will communicate a zero-vector with K zeros, where a phase distance for each zero to its two next-neighbor zeros is 2TT / K.

[0114] To obtain stability against additive distortions, all the zeros in the zero-vector a G CKshould have an equal phase-distance to its two next-neighbour zeros given by 2-K / K, i.e., it should hold with (3)

[0115] Hence, the complex-plane is separating in K cones, or ’’pizza slices”, as shown in Figure 1 .

[0116] In one embodiment, the guard zero-vector aGcan comprise guard-zeros chosen from a guard-zero-area Q c C of at least KQ elements.

[0117] In another embodiment, the guard zero-vector aGcan be empty, i.e. KQ = 0 and K = KQ. Hence, in this case, no guard-zeros are contained in the zero-vector. In this case, a special zero-constellation-vector-set ZQ = Z with Mk = M = 2 is given by the zero-constellation-sets we call this a BMOCZ (Binary Modulation on Conjugate-reciprocal Zeros) scheme, as introduced in [ ].

[0118] 1.1 Guard-Zeros

[0119] An embodiment of this disclosure is a device which comprises a guard zero-vector that com- prises one or more guard-zeros, wherein, in particular, the one or more guard zeros are char- acterized by one or more of the following characteristics in a complex plane:

[0120] • being placed on / near the unit-circle;

[0121] • being located as a contiguous block such that its phases are near a given phase;

[0122] • being placed at ”1”.

[0123] In the following examples, we will design various guard-zero-areas (7 c C from where the guard-zeros are chosen. The data-zero-sets {ZD^}^ have then to be chosen from C \ Q. This partitions the complex-plane C into two regions: Q and C \ Q. Hence, the definition of Q will restrict the possible data zero-sets and vice versa. The guard-area can be seen as a region of the complex plane where transmit zeros are not stable against certain filter-operations or further zeros will be inserted by certain filter-operations. By knowing in advance the possible filter-operations, the transmitter and receiver can correct this by the defining the guard-zero-area and the guard-zeros accordingly.

[0124] In one embodiment, the guard-zero-area contains cones, more precisely convex cones. However, g does not have to be a convex or connected set.

[0125] In one embodiment, the guard-zero-area g defines a convex cone, spanned between two phase values 0s and 0Ewith 0 < 0s < 0E < 2TT, by g -.= {a e C| arg(a) e [0S, 0E]}.

[0126] The most important guard-zero-area contains a cone, where the elements have its phases be- tween 0s < TTand 0E > 7T, i.e the guard-cone is directed to the negative real-axis, see Figure 1.

[0127] In the following examples, we let the zero-vector a have Kodata-zeros, defined by the first Kocoefficients, and let the number of guard-zeros be KG. Then we have K = Ko+ KGzeros in a MOZ symbol of order K. In one embodiment set JQj = |“J<D / 2"| and in another embodiment Kj = L^D / 2J .

[0128] In both cases, the guard-zero-area g could be defined by the cone in (9) with 0s = 2-KKU / K and 0E= 2TT(J<U + KG- V) / K. We will call this guard-zero-area the Cut-Guard-Zero-Area

[0129] Gc = gc(Ku, KG) := {a G C I arg

[0130] Example 1.1 (Guard-Zeros on the Unit-Circle). In one embodiment, the KGguard zeros chosen from gcwill be defining the guard zero-vector aG= the data-zeros in ZD)fcwill have phases arg

[0131] In Figure 1 we depicted the zeros of a zero-constellation-vector-set Z for an adapted BMOCZ scheme of order K = 8 with a single KG= 1 guard-zero at a8= el7r= -1, pictured as a square, and KQ = 7 data-zeros ax, . . . , a7, pictured as filled circles. The zeros of the data-zero-sets are pictured as circles, which are located on the outer-radius R, pictured as dashed-circle, or on the inner-radius R~\ pictured as a dotted-circle. Here we selected as guard-zero-area g = gG, the cut-guard-zero-area to prevent distortion by cut-out effects at the received channel output y. The start and end phases for the guard-zero-area are given here by 0s = 2TF(A'U+0.5) / 8 respec- tively 0E = 2TF(KU +0.5 + KQ) / K = 7TV / 8, where we chose for Ku = L7 / 2J ■ The complex-plane is here separated in K uniform cones, or ’’pizza slices”, including the guard-zero-area. Note, the cones are unbounded in this picture. Moreover, the MOZ symbols generated by these zero- vectors with KG > 0 will not be Huffman sequences anymore, since the guard-zeros absolute value is not R or R-1.

[0132] Example 1.2 (Guard-Zeros with Different Radii). The guard-zeros of example 1.1 can have arbitrary patterns of radii selections, i.e. Ri, . . . , RKG> 0 such that

[0133] In one embodiment, where M = Mk= 2 for all k = 1, . . . , KD, the radii of the guard-zeros are chosen from {J?, 1 / 7?}, where R is one of the radii used by the possible data zeros, defined in ^Difcfor some k = 1, 2 . . . , KD. This is called the KG-guarded BMOCZ (GBMOCZ) scheme of order K or a KG punctured BMOCZ scheme of order K. In one em- bodiment, the radii of the guard-zeros are chosen in alternating order, by |afe+i| = l / |afc| for k = {JfD+ 1, . . . , K} and |a7<D+i| = R. In both cases all GBMOCZ symbols are Huffman sequences of length K + 1.

[0134] Example 1.3 (Guard-Zeros containing DC zero). The guard-zeros can contain a zero equal to 1, this is called the DC guard-zero which ensures that the base signal based on MOZ has no DC offset, i.e.

[0135] X(l) = 0, (14) see also Example 2.2.

[0136] Example 1.4 (Guard-Zero-Area of Disconnected Cones). The guard-zero-area Q can also com- prise a union of multiple convex cones. This might be useful if the transmit and receive filters and hence its zeros are known in advance. For example for an RCC filter with 9 taps and

[0137] = 0.5 we will have 8 zeros in roughly 4 different phase-regions, which can be used to define 4 guard-zero-cones Hence more general, we define 0S;i, 0E,i for i = 1, . . . , IQ for some number IGand set (15)

[0138] Example 1.5 (Guard-Zero-Area containing Compact Sets). In another embodiment, the guard- zero-area Q can contain a union of disconnected compact sets QG- For example, the cones as described in Example 1.4 could be limited in radius by an inner-radius R\ > 0 and outer-radius Ro > 0, such that (16)

[0139] Furthermore, Q could be a combination of compact sets Qcand cones as defined in Example 1.4.

[0140] 1.2 T ransmitter Scheme

[0141] The transmitter scheme maps the message to the MOZ symbol, as described above, and then modulates the IQ samples / data on a time-continuous pulse g(t) with a given bandwidth and then up-convert it to a carrier-frequency, to form the transmitted time-continuous passband signal, which we call a MOZ signal, i.e., a signal based on the modulation on zeros [ ]. In a radio transceiver, this signal is then radiated, after amplifying, via an antenna. At the receiver we will observe, after down-conversion and sampling, the time-discrete baseband signal y = x * h + w G CJV(17) where h = (hQ, hL-i) G CLis the impulse response of the communication channel, also called a filter, and w = (w0, . . . , WN-I) G CNis the additive noise at the receiver with TV = K+L. We denote here by y = x * h in (17) the linear convolution of two vectors / sequences x G CK+1respectively h G CK, given component wise by where we set hi = 0 for I < 0 and I > L.

[0142] In general, below, we use the notation that dimension N refers to the length of a signal after application of a filter. All the applied time-discrete baseband filters can be always com- bined to one filter by convolution. These filters could describe various hardware effects. In one embodiment, we could set h = gtx * hc * gRx (19) where gtx is the transmit filter, he the multipath channel filter and g™ the receiver filter. Note, that the time-continuous pulse g(t) used in the transmitter and receiver, for modulating and demodulating, can be given in the time-discrete baseband version as the above transmit gtx re- spectively receive filter g^. In the same spirit, the channel impulse response filter he represents a finite sampled version of the time-continuous baseband channel impulse response.

[0143] If the transmitter has knowledge of the receive filter and some expected information of the channel in general, the guard-zero-area and guard-zeros can be chosen with respect to this information, as describe above in the examples.

[0144] 1.3 Receiver Scheme

[0145] In one embodiment, the receiver scheme comprises a time-synchronization algorithm, a timewindowing algorithm (Cut-Out operation), and a generalized DiZeT (Directly-Zero-Testing) Decoder, as introduced in [ ], which has the knowledge of the transmitter scheme. The timesynchronization algorithm at the receiver can be implemented as proposed in [ ].

[0146] The time-windowing operation performs a cut-out of the received IQ-samples in (18), by starting at the nsth sample and stop at the (ns+ Nc- l)th sample, i.e. (20)

[0147] In one embodiment, a time-windowing algorithm determines the optimal values for ns,Nc, by minimizing the length of Nc under keeping the energy-concentration over a certain threshold PE > 0. In one embodiment, the algorithm performs and then select the pair with the smallest length Nc, i.e.

[0148] In one embodiment, the threshold pEdepends on the received SNR.

[0149] The DiZeT decoder then decodes m by directly zero testing the received polynomial, de- fined by the time-windowed received baseband signal y = (yns, yNc+ns_i), at all possible data-zero-vectors OQ G ZD. In one embodiment, the decoding of the message can be done component-wise and independently, by testing for the feth zero all possible transmit zeros in the data-zero set ED,* in (4) and decide for the most likely one by where aresome positive weights. In one embodiment, the weights are given by

[0150] The start and end phases < / >s respectively < / >E of the Cut-Guard-Zero-Area Gc in (10) can depend on the number of zeros K, the filter length L of h, and mostly on the cut-out length Nc< N = K + L as-well as the start sample ns > 0 of the cut-out. The cut-out operation in (20) will have an effect on the energy concentration Ecof the received signal y in Ncvs. N or of the energy concentration of the filter, in particular the transmit and receive filters (without additive noise). Moreover, the transmit and receive filters will have a certain frequency response, which also can have influence in designing the guard-zero area. Note, that the energy concentration of the received signal is also dependent on the received SNR.

[0151] 1.4 Successive T ransmission of MOZ symbols

[0152] To prevent possible interference (Inter Symbol Interference, ISI) of successive transmitted MOZ symbols at the receiver, due to the convolution by the CIR h of length L in (17), we will need to zero-pad x by L - 1 zero IQ samples.

[0153] Example 1.6 (Zero-Padding of MOZ symbols). To avoid ISI of two successive MOZ symbols xW and x(2) by the convolutional delay of the filter h G CLin (18), the transmitter has to insert a guard-interval of length L - 1, i.e. the transmitter would transmit the sequence of baseband / IQ samples

[0154] Usually, we will append the guard-interval, zero-samples, at the end of the MOZ Symbol, by defining (27)

[0155] We call a zero-padded MOZ Symbol of order K by L - 1 zero samples a MOZ symbol of length N = K + L or simply a MOZ base signal, not specifying the length at all. Note, also zero-padding as a preamble is possible, to avoid for example synchronization issues.

[0156] 2 Convolutions and Linear T ransformations of MOZ symbols

[0157] 2.1 Linear Transformations of a MOZ Base Signal

[0158] An embodiment of this disclosure is a device, wherein one or more of the linear transformations are a composition of multiple linear transformations.

[0159] A base signal based on MOZ x can be also a linear-transformed MOZ base signal x G CN, as described in Section 1 , i.e., transformed by a TV x TV-matrix A as x = Ax. (28) In particular, if A = H, i.e. N = N, equal to the identity matrix, then the MOZ base signal is x = x.

[0160] In the following we give particular examples of linear transformations, given by a matrix A.

[0161] A composition of multiple linear transformations generates itself again a linear transforma- tion. Hence, we use compositions to obtain a more elegant or more computational efficient generation of the linear transformed MOZ base signal.

[0162] 2.2 Filters and Expanders

[0163] An embodiment of this disclosure is the device, wherein one or more of the linear transforma- tions are a deterministic or random filter combined with an expander.

[0164] An expander E G CJVE X7Vwith 7VE= (TV - 1)(LE - 1) is a linear transformation which places LE- 1 zeros between the coefficients of a vector x G CN, Hence we have

[0165] Ex = (x0, 0LE-I, XI, OLE-I, • • • , XN-I). (29)

[0166] In one embodiment of the invention we consider as matrix A applied on x the following construction (linear transformation): x = Ax := g * (Ex) (30) where x G CNwith N = K+l and the finite impulse response (FIR) filter of length Lgis g G CLB. Hence we first linear expand x by applying the expander E and then filter it by the filter g. Both applications are linear-transformations, hence the combination is also a linear-transformation, denoted by A.

[0167] Note that a fixed filter g of length Lgis determined up to a scaling factor by Lg- 1 zeros, i.e., can be represented within the context of ’’Guard zeros”, as in (6) above, and be included already in (1).

[0168] Particular cases for g are (i) fixed filters and (ii) random filters like gi ~ exp(z27r0z) where 0i ~"dunif([0, 1]) (uniform iid. phase). Intuitively, regions close to the zeros of the filters should be avoided in the construction of the data (and control) constellation-vector-set Z. In particular, constant-amplitude filters, reduce the PAPR by a factor of Lg- 1. Since a filter g is fixed, the convolution with a signal Ex G can be written also as a matrix G given as a N x TVE banded-Toeplitz matrix generated by the vector g as x = Ax = GEx, (31) where N = TVE + Lg- 1.

[0169] Example 2.1 (Guard-Zero Filter). A guard-zero-filter g can be represented by a MOZ Symbol of order KQ where the KQ = Lg- 1 zeros in SQ are chosen from a guard-zero-area Q. See the examples for aGand Q in Section 1.1. Then the guard-zero filtered symbol x in (30) is given by setting = 1 such that E = I, N = K + KQ and K = KQ. The guard-zeros can then be added to a MOZ symbol x of order K by x = g * x. (32)

[0170] Example 2.2 (DC-Offset-Correction Filter). By observing that Hence, a MOZ signal has a mean of 0 if its polynomial has a zero at 1, i.e., if 1 is a guard-zero, see the DC-guard-zero Example 1.3. A DC-filter can be written as gDc = (-1, 1) and each baseband signal x G CNconvolved with the DC-filter, i.e. x = goc * x with N = N + 1 has no DC offset by (33).

[0171] An embodiment of this disclosure is the device according to one of the preceding claims 4 or 10, use an internal fingerprinting to encode additional fixed information.

[0172] Example 2.3 (Inserting fingerprints by filtering). Adding a special fixed zero-signature (given by the filter), can be done by the transmitter, repeater / forwarding / hopping, reflector, receiver and / or channel in general. Here one can distinguish between internal (meaning controllable, like DU (Digital Unit)) and external fingerprints (like the channel or some third party, which we will discuss in Section 2.2.1. For an internal fingerprinting, which could be the hardware- characteristics of the transmitter or some ID-tag information of the transmitter. The fingerprint, performed by a filter g, is like inserting a fixed guard-zero-vector which is message independent.

[0173] Example 2.4 (Guard-Interval Filter). The zero-padding described in 1 .4, can be also realized by a guard-interval filter g = (1, 0, . . . , 0) G CLto add a guard-interval of length L - 1 to a MOZ symbol x of order K. Here 2VE= K + 1, Lg= L and N = K + L. Moreover, the guard-interval filter can be also applied by a banded-Toeplitz Matrix G G C- / VXJVE, as described in (31 ). Hence we have x = g * x = Gx. (34)

[0174] If the matrix A = diag(a) is given as a diagonal matrix, given by the diagonal-vector a, then we have element-wise (point-wise) multiplication of the vector a with the base signal x G CN.

[0175] An embodiment of this disclosure is the device, wherein one or more of the linear transfor- mations can be a deterministic and / or random time-frequency transformation.

[0176] Example 2.5 (Frequency-Shifts). Lets define the JVth root of unity by

[0177] Then a typical example for a point-wise multiplication is given by the modulation-matrix such that Ax is doing a integer frequency-shift in the signal x. More generally, we can extend this to arbitrary frequency-shifts by taking M to the power of v G [0, 7V - 1]. Hence we can generate a Frequency Shifted MOZ base signal from an arbitrary MOZ base signal x G CNwith TV = TV by x = Ax = M' x. (37)

[0178] Example 2.6 (Time-Frequency Transformations). In one embodiment we consider quadratic linear transformations B G CNXNgiven by linear combinations of numbers btj G C of time- frequency shifts: Here M is the modulation matrix defined in (36) and a circular-time-shift matrix

[0179] (39) allowing arbitrary weighted combinations of time-frequency shifts of a MOZ base signal x by x = Bx (40)

[0180] An embodiment of this disclosure is the device, wherein a linear transformation could be a mapping that performs a weighted repetition of a vector.

[0181] Example 2.7 (Redundancy). Lets define a matrix related to a diversity pattern matrix G CNxNwhiCh repeats a MOZ symbol x G CNby D times and multiplies it with weights e C for d = 1, 2, . . . , D as (41 )

[0182] In one embodiment of the invention, we can use for a linear matrix A := Aein (45) the con- catenation of a quadratic linear transformation B in (38) and a diversity pattern matrix D$ in (41) as

[0183] In one example, the quadratic matrix B in (38) can be a time-frequency transformation with bi:j= Si-j / D for i, j = 1, . . . , D given by (43)

[0184] 2.2.1 External Fingerprinting

[0185] An embodiment of this disclosure is to:

[0186] • add to a provided base signal an additional MOZ base signal by a third party or by itself, wherein the adding is performed by a convolution and / or a correlation of the base signal with the MOZ base signal.

[0187] The device according to the preceding claim, wherein the provided signal is a MOZ base sig- nal using a zero-constellation-vector set which has no common zero to the zero-constellation- vector-set used by the added MOZ signal.

[0188] The device, wherein the convolution and / or correlation is done in a baseband and / or in a passband.

[0189] In one embodiment, an additional message, called an external fingerprint, can be imprinted to a received signal of some third-party transceiver in a hopping or relaying scenario. We call such a third-party transceiver a device for relaying a signal. For example, in a traffic-junction case, a Re-configurable Intelligent Surface Cube, with foursides, could add a direction formation to a received signal depending on the side it receives it and relay the signal further into all other directions. This would not require to decode the information from the received signal but rather append some further signal based on MOZ to the received signal, which is the transmitted again.

[0190] In one embodiment, the external fingerprinting could be another base signal based on MOZ received by some third party / relay, which combines and relays the new signal to another re- ceiver.

[0191] Potential applications are "block-Chain over the air” or ’’collision avoidance at intersections”.

[0192] Example 2.8 (External Fingerprinting). Note, that a fingerprint by a baseband filter can be also applied on the analog radio unit. In one embodiment, a pass-band signal via an Antenna A could be received by a third party, for example a cube placed in the center of a junction, then analog mixed by a pass-band filter based on a MOZ fingerprint as in Example 2.3, and re-transmitted via another Antenna B. Here Antenna A could receive in a certain direction, for example the street direction where Vehicle A is approaching and Antenna B could be transmitting into the street where Vehicle B is approaching, see Figure 14. The fingerprint information might here depend on the received direction, for example street direction A in our example. This information can then be added by the third-party by convolution / mixing in an analog fashion, without the need to decode the received signal or to apply any Digital Signal Processing (DSP). However, another vehicle can receive the fingerprinted relayed signal and decode the street direction of the transmitter and its ID from the data information.

[0193] A RIS (Reconfigurable Intelligent Surface) can also contain an active transmitter. In many situation, a RIS only shapes the phases of the micro-antenna on the surface to direct an in- coming beam / signal into a certain direction, see for example [ ]. Moreover, an active RIS could add certain information by performing a convolution with a fixed signal, as is done for relays. In one embodiment, the relay could recover the baseband signal, convolve with the fingerprint baseband signal and then radiate the passband signal over another antenna. This would re- quire some storage capabilities of the relay and also creates some additional processing delay. In another embodiment, the relay could convolve the fingerprint signal in the passband without doing any digital signal processing.

[0194] Example 2.9 (Block-Chain Computation Over the Air). Computation over the Air gained recently a lot of interest. With MOZ, chaining of information by successive third-parties is possible by convolution / filtering. Moreover, the channel itself is a filtering operation and if known or design- able, known and controllable information can be added over the air. This could be especially useful in the realm of RIS systems, which can due to their steering in a big RIS system create certain CIR filtering for a transmitted MOZ signal by some user to its receiver at some desired user

[0195] 2.3 Combinations of Multiple MOZ Base Signals

[0196] An embodiment of this disclosure is to:

[0197] • obtain and / or determine multiple MOZ base signals;

[0198] • provide a further signal based on one or more convolutions and / or correlations between individual linear transformations of the multiple MOZ base signals.

[0199] The combination of multiple MOZ base signals to a new MOZ base signal can be done multi-linearly by convolutions or by linear transformations. Lets assume we have E MOZ base signals Xi, . . . ,x#. Here the zth MOZ base signal Xj consist of a linear transformation Aj and a MOZ base signal generated by a zero-constellation-vector-set Z.tc C and a message m;. In one embodiment, the MOZ base signal could be MOZ symbol of order Ki which maps the message to a zero-vector a(mj) = (a^m*), . . . , G Zi of Ki zeros. The zero-vector a(mj) defines then with some phase < / >, by Algorithm 1 the coefficients

[0200] Xi(mi) = (^(nii), . . . , a?i,K(mi)). (44)

[0201] In another embodiment we will zero-padd the MOZ Symbols as constructed before by L - 1 zero IQ samples, as described in Section 1.4.

[0202] 2.3.1 Convolutions of Multiple MOZ Base Signals:

[0203] The MOZ base signal is then the time-discrete baseband signa = AjXi(mj). These MOZ base signal can then be combined to a new MOZ base signal by (45)

[0204] Each of the multiple base signals, as defined above, can be individually linear-transformed and may have its individual zero-constellation-vector-sets Zi, . . . , ZE- The goals for combining multiple base signals could e.g. (i) perform a Peak-to-Average-Power-Ratio (PAPR) reduction or / and (II) introduce redundancy by creating multiple signals carrying the same information for exploiting diversity and / or (iii) perform use / data multiplexing.

[0205] Note that in the convolution product (45) the zeros of the polynomials with coefficients are zeros of the polynomial with coefficients x.

[0206] Let E = D denote the diversity order. Then a MOZ symbol x of order K = K& is diversified by D times if we set in (45) for the MOZ base signals xdand Adfor d = 1, . . . , D accordingly. Here two examples:

[0207] Example 2.10 (Zero-Block Diversity Mode). Start with a MOZ symbol x G of order K where all next-neighbour zeros in a have same phase distance of 2n / K. Next, set for d = 1... D (46)

[0208] Example 2.11 (Zero-Distributed Diversity Mode). Start with a MOZ symbol x G CK+ Iof order K = KDwhere the zeros in the data-zero-set ZD fchave phases 2?r(A: - 1) / (DK). Next, set for d = l .. . D (47)

[0209] Another way to create a MOZ base signal x with diversity order D is to rotate each data-zero in the data zero-vector aDG ZDby Z> times, i.e. , k — 1, . . . , K. (48)

[0210] Here, we use the D times redundancy operation1in (41) with (40)

[0211] Then with the Vieta Algorithm 1 , by setting we create and set E = K in (45) to create x by convolving all factors.

[0212] As a third creation method, one could also use in (48) the whole data-zero-vector «D to create aDand then apply the Vieta Algorithm 1 to generate x for some 0.

[0213] Note, potential guard-zeros have to be added in all examples afterwards. Example 2.12 (Piggybacking of Information). Assume we have multiple parties E, each with its own MOZ transceiver and zero-constellation-vector set {Ze}^=1. If the zero-constellation- vector-sets are chosen to have no common zeros, then the eth party can piggy-back new in- formation to the received signal xe_i of the e - 1th party and re-transmit the new concatenated signal xe*xe_i by (45) to the following e + 1th party, which either can decode the information of all previous parties or imprint itself new information and re-transmit it further. Note, the matrix Aeapplied to xecould be also reflect the unknown channel propagation in xe= Aexe.

[0214] In Figure 2 we showed the piggybacking of information by Sensor B, party two, given by the zero-vector aD,2> pictured as filled square points, on a MOZ base signal of Sensor A, party one, having the zero-vector CKD,I > pictured as filled circle points. Here the zero-constellation- vector-set ZDj and ZD>2are subsets of a BMOCZ zero-constellation-vector-set as described in (8). Note, they both are not creating Huffman sequences a MOZ base signals.

[0215] Example 2.13 (Continuous Codebook Expansion). The zero-codebook Z can be extended by a construction formula, so that continuous expansion is possible. At level I = 0 a zero- codebook ZQwith phase-zero-spacing Ad0= 27r / Kbaseand phase-zero-offset ^offset, o = ° is created, resulting in two pairs of zeros. The phase-zero-offset ^offset, o = 0canalso have an arbitrary value, which have to be taken into account in the construction of the level I > 0. For example in Figure 3 the black dotted vertical line denotes the possible positions of the zeros at level zero. For each level I > 0 a further zero-codebook Ztwith phase-zero-spacing A<^ = 2TT / (2Z- 1• Kbase) and phase-zero-offset Offset, / = 2TF / (2Z• Abase) can be created. Therefore, at each level I > 0 the codebook is expanded by 2Z-1number of bits. The complete zero- codebook is given by Z = {Zo, Zi, ..., ZL}, SO that all K > 2L■ Kbasezeros of a signal can be represented. Therefore, knowing Abaseat transmitter and receiver, the codebook can be continuously expanded.

[0216] In Figure 4 a MOCZ-signal with ATbase= 5 is shown examplarily.

[0217] 2.3.2 Linear Transformations of Multiple Base Signals

[0218] An embodiment of this disclosure is the device, wherein a linear transformation could be com- prised in a sum of time-frequency transformation of weighted repetitions applied on one or more MOZ base signals.

[0219] In another embodiment, more generally, we use D MOZ symbols xdG CNdfor d = 1 . . . D and mix them in the sum, which will then be a linear combination of linear transformed MOZ symbols, given by

[0220] (50) where A is ) matrix. This can be seen as a linear multiplexing of D users. A particular case is when is a block matrix with the dth block given by the x Nd matrix Aj (52) In another embodiment, we have the following construction {Nd = N for all d = 1 . . . D)\ (53) where the N x N matrices with N = ND have the explicit given time-frequency transformation of weighted repetitions form above.

[0221] 2.3.3 Mixed Combinations of Multiple Base Signals

[0222] One can also combine Convolution, as defined in Section 2.3.1 , and Linear-Transformations, as defined in Section 2.3.2, of multiple base signals.

[0223] Here we can for example use zero-diversity modes on xdin (54). For example the matrices Aj defined in (46) or (47) such that (54)

[0224] 3 ISAC Schemes with Interference Suppression

[0225] In one embodiment of this invention we present an ISAC (Integrated Sensing and Communica- tion), or sometimes also referred to ICAS (Integrated Communication and Sensing), signaling scheme, using a spatial-temporal-spreading technique based on signals generated by MOZ, to communicate and / or sense a target in a given observable region.

[0226] The device, wherein the multiple MOZ base signals comprise individual zero-constellation vector-sets of pre-defined, individual size.

[0227] 3.1 ISAC Signaling Scheme for Hosts and Targets

[0228] Figure 5 illustrates the general ISAC signaling scheme for four parties A, B, C and D in various use cases. The signaling is here separated in three Phases.

[0229] The first case is depicted in Figure 5a. In Phase 1 , the host vehicle A transmits an ISAC signal (blue solid line), comprised of a data payload and, if necessary, a control payload, which will be received by a designated target vehicle B. Here the target vehicle B recovers in Phase 2 the data payload from the ISAC signal without need of knowing the environment (the transmission channel). In Phase 3, the reflected ISAC signal (red dashed line) from target vehicle B will be sensed by the host vehicle A, which then estimates the relative position and speed of the vehicle B, by eventually using the transmitted signal information.

[0230] In an optional case, illustrated in Figure 5c, a third party vehicle C or infrastructure / base-station D is present. In this case, multiple ISAC signals could be transmitted in Phase 1 , e.g. as de- picted in Figure 5, one from host vehicle A and one from host vehicle C / infrastructure D. In Phase 3, each host will then receive its own reflection and the reflection from the other host, which both can be suppressed by the receiving host.

[0231] Moreover, in another variant of Phase 3, illustrated in Figure 5b, the receiving host could also identify the relative position and speed of the target vehicle B if the relative speed and position of the other host is known to it, even if it has not transmitted any signal. If both host vehicles transmitted different ISAC signals, and the Signal Codebook are known by both hosts, then each host can even blindly determine the relative position and speed of the other host by learn- ing first the relative position and speed of the target-vehicle B. Figure 6 describes the transmission of Phase 1 in 2D to identify the relative speed and posi- tion of a target vehicle B from the host vehicle A. The angular-area Q = [0min, ^max] defines the Field-of-View (FoV) of the host and is defined by the angles < / >min, 0max G [-180, 180]°. The range region R = [-Rmin, #max] is defined by a minimal distance J?mjnand a maximal distance #max, defined by a certain threshold of the Constant False Alarm Rate (CFAR) for the target detection. The target is then described by a triple © = (r, < / >, i / ), where r is the Time-Of-Flight (TOF) along the Line-Of-Sight (LOS) path from host to target (green line), defining the LOS- distance d = cr G R, the angle of arrival < / > G Q and v the Doppler-shift, corresponding to the relative velocity v = cv / fc= vT- vHof the target with respect to the host. Here c denotes the speed of light in the medium (usually air or vacuum). The TOF T can be easily determined by the host from the round-trip-time TRTT> which is the time the signal needs to travel from host to the target and back. Then it holds r = TRTT / 2. TO obtain high-accuracy in position and speed of the target vehicle, a high angular and temporal resolution is needed. To achieve high angular resolution, Q narrow beams Bi, . . . , BQ are used, all with same 3dB beamwidth B. Hence, to cover the FoV we need Q = |Q| / B beams.

[0232] Figure 7 shows the transmit signaling scheme for host vehicle A using a (classical) state-of-the- art pulsed-radar technique of the angular-temporal-domain (Q, T). Here, the angular-domain is partitioned in Q consecutive angular-areas QQ, such that Q = and |Q9| = |Q| / Q < B. The signaling time T = T$ is also partitioned in 1 = QP consecutive time-slots Tj, each with duration |TJ = NTS, where Ts= 1 / W is the sample-period given by the inverse of the signal bandwidth W and N is the total number of received samples at the host. For simplicity, we assume that the duration |Ti U • • • U TQ| = QNTS< 7CPI> i-e. the signaling time for one-beam- sweep of Q, including all signal- and hardware-processing delays, is less than the duration of Coherent Processing Interval TCPI> the time duration over which the channel and target are as- sumed to not change. In time-slot Tj a pulsed-radar signal xyg\ is transmitted and received via the same beam B1+(i modQJ , covering roughly the angular-areaMODQ). In the next time-slot Ti+ithe pulsed-radar signal X^ / Q^ is again transmitted and received via the adjacent beam B1+(i+1 modQ) . This means, each of the blocks transmits the radar-signal X^ / Q^ , carrying a potential data message for the target vehicle B. After reaching the last beam BQ, the radar flips back to beam Bi and starts the next beam-sweep with another radar-signal, carrying another potential data message. Hence, the Pulse-Repetition-Frequency (PRF) is 1 / NTS.

[0233] 3.2 MOZ Signal Scheme with Interference Suppression

[0234] An embodiment of this disclosure is a device for providing a communication signal, configured to:

[0235] • provide a MOZ base signal; wherein the zeros are based on at least two different zero- constellation vector-sets for encoding different control and / or data payloads.

[0236] An embodiment of this disclosure is a receiver for a communication signal, configured to:

[0237] • obtain information on one or more used zero-constellation-vector-sets, each comprising a data zero-constellation-vector-set and a control zero-constellation-vector-set;

[0238] • obtain a MOZ signal comprising a zero-constellation-vector that comprises a data zero- constellation-vector and a control zero-constellation-vector;

[0239] • extract data from the obtained MOZ signal based the data zero-constellation-vector, on the control zero-constellation-vector, and on the data zero-constellation-vector-sets and the control zero-constellation-vector-sets. The receiver, configured to:

[0240] • receive a MOZ base signal comprising data zeros and control zeros;

[0241] • determine a control MOZ-base signal based on known control zeros;

[0242] • convolve and / or correlate received MOZ base signal with the determined control MOZ- base signal to determine a data signal from the MOZ base signal.

[0243] In this section we describe our main-invention for an ISAC application by designing MOZ symbols with a hardening Interference-Suppression to distinguish between multiple beams and users in the previous explained signaling setup.

[0244] Figure 8 shows our proposed spatial-temporal-signaling scheme. To increase the angular res- olution by a factor of S, a decrease of beamwidth to B / S is required, hence an increase of the number of beams to SQ, which then would take S times longer to beam-sweep Q. Since this would violate at some point the constraint S we have to transmit multiple beams at once. In particular, we will transmit S signals during the time-slot Tgvia S consecutive beams Bg;i, . . . , Bg;s covering the angular-area = QQ;I U ■ ■ Here, we will transmit in time-slot i)

[0245] Figure 9 shows the host’s Hybrid-Digital-Analog (HDA) beamforming architecture [ ] with 7V£Ftransmit (tx) RF-chains and 7V£Freceive (rx) RF-chains to transmit and receive with a phase- array the ISAC signals (57) via SQ different beams. In particular, both transmitter and receiver HDA are identical, i.e. S = = 7V£F. Each of the RF chains uses SQ < Naantenna- elements of a uniform-linear-array (ULA) (fully-connected architecture), which allows a beam- forming by a matrix VRF = WRF = (vi, . . . , vs) G cJV“xS. In fact, we will choose here the first S columns of the FFT matrix F G cNaXNa. The sth RF-Chain allows to transmit and receive in the beam-direction Bga narrower beam Bq<sin with beamwidth |BQ)S| < B / S, by selecting Na(analog) phases vsfor the Naantenna-elements (phase-array). In particular, we will only be covering . To cover the angular-area we need to phase-shift all S RF-chains by el27r(9-1)

[0246] In particular, for the pth beam-sweep, the Digital Precoder G maps S MOCZ signals to the S RF-chains which form the S consecutive beams BQJI, . . . , BQ]S(different pattern, phase and amplitude). Hence . For q = 1, . . . , Q, this allows to illuminate the whole FoV Q.

[0247] Here are the reduction matrix for the ISAC signal yielding the transmit signal at the antenna elements

[0248] In one embodiment the ISAC signals (55) for the HDA in Figure 9 are MOZ signals [ ], generated in the passband by the MOZ symbol G CK+1and a pulse g(t} with bandwidth W, for example for g e {1, 2, ... , Q},p G {1, 2, ... , P}, which will be transmitted in the pth beam-sweep via the narrower-beam B9)Sin the wide-beam Bg, pictured as the dotted-beam-pattern in Figure 9. To prevent interference of the next Beam-group B?+iand to fully receive the reflected signal from the objects in the observable Region O, we add a guard-interval of NTSzero-samples, where N = K + LGI and LGI > 2L, i.e. twice the maximal channel delay spread between target and host. Here, the MOZ symbols are given by the convolution * of two MOZ symbols where G (CD is the (q,p) data-signal for the target vehicle B Q the control- signal to suppress the signal interference at the receiver of host A from other beams B9)iwith i ± s or even from a second host D. Similar to (5), the MOZ symbol-constellation-vector-sets 1are given for the data-signal by MDKDcomplex-numbers, forming the data-zero-constellation-vector-set for the data payload by the Cartesian product of the data- zero-sets {^o,k,MD}k=ias(59) where the Zcth data-zero-set ZD>fe>AfD= {®D,fc,i5• • • , «D,fc,MD} is given by MDzeros, allowing to encode maximal KDlog MDbits of data payload, and similar for the control-zero-set ZCtk,Mc= {«c,jfc,i> • • • , ctc,k,Mc} by MCKCzeros, forming the control-zero-constellation-vector-set for the control payload (60) such that ZDn Zc= 0. Hence we have CD ■= {x= Vieta(aD> 0) | aDG ZD} and CQ:= {X= Vieta(ac> 0) I «c G ^c}. where Vieta is the Vieta algorithm in 1, which calculates the K + 1 complex-valued coefficients x = (XQ, XI, . . . , xK) of the polynomial X(z) = ^k=oxkzkfromthe K zeros OL = (cni, . . . , a^). In one embodiment of the invention the zero-sets can consist of conjugate-reciprocal zero-pairs, i.e., Mc= MD= 2 (BMOCZ), with two different radii RQ for the data-zeros and Rc for the control zeros where wKis the Kth root of unity, see (35). In this case, both symbol-constellation-vector-sets, €cand are energy-normalized Huffman sequences with Korespectively KQ zeros, also called BMOCZ symbols. In a particular mode, to align them to K = KD+ KCzeros with uniform distributed phases, we phase-shifted the control zero-set in (61) by . We will call the MOZ symbols in (58) generated by the BMOCZ zero codebooks in (61) MOCZ symbols. As long as KD / Kcthe energy of the combined MOCZ symbol is always 1, irrespective of the used radii Rc, RD- However, if Kc = KQ, then the combined MOCZ symbol has the energy 1 + 2%%.

[0249] From here on, we will only consider the time-discrete baseband signals, including the chan- nel, given by the sampled Channel Impulse Response (CIR) h = (ho, h]_ . / iL-i) (62) of length L. 3.2.1 Target Receive Phase

[0250] To ensure a good angular resolution, we will design the control signals in each beam to be well distinguishable, but still to allow a good diversity for the received signal at the target by utilizing multipath propagation in the channel.

[0251] In Figure 10, for a fixed (g,p), the target B observes in Phase 2 of Figure 5 the ISAC signal via a multipath channel h = h(9’p\ Actually, due to the spatial separation of the S signals, each signal xswill be transmitted over a different channel hs6 CL, which all add at the target receiver to (63)

[0252] A particular case is A := Ai = • • = Asand then due to linearity this yields: (64) where w is the noise at the receiver. Here, the resulting channel h e CL, a combination of the single channels and control signals, will increase diversity in the received signal, which yields to an increase of the received SNR of the data signal d. Since the number of additional zeros is limited to KC(L-1), we can simply use the DiZeT decoder to identify the data-zeros in ZD. Using the TriED (Trident-Energy-Detector) and CIRED algorithm [ ], the number of channel zeros L can be reduced and a time-synchronization can be obtained. With the SPBS algorithm, the target receiver can identify the LOS path in h, even without beamforming. A possible Doppler- shift and Carrier-frequency offset can be compensated by using ACP-Coding and oversampling techniques [ ].

[0253] 3.2.2 Host Receive Phase

[0254] In Phase 3 of Figure 5, the host A performs a target detection for each sub-beam BgtS. For this, The sth received time-discrete baseband signal ysof the observations of the (g,p)-Beam-group in Figure 9 will be correlated * with the transmitted MOZ symbol xs= xi9,p\ yielding the output sequence

[0255] Lets define || • || to be any norm, e.g. the p-norms ||x||£ = Y.k=o la:fcl2’ forp > 0 and forp = 00 the maximum norm ||x||oo = maxfc=0K-I |Z&| of the If-dimensional vector x. Then we have to set a threshold by p > 0, to make a Hypothesis test for a positive target detection:

[0256] (66)

[0257] In one embodiment, the threshold p might depend here on the noise-power, antenna gain, antenna array factor, range region, received SNR, velocity and radar-cross-section, number of beams or the CPI.

[0258] If a target in beam-direction Bq.sis detected, then we can estimate the round-trip-time (RTT). In particular, the RTT can be determined from where n finds the strongest path in the matched-filter output. If xsis a Huffman-Sequence of length N = K + 1 we will observe a strong echo of the channel hS)S. If there was a none obstructed LOS path between host and target, the strongest-peak will correspond to the RTT of the LOS path given by: (68)

[0259] With a Single Host: An embodiment of this disclosure is a device for integrated communi- cation and sensing, configured to:

[0260] • provide a first signal comprising communication data, wherein the first signal is based on a MOZ;

[0261] • obtain a second signal which is based on a reflection of the first signal;

[0262] • correlate a third signal, based on characteristics of the first signal, with the second signal;

[0263] • determine a time-based, a position-based, phase-based, and / or Doppler-based parame- ter based on a similarity measure, for example correlation.

[0264] In Figure 11 we illustrate the beam interference of the received signal at the host A. Choosing the receive beams equal to the transmit beams, it can occur that due to multipath propagation, that ysreceived via beam Bs, pointing to the LOS direction from host A to target B, will also observe the MOZ signal xs, = d * cs, , transmitted via beam Bs / with s / s', via a reflection path (dashed-line) of some other vehicles or objects. To suppress this beam interference, the host receiver will perform for each stream output (sth Beam) in Figure 9 the correlation ★ with the transmit signal for the sth Beam where and hs / sis the combined round-trip channel observed via the s' transmit Beam and s receive Beam. The correlation will lead to a good suppression of the other Beams (the second term in (70)) if i.e., if the cross-correlations of the control-signals are weak.

[0265] In one embodiment, where all the data MOZ symbols c and all the control MOZ symbols d are Huffman Sequences, the autocorrelation will be impulsive-like, and hence the suppression very effective. Moreover, the estimation of hs swill be much better and hence the radar-feature.

[0266] With Two Hosts: An embodiment of this disclosure is device for providing a communication signal, configured to:

[0267] • provide a first signal based on a MOZ and based on a first spatial and / or temporal char- acteristic; provide a second signal based on a MOZ and on a second spatial and / or temporal char- acteristic; • identify a reflection based on the first signal and a reflection based on the second signal, wherein the identification is based on one or more correlations.

[0268] In Figure 12 a second host vehicle C will also transmit an ISAC signal x<, but with a different data and control signal which then will reflect (back-scatter) from the target vehicle B to the first host A. At the receiver outputs of host A we then can apply the matched filter which even leads to a bigger suppression, since data and control signal are different, which yields a suppression of userand beam interference. The Zero-Constellation-Vector-sets ZDjAu Zc>A for host A an for host B could also designed to be disjoint or the pass-band signals could be separated by different frequency bands.

[0269] Figure 13 depicts a scenario where the target detection in one Beam-direction Bs, the time it takes for the radar signal to travel to the minimal range 7?min> will take much longer than the maximal-delay spread of the multipath channel hsof the target surrounding environment. Lets define the minimal delay of the overall channel hsto be £minmeasured in sampling periods Ts. If the effective delay spread in hsis only Lcs< Lmjn, then we can split the channel in a clutter-channel hf and a delay-channel 0Lminof Zmjndelay taps (zero coefficients), given as where .

[0270] Here, the LOS path hg^ arrives at T0= IQTS= (Z§ + £mjn)Tsat the target B, see Figure 13.

[0271] Moreover, the maximal range Emaxdefines also by Lmax= Rmax / (Tsc) a maximal delay spread of the channel hsgiven by L < Lmgx. So lets assume that DN < Lm\n, where N = Lc+K, then we can superimpose D time-frequency shifted versions of D repetitions inside one ISAC signal xsgiven by and increase the receive SNR by a factor of D and reduce with the time-overlap the PAPR of the transmitted ISAC signal xsin (76).

[0272] In one embodiment, we can neglect the time-frequency shifts in (76) and use only the D repetition with A = D and £ = 1.

[0273] In another variant, we could also use a certain repetition-weight pattern £sfor each user or beam s to increase suppression of the user-beam interference in the correlation-receiver (73) and (70). For D = S, one could also use D repetition in each beam Bsand shift-them on a different frequency band with Ms-1to This would increase even further the adjacent-beam suppression as presented in the previ- ous section and reduce the overall PAPR transmitted in one-time slot to via the HDA, since in y(g)s(?,p) the S streams in (77) will be imposed together in the beam group Bq.

[0274] References

[0275] [1] P. Walk, B. Hassibi, and P. Jung, “Systems and methods for communicating by modulating data on zeros,” Patent US 10,797,926 B2, Oct., 2020, appl. No. 16 / 260,059. [Online]. Available: https: / / uspto.report / patent / grant / 10797926

[0276] [2] L. Liu, X. Liang, Y. Li, Y. Liu, X. Bu, and M. Wang, “A spatial-temporal joint radar- communication waveform design method with low sidelobe level of beampattern,” Remote Sensing, vol. 15, no. 4, p. 1167, feb 2023.

[0277] [3] E. Vinberg and A. Retakh, A course in algebra. American Mathematical Society, 2003.

[0278] [4] P. Walk, P. Jung, and B. Hassibi, “MOCZ for blind short-packet communication: Basic prin- ciples,” IEEE Transactions on Wireless Communications, vol. 18, no. 11 , pp. 5080-5097, 11 2019.

[0279] [5] P. Walk, B. Hassibi, P. Jung, and H. Jafarkhani, “Systems and methods for communicating by modulating data on zeros in the presence of channel impairments,” Patent US 10,804,982 B2, Oct., 2020, appl. No. 16 / 260,059. [Online], Available: https: / / uspto.report / patent / grant / 10804982

[0280] [6] S. Hassouna, M. A. Jamshed, J. Rains, J. u. R. Kazim, M. U. Rehman, M. Abualhayja, L. Mohjazi, T. J. Cui, M. A. Imran, and Q. H. Abbasi, “A survey on reconfigurable intelligent surfaces: Wireless communication perspective,” vol. 17, no. 5, pp. 497-537.

[0281] [7] F. Sohrabi and W. Yu, “Hybrid digital and analog beamforming design for large-scale an- tenna arrays,” IEEE Journal of Selected Topics in Signal Processing, vol. 10, no. 3, pp. 501-513, apr 2016.

Claims

Claims1 . A device for providing a communication signal, configured to:- provide a base signal, wherein the base signal is based on modulation on zeros, MOZ, wherein a zero-vector is chosen from a zero-constellation vector- set, to encode data into a data zero-vector, and in particular a guard zero- vector, to provide control information or to shape properties of the base signal.

2. The device according to the preceding claim, configured to:- provide the MOZ base signal is based on a guard zero-vector that comprises one or more guard-zeros, wherein, in particular, the one or more guard zeros are characterized by one or more of the following characteristics in a complex plane:- being placed on / near the unit-circle;- being located as a contiguous block such that its phases are near a given phase;- being placed at "1".

3. The device according to one of the two preceding claims, configured to:- provide a MOZ base signal of order K that comprises a zero-vector with K zeros; wherein a phase distance for each zero to its two next-neighbor zeros is 2TT / K in the complex plane.

4. A device for providing communication signal, configured to:- obtain and / or determine multiple MOZ base signals;- provide a further signal based on one or more convolutions and / or correlations between individual linear transformations of the multiple MOZ base signals.

5. The device according to the preceding claim, wherein the multiple MOZ base signals comprise individual zero-constellation vector-sets of pre-defined size.

6. The device according to one of the preceding claims 4 to 5, wherein one or more of the linear transformations are a composition of multiple linear transformations.

7. The device according to one of the preceding claims 4 to 6, wherein one or more of the linear transformations are a deterministic or random filter g combined with an expander E.

8. The device according to one of the preceding claims 4 or 7, wherein one or more of the linear transformations are based on a deterministic and / or random time-frequency transformation.

9. The device according to one of the preceding claims 4 or 8, wherein a linear transformation is a mapping D_£ based on a weighted repetition of a vector.

10. The device according to one of the preceding claims 4 or 9, wherein a linear transformation is comprised in a sum of time-frequency transformation of weighted repetitions applied on one or more MOZ base signals.11 . The device according to one of the preceding claims 4 or 10, configured to:- provide a MOZ signal with a fingerprinting that encodes additional pre- determined information.

12. A device for providing, in particular relaying, a communication signal, configured to:- obtain and / or determine a base signal;- add to the obtained and / or determined base signal an additional MOZ base signal by a third party or by itself, wherein the adding is based on a convolution and / or a correlation of the base signal with the MOZ base signal.

13. The device according to the preceding claim, wherein the obtained and / or determined signal is a MOZ base signal using a zero-constellation-vector set which has no common zero to the zero- constellation-vector-set used by the added MOZ signal.

14. The device according to one of the preceding two claims, wherein the convolution and / or correlation is based on a baseband and / or a passband.

15. A device for providing a communication signal, configured to:- provide a MOZ base signal; wherein the zeros of the MOZ base signal are based on at least two different zero-constellation vector-sets for encoding different control and / or data payloads.

16. A receiver for obtaining a communication signal, configured to:- obtain information on one or more used zero-constellation-vector-sets, each comprising a data zero-constellation-vector-set and a control zero- constellation-vector-set;- obtain a MOZ signal comprising a zero-constellation-vector that comprises a data zero-constellation-vector and a control zero-constellation-vector;- extract data from the obtained MOZ signal based the data zero-constellation- vector, on the control zero-constellation-vector, and on the data zero- constellation-vector-sets and the control zero-constellation-vector-sets.

17. The receiver according to the preceding claim, configured to:- obtain a MOZ base signal comprising data zeros and control zeros;- determine a control MOZ-base signal based on known control zeros of the control zero-constellation vector sets;- convolve and / or correlate the obtained MOZ base signal with the determined control MOZ-base signal to determine a data signal from the MOZ base signal.

18. A device for integrated communication and sensing, configured to:- provide a first signal comprising communication data, wherein the first signal is based on a MOZ;- obtain a second signal which is based on a reflection of the first signal;- correlate a third signal, based on characteristics of the first signal, with the second signal;- determine a time-based, a position-based, phase-based, and / or Doppler- based parameter based on a similarity measure, for example correlation.

19. A device for providing a communication signal, configured to:- provide a first signal based on a MOZ and based on a first spatial and / or temporal characteristic;- provide a second signal based on a MOZ and on a second spatial and / or temporal characteristic;- identify a reflection based on the first signal and a reflection based on the second signal, wherein the identification is based on one or more correlations.

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