Computer-implemented methods for transforming a message of multiple bits to a t-dimensional transmit vector for transmission via t physical resources

Abstract

The present disclosure relates to a computer-implemented method for transforming a message of multiple bits to a T-dimensional transmit vector for transmission via T physical resources, wherein T is an integer greater than one. The method comprises generating two subsets of bits by splitting the multiple bits, and generating, using a first subset of bits of the two subsets of bits, a block-partitioned spreading matrix that is not a block-diagonal matrix. The method comprises generating, using a second subset of bits of the two subsets of bits, an information-bearing symbol vector, and generating the transmit vector using the spreading matrix and the information-bearing symbol vector. A communication device for wirelessly transmitting a message of multiple bits via the T physical resources is provided. The communication device is configured to transform the message to a T-dimensional transmit vector by performing the aforementioned method.

Description

[0001]COMPUTER-IMPLEMENTED METHODS FOR TRANSFORMING A MESSAGE OF MULTIPLE BITS TO A T-DIMENSIONAL TRANSMIT VECTOR FOR TRANSMISSION VIA T PHYSICAL RESOURCES TECHNICAL FIELDThe present disclosure relates to computer-implemented methods for transforming a message of multi-ple bits to a ^-dimensional transmit vector for transmission via ^ physical resources, wherein ^ is aninteger greater than one. Further, communication devices for wirelessly transmitting a message ofmultiple bits via ^ physical resources are disclosed.BACKGROUND This disclosure is related to a transmitter-side processing design for multiple access scenarios between multiple transmitters and a receiver in wireless communication systems. In particular, such wireless communication systems may exist with regard to a massive Internet-of-things (IoT) scenario or massive machine-type communications (MTC) scenario. Such scenarios may involve a very large number oftransmitters communicating intermittently a small payload with a single receiver. In that case, a limitednumber of supported users supported by orthogonal multiple access given a limited number of availableradio resources and a signaling overhead required by conventionally grant-based techniques result inintolerable delays and / or inefficient use of communication resources. SUMMARY In view of the above, this disclosure aims to allow wirelessly transmitting a message of multiple bitsvia ^ physical resources (^ being an integer greater than one), wherein transforming the message ofmultiple bits to a ^-dimensional transmit vector for the transmission via the ^ physical resources isimproved. These and other objectives are achieved by the solution of this disclosure as described in the independ- ent claims. Advantageous implementations are further defined in the dependent claims. A first aspect of this disclosure provides a computer-implemented method for transforming a messageof multiple bits to a ^-dimensional transmit vector for transmission via ^ physical resources, wherein^ is an integer greater than one. The method comprises generating two subsets of bits by splitting themultiple bits, and generating, using a first subset of bits of the two subsets of bits, a block-partitionedspreading matrix that is not a block-diagonal matrix. The method comprises generating, using a secondsubset of bits of the two subsets of bits, an information-bearing symbol vector, and generating thetransmit vector using the spreading matrix and the information-bearing symbol vector.By transforming the message of multiple bits to the ^-dimensional transmit vector, the method of thefirst aspect allows a wireless transmission of the message of the multiple bits via the ^ physical re-sources. The method of the first aspect allows a multiple access scheme in a wireless communication system comprising a large number of communication devices under the concepts of massive access, random access, grant-free access and unsourced access. Massive access means that a large set of com- munication devices (referred to as transmitters in the following) are willing to communicate with a de-sired communication device (referred to as receiver in the following). Random access means that arandom (possibly large) number from the large set of transmitters is active at a given time. Grant-freeaccess means that active transmitters transmit messages to a receiver without any prior request or anytransmitter-specific resource allocation. Unsourced access means that the identities of the transmittersare not known by the receiver before payload decoding since all transmitters may use the same trans-mitter-side processing, i.e., the method of the first aspect for generating a respective ^-dimensionaltransmit vector for transmitting a respective message of multiple bits via the ^ physical resources.The first aspect proposes transforming the multiple bits of the message to be transmitted to a block-partitioned spreading matrix, which is not block-diagonal, and an information-bearing symbol vector, and generating the transmit vector using the spreading matrix and the information-bearing symbol vec-tor. The block-partitioned spreading matrix not being block-diagonal allows a more flexible allocationof spreading sequences for reference symbols that act as pilots, e.g., pilot signals. This provides a bet-ter user separation performance and a lower average error rate. Thus, the method of the first aspect al-lows decreasing the probability of decoding error for a given number of active transmitter devices thatuse the method as a transmitter-side processing for transmitting a respective message via the ^ physi-cal resources. In addition, the method of the first aspect allows increasing the maximum number of ac-tive transmitter devices that may be supported for a given probability of decoding error. The term“spreading signals” may be used as a synonym for the term “spreading sequences”. The method of the first aspect may be used as transmitter-side processing in a general scenario in which a random set of active communication devices (active transmitters) want to transmit a respec-tive message of multiple bits (e.g., sequence of ^ information bits) to a desired communication device(receiver) while sharing a given set of ^ physical transmission resources, ^ being an integer greaterthan one. The terms “transmitter” and “transmitter device” may be used as synonyms. The terms “receiver” and“receiver device” may be used as synonyms. The term “payload” may be used as a synonym for theterm “message”. The ^ physical resources may be referred to as “^ physical transmission resources”.The term “signal vector” may be used as a synonym for the term “transmit vector”. Herein, the side where the method of the first aspect is performed for transmitting the message, e.g.,the transmitter device, is referred to as transmitter side. The side at which the message, which is trans-mitted using the transmit vector generated with the method of the first aspect, is to be received, e.g., the receiver device, is referred to as receiver side.The multiple bits may be multiple information bits. The multiple bits may be a sequence of ^ bits(e.g., ^ information bits), wherein ^ is an integer greater than one. The ^ physical resource may be forexample time-frequency slots for an orthogonal frequency-division multiplexing (OFDM) waveform.The message may be transmitted to a receiver device with ^ antennas, wherein ^ is an integer greaterthan one. The multiple bits are ^ bits, wherein ^ is an integer greater than one. The spreading matrixis not block-diagonal.The spreading matrix is a matrix that assigns to each of the ^ physical resources a linear combinationof information symbols generated from the second subset of bits with coefficients for the linear combi-nation being comprised in the columns of the matrix.The method of the first aspect may be used as a transmitter-side processing in a wireless communica- tion system comprising multiple communication devices. For example, all the communication devicesthat are configured to act as transmitter devices are configured to perform the method of the first as-pect as transmitter-side processing. The method of the first aspect may be used in a scenario in which receiver devices, to which multiple active transmitter devices transmit a respective message using themethod of the first aspect, cannot distinguish between the active transmitter devices before decodingthe respective information bits of the respective message.In an implementation form of the first aspect, the method comprises generating the two subsets of bitsby splitting the multiple bits into two sequences of bits. The method may comprise generating the first subset of bits by processing a first sequence of bits of the two sequences of bits using at least one of a channel encoder, a bit interleaver and a bit scrambler. In addition or alternatively, the method may comprise generating the second subset of bits by processing a second sequence of bits of the two se- quences of bits using at least one of a channel encoder, a bit interleaver and a bit scrambler.The sequence of bits of the two sequences used for generating the second subset of bits is differentcompared to the sequence of bits of the two sequences used for generating the first subset of bits. The sequence of bits of the two sequences used for generating the second subset of bits and the sequence of bits of the two sequences used for generating the first subset of bits together form the multiple bits.In an implementation form of the first aspect, generating the spreading matrix comprises transformingthe first subset of bits to spreading sequences for reference symbols and spreading sequences for infor-mation symbols, generating orthogonal spreading sequences for the information symbols that are or-thogonal to the spreading sequences for the reference symbols by performing an orthogonalization of the spreading sequences for the information symbols using the spreading sequences for the referencesymbols, and mapping the spreading sequences for the reference symbols and the orthogonal spread-ing sequences for the information symbols to blocks of the spreading matrix.The reference symbols carry information that is known a priori and shared by transmitter and receiver,i.e., the device transmitting the message and the device for which the message is intended. The infor-mation symbols carry the information to be transmitted, i.e., the information of the message.Optionally generating the spreading matrix comprises generating a vector by combining the spreadingsequences for the reference symbols and the orthogonal spreading sequences for the information sym- bols, and mapping elements of the vector to blocks of the spreading matrix.In an implementation form of the first aspect, generating the spreading matrix comprises performing adelay distortion and / or Doppler distortion of the spreading sequences for the reference symbols and using for the orthogonalization the delay distorted and / or Doppler distorted spreading sequences for the reference symbols as the spreading sequences for the reference symbols. In addition or alterna- tively, generating the spreading matrix may comprise performing a delay distortion and / or Dopplerdistortion of the spreading sequences for the information symbols and using for the orthogonalizationthe delay distorted and / or Doppler distorted spreading sequences for the information symbols as the spreading sequences for the information symbols. Performing a delay distortion and / or Doppler distortion of spreading sequences, such as the spreading sequences for the reference symbols and / or the spreading sequences for the information symbols, al- lows a lower average error rate by adding randomness in the transmitter time arrivals “perceived” by the receiver. In an implementation form of the first aspect, mapping the spreading sequences for the reference sym-bols and the orthogonal spreading sequences for the information symbols to the blocks of the spread-ing matrix comprises mapping the spreading sequences for the reference symbols to blocks of the firstcolumn of the spreading matrix, and mapping the orthogonal spreading sequences for the informationsymbols to blocks in the main diagonal of the spreading matrix starting from the second block. In other words, mapping of the orthogonal spreading sequences for the information symbols may com-prise mapping the orthogonal spreading sequences for the information symbols to the blocks of thespreading matrix such that, when removing the first row and first column of blocks of the spreading matrix, the resulting sub-matrix is block-diagonal. Such block-diagonal sub-matrix comprises the or- thogonal spreading sequences for the information symbols as the blocks in the main diagonal. That is, the orthogonal spreading sequences for the information symbols may be mapped to blocks of the main diagonal of the spreading matrix starting from the second block of the main diagonal of the spreading matrix. In an implementation form of the first aspect, transforming the first subset of bits to the spreading se- quences for the reference symbols and the spreading sequences for the information symbols comprisesperforming a discrete mapping of the first subset of bits to the spreading sequences for the referencesymbols and the spreading sequences for the information symbols. In an implementation form of the first aspect, transforming the first subset of bits to the spreading se- quences for the reference symbols and the spreading sequences for the information symbols comprises generating the spreading sequences for the reference symbols by selecting the spreading sequences forthe reference symbols from a first discrete codebook using the first subset of bits, and generating thespreading sequences for the information symbols by selecting the spreading sequences for the infor- mation symbols from a second discrete codebook using the first subset of bits. In an implementation form of the first aspect, the first discrete codebook may comprise at least one of Galois sequences, Hadamard sequences, random Gaussian sequences, Grassmannian sequences,Zadoff-Chu sequences, standard legacy preamble sequences, demodulation reference signal (DMRS)sequences, and arbitrary permutations and rotations of any of the previous sequences. In addition or alternatively, the second discrete codebook may comprise at least one of Galois sequences, Hadamard sequences, random Gaussian sequences, Grassmannian sequences, Zadoff-Chu sequences, standardlegacy preamble sequences, demodulation reference signal (DMRS) sequences, and arbitrary permuta-tions and rotations of any of the previous sequences. In an implementation form of the first aspect, transforming the first subset of bits to the spreading se- quences for the reference symbols and the spreading sequences for the information symbols comprisesperforming a continuous mapping of the first subset of bits to the spreading sequences for the refer-ence symbols and the spreading sequences for the information symbols. The continuous mapping allows a lower complexity at the receiver side by defining a low complexity user detection process. In an implementation form of the first aspect, transforming the first subset of bits to the spreading se- quences for the reference symbols and the spreading sequences for the information symbols comprisessplitting the first subset of bits into multiple sequences of bits of a common length, generating multiplecomplex-valued symbols by mapping the multiple sequences of bits of the common length to the mul- tiple complex-valued symbols using scalar modulators of cardinality two to the power of the commonlength, generating a first vector by combining the multiple complex-valued symbols, continuouslymapping the first vector to a second vector that has a greater dimension compared to the first vector, and splitting the second vector into the spreading sequences for the reference symbols and the spread- ing sequences for the information symbols. In an implementation form of the first aspect, continuously mapping the first vector to the second vec-tor comprises duplicating information of the first vector, and transforming each duplicate of the dupli-cated information of the first vector to a transformed version of the first vector using a chaotic function, the second vector being the transformed version of the first vector. In an implementation form of the first aspect, continuously mapping the first vector to the second vec-tor comprises generating a third vector by combining the first vector with a fixed reference sequence,and transforming the third vector using a chaotic function.The passage “concatenating the first vector with a fixed reference sequence” may be used as a syno-nym for the passage “combining the first vector with a fixed reference sequence”. The second vector isa result of the transformation of the third vector using the chaotic function. In an implementation form of the first aspect, generating the transmit vector using the spreading ma-trix and the information-bearing symbol vector comprises generating a block-partitioned matrix com-prising, as a first column, a vector of spreading sequences for reference symbols and, as furthercolumns, columns of the spreading matrix selected using the first subset of bits, and computing thetransmit vector by vector multiplying the information-bearing symbol vector and the generated block- partitioned matrix. This allows a lower complexity at a receiver equalizer at the receiver side.In order to achieve the computer-implemented method according to the first aspect of this disclosure,some or all of the implementation forms and optional features of the first aspect, as described above,may be combined with each other. A second aspect of this disclosure provides a communication device for wirelessly transmitting a mes-sage of multiple bits via ^ physical resources, wherein ^ is an integer greater than one. The communi-cation device is configured to transform the message to a ^-dimensional transmit vector by performing the method according to the first aspect, as described above. The communication device may be referred to as transmitter device. It optionally may be configured to receive messages. In this case, it may be referred to as transceiver device. The communication device may comprise a single antenna. That is, it may be a single antenna communication device. Alterna- tively, the communication device may comprise multiple antennas. The communication device may be configured to transmit the message using the transmit vector. For example, the communication device may be configured to transmit to a communication device with ^antennas the message using the transmit vector, wherein ^ is an integer greater than one. The terms“wirelessly transmit” and “wirelessly communicate” may be used as synonyms for the terms “trans- mit” and “communicate”, respectively. The above description of the computer-implemented method according to the first aspect is correspondingly valid for the communication device of the second aspect.The communication device of the second aspect and its implementation forms and optional featuresachieve the same advantages as the computer-implemented method of the first aspect and its respective implementation forms and respective optional features.In order to achieve the communication device according to the second aspect of this disclosure, some orall of the implementation forms and optional features of the second aspect, as described above, may be combined with each other. A third aspect of this disclosure provides a computer-implemented method for transforming a messageof multiple bits to a ^-dimensional transmit vector for transmission via ^ physical resources,wherein ^ is an integer greater than one. The method comprises generating two subsets of bits by split-ting the multiple bits. The method comprises performing a continuous mapping of a first subset of bitsof the two subsets of bits to spreading sequences for reference symbols and spreading sequences for information symbols. The method comprises generating orthogonal spreading sequences for the infor- mation symbols that are orthogonal to the spreading sequences for the reference symbols by perform- ing an orthogonalization of the spreading sequences for the information symbols using the spreading sequences for the reference symbols. The method comprises mapping the spreading sequences for thereference symbols and the orthogonal spreading sequences for the information symbols to blocks of ablock-partitioned spreading matrix. The method comprises generating, using a second subset of bits ofthe two subsets of bits, an information-bearing symbol vector, and generating the transmit vector usingthe spreading matrix and the information-bearing symbol vector. The continuous mapping allows a lower complexity at the receiver side by defining a low complexityuser detection process. The block-partitioned spreading matrix may be block-diagonal or not.In an implementation form of the third aspect, performing the continuous mapping of the first subset of bits to the spreading sequences for the reference symbols and the spreading sequences for the infor- mation symbols comprises splitting the first subset of bits into multiple sequences of bits of a commonlength, generating multiple complex-valued symbols by mapping the multiple sequences of bits of thecommon length to the multiple complex-valued symbols using scalar modulators of cardinality two tothe power of the common length, generating a first vector by combining the multiple complex-valuedsymbols, continuously mapping the first vector to a second vector that has a greater dimension com-pared to the first vector, and splitting the second vector into the spreading sequences for the reference symbols and the spreading sequences for the information symbols. In an implementation form of the third aspect, continuously mapping the first vector to the second vec-tor comprises duplicating information of the first vector, and transforming each duplicate of the dupli-cated information of the first vector to a transformed version of the first vector using a chaotic function, the second vector being the transformed version of the first vector.In an implementation form of the third aspect, continuously mapping the first vector to the second vec-tor comprises generating a third vector by combining the first vector with a fixed reference sequence,and transforming the third vector using a chaotic function.The second vector is a result of the transformation of the third vector using the chaotic function.In an implementation form of the third aspect, the method comprises generating the two subsets of bitsby splitting the multiple bits into two sequences of bits. The method may comprise generating the first subset of bits by processing a first sequence of bits of the two sequences of bits using at least one of a channel encoder, a bit interleaver and a bit scrambler. In addition or alternatively, the method may comprise generating the second subset of bits by processing a second sequence of bits of the two se- quences of bits using at least one of a channel encoder, a bit interleaver and a bit scrambler. In an implementation form of the third aspect, the method comprises performing a delay distortion and / or Doppler distortion of the spreading sequences for the reference symbols and using for the or- thogonalization the delay distorted and / or Doppler distorted spreading sequences for the reference symbols as the spreading sequences for the reference symbols. In addition or alternatively, the method may comprise performing a delay distortion and / or Doppler distortion of the spreading sequences for the information symbols and using for the orthogonalization the delay distorted and / or Doppler dis- torted spreading sequences for the information symbols as the spreading sequences for the information symbols. The above description of the computer-implemented method according to the first aspect is correspondingly valid for the computer-implemented method of the third aspect. The computer-implemented method of the third aspect and its implementation forms and optional features achieve the same advantages as the computer-implemented method of the first aspect and its respective implementation forms and respective optional features. In order to achieve the computer-implemented method according to the third aspect of this disclosure, some or all of the implementation forms and optional features of the third aspect, as described above, may be combined with each other.A fourth aspect of this disclosure provides a communication device for wirelessly transmitting a mes-sage of multiple bits via ^ physical resources, wherein ^ is an integer greater than one. The communi-cation device is configured to transform the message to a ^-dimensional transmit vector by performing the method according to the third aspect of this disclosure. The communication device may be referred to as transmitter device. It optionally may be configured to receive messages. In this case, it may be referred to as transceiver device. The communication device may comprise a single antenna. That is, it may be a single antenna communication device. Alterna- tively, the communication device may comprise multiple antennas. The communication device may be configured to transmit the message using the transmit vector. For example, the communication device may be configured to transmit to a communication device with ^antennas the message using the transmit vector, wherein ^ is an integer greater than one. The above description of the computer-implemented method according to the third aspect is correspondingly valid for the communication device of the fourth aspect. Optionally, the communication device of the fourth aspect is configured to transform the message to a ^-dimensional transmit vector by performing the method according to the first aspect of this disclo- sure.The above description of the computer-implemented method according to the first aspect and thecommunication of the second aspect may be correspondingly valid for the communication device of thefourth aspect. The communication device of the fourth aspect and its implementation forms and optional features achieve the same advantages as the computer-implemented method of the third aspect and its respective implementation forms and respective optional features. In order to achieve the communication device according to the fourth aspect of this disclosure, some or all of the implementation forms and optional features of the fourth aspect, as described above, may be combined with each other.A fifth aspect of this disclosure provides a computer program comprising instructions which, when theprogram is executed by a computer, cause the computer to perform the method according to the first aspect or any of its implementation forms.A sixth aspect of this disclosure provides a storage medium storing executable program code which,when executed by a processor, causes the method according to the first aspect or any of its implemen-tation forms to be performed.The computer program of the fifth aspect and the storage medium of the sixth aspect achieve the same advantages as the computer-implemented method of the first aspect and its respective implementation forms and respective optional features. A seventh aspect of this disclosure provides a computer program comprising instructions which, when the program is executed by a computer, cause the computer to perform the method according to the third aspect or any of its implementation forms.An eighth aspect of this disclosure provides a storage medium storing executable program code which,when executed by a processor, causes the method according to the third aspect or any of its implemen-tation forms to be performed. The computer program of the seventh aspect and the storage medium of the eighth aspect achieve the same advantages as the computer-implemented method of the third aspect and its respective implementation forms and respective optional features. It has to be noted that all devices, elements, units and means described in the present application could be implemented in software or hardware elements or any kind of combination thereof. All steps which are performed by the various entities described in the present application as well as the functionalities described to be performed by the various entities are intended to mean that the respective entity is adapted to or configured to perform the respective steps and functionalities. Even if, in the following description of specific embodiments, a specific functionality or step to be performed by external enti- ties is not reflected in the description of a specific detailed element of that entity which performs that specific step or functionality, it should be clear for a skilled person that these methods and functionali- ties can be implemented in respective software or hardware elements, or any kind of combination thereof. BRIEF DESCRIPTION OF DRAWINGS The above-described aspects and implementation forms will be explained in the following description of specific embodiments in relation to the enclosed drawings, in whichFIG. 1 shows an example of a computer-implemented method according to an embodiment ofthis disclosure for transforming a message of multiple bits to a ^-dimensional transmit vector for transmission via ^ physical resources, wherein ^ is an integer greater thanone.FIG. 2 shows an example of an implementation form of the step 1000 of generating the twosubsets of bits of the method of FIG.1.FIG. 3 shows an example of an implementation form of the step 2000 of generating theblock-partitioned spreading matrix of the method of FIG.1.FIG. 4 shows an example of optional steps that may be performed in the implementation formof FIG. 3 of the step 2000 of generating the block-partitioned spreading matrix of themethod of FIG.1.FIG. 5 shows an example of an implementation form of the step 2300 of mapping the spread-ing sequences for the reference symbols and the orthogonal spreading sequences for the information symbols to blocks of the spreading matrix of the implementation form of FIG.3 of the step 2000 of generating the block-partitioned spreading matrix of the method of FIG.1.FIG. 6 (a) shows an example of an implementation form of the step 2100 of transforming thefirst subset of bits to spreading sequences for reference symbols and spreading se- quences for information symbols of the implementation form of FIG.3 of the step 2000 of generating the block-partitioned spreading matrix of the method of FIG.1.FIG. 6 (b) shows an example of an implementation form of the step 2100 of transforming thefirst subset of bits to spreading sequences for reference symbols and spreading se- quences for information symbols of the implementation form of FIG.3 of the step 2000 of generating the block-partitioned spreading matrix of the method of FIG.1.FIG. 7 shows an example of an implementation form of the step 2100 of transforming thefirst subset of bits to spreading sequences for reference symbols and spreading se-quences for information symbols of the implementation form of FIG.3 of the step 2000 of generating the block-partitioned spreading matrix of the method of FIG.1.FIG. 8 shows an example of an implementation form of the step 2100 of transforming thefirst subset of bits to spreading sequences for reference symbols and spreading se- quences for information symbols of the implementation form of FIG.3 of the step 2000 of generating the block-partitioned spreading matrix of the method of FIG.1.FIG. 9 shows an example of an implementation form of the step 2143 of continuously map-ping the first vector to a second vector that has a greater dimension compared to the first vector of the implementation form of FIG.8 of the step 2100 of the implementa- tion form of FIG.3.FIG. 10 shows an example of an implementation form of the step 2143 of continuously map-ping the first vector to a second vector that has a greater dimension compared to the first vector of the implementation form of FIG.8 of the step 2100 of the implementa- tion form of FIG.3.FIG. 11 shows an example of an implementation form of the step 4000 of generating the trans-mit vector using the spreading matrix and the information-bearing symbol vector ofthe method of FIG.1.FIG. 12 shows an example of an implementation form of the method of FIG. 1.FIG. 13 shows an example of an implementation form of step 2000 of generating the block-partitioned spreading matrix of the method of FIG. 1.FIG. 14 shows an example of the spreading sequence generator used in the implementationform of FIG.13.FIG. 15 shows an example of the spreading sequence generator used in the implementationform of FIG.13.FIG. 16 shows an example of the bilinear combiner used in the implementation form of FIG.12.FIG. 17 shows an example of a receiver-side processing of the ^-dimensional transmit vectorgenerated by one of the methods of FIGs.1 to 16 and 18, after the ^-dimensional transmit vector has been received, e.g., by a communication device.FIG. 18 shows an example of a computer-implemented method according to an embodiment ofthis disclosure for transforming a message of multiple bits to a ^-dimensional transmit vector for transmission via ^ physical resources, wherein ^ is an integer greater thanone.FIG. 19 shows an example of a communication device for wirelessly transmitting a message ofmultiple bits via ^ physical resources, wherein ^ is an integer greater than one.Same elements shown in the Figures are labeled with the same reference sign, and may be imple- mented likewise. DETAILED DESCRIPTION OF EMBODIMENTS FIG.1 shows an example of a computer-implemented method according to an embodiment of this dis- closure for transforming a message of multiple bits to a ^-dimensional transmit vector for transmissionvia ^ physical resources, wherein ^ is an integer greater than one. The method of FIG. 1 is an exampleof the computer-implemented method according to the first aspect of this disclosure. Thus, the descrip- tion of the method according to the first aspect is correspondingly valid for the method of FIG.1. As shown in FIG.1, in a step 1000 the method comprises generating two subsets of bits by splitting the multiple bits. In a step 2000 following the step 1000, the method comprises generating, using a first subset of bits of the two subsets of bits, a block-partitioned spreading matrix that is not a block- diagonal matrix. In a step 3000 following the step 2000, the method comprises generating, using a sec- ond subset of bits of the two subsets of bits, an information-bearing symbol vector. In contrast to FIG.1, the step 3000 may be performed before the step 2000 or simultaneously with the step 2000. In step4000, after steps 2000 and 3000, the method comprises generating the transmit vector using the spreading matrix and the information-bearing symbol vector. The block-partitioned spreading matrix not being a block-diagonal matrix allows a more flexible allo-cation of spreading sequences for reference symbols that act as pilots, e.g., pilot signals. This providesa better user separation performance and a lower average error rate.FIG. 2 shows an example of an implementation form of the step 1000 of generating the two subsets ofbits of the method of FIG. 1. The description of the method according to the first aspect is correspond-ingly valid for the method steps of FIG.2. As shown in FIG.2, in a step 1100 the two subset of bits may be generated by splitting the multiple bits into two sequences of bits. Optionally, in a followingstep 1100a the first subset of bits may be generated by processing a first sequence of bits of the twosequences of bits using at least one of a channel encoder, a bit interleaver and a bit scrambler. In addi-tion or alternatively, in a step 1100b following the step S1100 the second subset of bits may be gener-ated by processing a second sequence of bits of the two sequences of bits using at least one of a channel encoder, a bit interleaver and a bit scrambler. In case, the step S1100a is not performed, thefirst subset of bits is the first sequence of bits. In case the step S1100b is not performed, the secondsubset of bits is the second sequence of bits. FIG.3 shows an example of an implementation form of the step 2000 of generating the block-parti-tioned spreading matrix of the method of FIG. 1. The description of the method according to the firstaspect is correspondingly valid for the method steps of FIG.3. As shown in FIG.3, for generating the spreading matrix the following steps may be performed: In a step 2100, the first subset of bits may betransformed to spreading sequences for reference symbols and spreading sequences for informationsymbols. In a next step 2200, orthogonal spreading sequences for the information symbols that are or- thogonal to the spreading sequences for the reference symbols may be generated by performing an or- thogonalization of the spreading sequences for the information symbols using the spreading sequences for the reference symbols. In a next step 2300, the spreading sequences for the reference symbols andthe orthogonal spreading sequences for the information symbols may be mapped to blocks of thespreading matrix. FIG.4 shows an example of optional steps that may be performed in the implementation form of FIG.3 of the step 2000 of generating the block-partitioned spreading matrix of the method of FIG. 1. Thedescription of the method according to the first aspect is correspondingly valid for the method steps ofFIG. 4. As shown in FIG. 4, in an optional step 2400a a delay distortion and / or Doppler distortion ofthe spreading sequences for the reference symbols may be performed. In this case, for the orthogonali- zation (performed during method step 2200 of the implementation form of FIG.3) the delay distorted and / or Doppler distorted spreading sequences for the reference symbols may be used as the spreading sequences for the reference symbols. In addition or alternatively, in an optional step 2400b, a delay distortion and / or Doppler distortion of the spreading sequences for the information symbols may be performed. In this case, for the orthogonalization (performed during method step 2200 of the imple- mentation form of FIG.3) the delay distorted and / or Doppler distorted spreading sequences for the in-formation symbols may be used as the spreading sequences for the information symbols. The optionalstep S2400a and / or the optional step 2400b may be performed before the method step 2200 of the im- plementation form of FIG.3. FIG.5 shows an example of an implementation form of the step 2300 of mapping the spreading se- quences for the reference symbols and the orthogonal spreading sequences for the information sym- bols to blocks of the spreading matrix of the implementation form of FIG.3 of the step 2000 ofgenerating the block-partitioned spreading matrix of the method of FIG. 1. The description of themethod according to the first aspect is correspondingly valid for the method steps of FIG.5.As shown in FIG. 5, the step 2300 of mapping the spreading sequences for the reference symbols andthe orthogonal spreading sequences for the information symbols to blocks of the spreading matrix may comprise, in a step 2300a, mapping the spreading sequences for the reference symbols to blocks of the first column of the spreading matrix. In a step 2300b following the step 2300a, the orthogonal spread- ing sequences for the information symbols may be mapped to blocks in the main diagonal of thespreading matrix starting from the second block. In contrast to FIG. 5, the step 2300b may be per-formed before the step 2300a or simultaneously with the step 2300a.FIG. 6 (a) shows an example of an implementation form of the step 2100 of transforming the firstsubset of bits to spreading sequences for reference symbols and spreading sequences for information symbols of the implementation form of FIG.3 of the step 2000 of generating the block-partitionedspreading matrix of the method of FIG. 1. The description of the method according to the first aspectis correspondingly valid for the method steps of FIG. 6 (a). As shown in FIG. 6 (a), the step 2100 oftransforming the first subset of bits to the spreading sequences for the reference symbols and thespreading sequences for the information symbols may comprise the step 2110 of performing a discretemapping of the first subset of bits to the spreading sequences for the reference symbols and the spread-ing sequences for the information symbols.FIG. 6 (b) shows an example of an implementation form of the step 2100 of transforming the firstsubset of bits to spreading sequences for reference symbols and spreading sequences for information symbols of the implementation form of FIG.3 of the step 2000 of generating the block-partitionedspreading matrix of the method of FIG. 1. The description of the method according to the first aspectis correspondingly valid for the method steps of FIG.6 (b). As shown in FIG.6 (b), the step 2100 oftransforming the first subset of bits to the spreading sequences for the reference symbols and thespreading sequences for the information symbols may comprise the step 2120 of generating thespreading sequences for the reference symbols by selecting the spreading sequences for the referencesymbols from a first discrete codebook using the first subset of bits, and the step 2121 of generatingthe spreading sequences for the information symbols by selecting the spreading sequences for the in- formation symbols from a second discrete codebook using the integer index. In contrast to FIG.6 (b),the step 2121 may be performed before the step 2120 or simultaneously with the step 2120.FIG.7 shows an example of an implementation form of the step 2100 of transforming the first subset of bits to spreading sequences for reference symbols and spreading sequences for information symbols of the implementation form of FIG.3 of the step 2000 of generating the block-partitioned spreadingmatrix of the method of FIG. 1. The description of the method according to the first aspect is corre-spondingly valid for the method steps of FIG. 7. As shown in FIG. 7, the step 2100 of transforming thefirst subset of bits to the spreading sequences for the reference symbols and the spreading sequences for the information symbols may comprise the step 2130 of performing a continuous mapping of the first subset of bits to the spreading sequences for the reference symbols and the spreading sequences for the information symbols. FIG.8 shows an example of an implementation form of the step 2100 of transforming the first subset of bits to spreading sequences for reference symbols and spreading sequences for information symbols of the implementation form of FIG.3 of the step 2000 of generating the block-partitioned spreadingmatrix of the method of FIG. 1. The description of the method according to the first aspect is corre-spondingly valid for the method steps of FIG. 8. As shown in FIG. 8, the step 2100 of transforming thefirst subset of bits to the spreading sequences for the reference symbols and the spreading sequences for the information symbols may comprise the following steps: In a step 2140, the first subset of bits may be split into multiple sequences of bits of a common length. In a next step 2141, multiple com-plex-valued symbols may be generated by mapping the multiple sequences of bits of the commonlength to the multiple complex-valued symbols using scalar modulators of cardinality two to the power of the common length. In a next step 2142, a first vector may be generated by combining the multiple complex-valued symbols. In a next step 2143, the first vector may be continuously mapped to a second vector that has a greater dimension compared to the first vector. In a next step 2144, the second vector may be split into the spreading sequences for the reference symbols and the spreading sequences for the information symbols. FIG.9 shows an example of an implementation form of the step 2143 of continuously mapping the first vector to a second vector that has a greater dimension compared to the first vector of the imple-mentation form of FIG. 8 of the step 2100 of the implementation form of FIG. 3. The description ofthe method according to the first aspect is correspondingly valid for the method steps of FIG. 9. Asshown in FIG. 9, the step 2143 of continuously mapping the first vector to the second vector may com-prise a step 2143a of duplicating information of the first vector. In a next step 2143b each duplicate ofthe duplicated information of the first vector may be transformed to a transformed version of the first vector using a chaotic function, wherein the second vector is the transformed version of the first vectorFIG. 10 shows an example of an implementation form of the step 2143 of continuously mapping thefirst vector to a second vector that has a greater dimension compared to the first vector of the imple-mentation form of FIG. 8 of the step 2100 of the implementation form of FIG. 3. The description ofthe method according to the first aspect is correspondingly valid for the method steps of FIG. 10. Asshown in FIG. 10, the step 2143 of continuously mapping the first vector to the second vector maycomprise a step 2143c of generating a third vector by combining the first vector with a fixed referencesequence. In a next step 2143d the third vector may be transformed using a chaotic function. The sec-ond vector is a result of the transformation of the third vector using the chaotic function.FIG. 11 shows an example of an implementation form of the step 4000 of generating the transmit vec-tor using the spreading matrix and the information-bearing symbol vector of the method of FIG. 1. Thedescription of the method according to the first aspect is correspondingly valid for the method steps ofFIG. 11. As shown in FIG. 11, the step 4000 of generating the transmit vector may comprise a step4100 of generating a block-partitioned matrix comprising, as a first column, a vector of spreading se-quences for reference symbols and, as further columns, columns of the spreading matrix selected usingthe first subset of bits. In a next step 4200, the transmit vector may be computed by vector multiplyingthe information-bearing symbol vector and the generated block-partitioned matrix.FIG. 12 shows an example of an implementation form of the method of FIG. 1.The method of FIG. 1 and, thus, the method of FIG. 12 allows providing an improved transmitter-sideprocessing, e.g., for unsourced massive grant-fee random access. For example, a communication systemcomprising ^ single-antenna wireless transmitters may be considered. Further, it may be assumed thata random subset ^ of ^^ = |^| of these transmitters communicate (without requiring a prior grant)their ^^ respective messages ^^ of ^ bits to a receiver with ^ antennas. The terms “active transmitters”and “active users” may be used for referring to transmitters communicating their respective messages.The transmitters use ^ transmit physical resources to send their transmit vectors ^^ obtained from theirrespective messages ^^ , ^ ∈ ^. Furthermore, it is assumed that the transmitters are synchronized in thesense that the receiver receives in the first physical resource the sum of the contribution that each trans- mitter transmitted in the first physical resource, the receiver receives in the second physical resource the sum of the contribution that each transmitter transmitted in the second physical resource, etc.By collecting the signal received over the ^ antennas and the ^ physical resources, the receiver observessignal ^ that may be modeled as In above equation (1), ^ is a ^ × ^ matrix representing the received symbols collected at the receiverover the ^ physical resources and the ^ receive antennas, ^ is the subset of transmitters that wereactive, i.e., that transmitted simultaneously over the ^ physical resources, ^^ is a ^-dimensional transmitvector belonging to constellation ^ and representing the signal transmitted by the user indexed by ^, ^^is a ^-dimensional vector representing the channel state information (CSI) between the receiver andtransmitter ^, which is unknown to the receiver, and ^ is a ^ × ^ matrix representing the noise per-turbing the received signal.The signal vectors ^^ may be chosen from a constellation ^ comprising 2^vectors, each vector corre-sponding to a different sequence of ^ bits. The transmitter-side processing and, hence, the constellation^ may be common to all transmitters. That is, the transmitters (i.e., communication devices configuredto transmit a respective message ^^) may be configured to perform the method of FIG. 1, e.g., themethod of FIG. 12, for transforming the respective message ^^ of multiple bits (^ bits) to the ^-dimen-sional transmit vector ^^ for transmission via the ^ physical resources.The method of FIG. 1 (e.g., the method of FIG. 12) allows designing such constellation ^, ensuringthat the receiver is able to decode the transmitters’ payloads (i.e., the messages ^^ , ^ ∈ ^) after ob-serving the received signals comprised in the matrix ^.For example, this disclosure proposes with the method of FIG. 1 and the following FIGs. 2 to 18 a constellation design based on the bilinear structure: ^^ = ^(^^)^(^^) where ^^ denotes the ^-dimensional transmit vector comprising ^ complex symbols to be transmittedover the ^ available physical resources, ^ ≜ ^(^^) is a ^ × (^ + 1) matrix representing a symbolspreading procedure (the matrix Z being dependent on the block-partitioned spreading matrix not beingblock diagonal), and ^ ≜ ^(^^) is the information-bearing symbol vector being an (^ + 1)-dimen-sional symbol vector with the following structure: with ^^ for ^ = 1, … , ^ being complex symbols outputted by a scalar modulator (e.g., quadrature am-plitude modulation (QAM), phase-shift keying (PSK), etc.).For simplicity, in the following, the dependence of both ^ and ^ (and related variables) on the message^^is omitted.The first column of ^ may be denoted by ^ and the (^ + 1)-th column of ^ may be denoted by ^^, ^ =that^ = (^ ^^ ⋯ ^^). (4)The signal vector ^^in equation (2) can be then alternatively written as FIG.12 shows a general block diagram of the transmitter-side processing applied to message ^^com-prising ^ information bits (i.e., multiple bits) to obtain the ^-dimensional transmit vector ^^.As shown in FIG. 12, the ^ bits (labeled with reference sign “1”) of the message ^^ (labeled withreference sign „2“), may be split into two parts, i.e., two sequences of bits, using a splitter 100. The twosequences of bits are a first sequence of bits 1a’ comprising ^^bits and a second sequence of bits 1b’comprising ^^ bits, wherein the first sequence of bits 1a’ and the second sequence of bits 1b’ form themultiple bits 1 comprising the ^ bits (i.e., ^^ + ^^ = ^). As shown in FIG. 12, the first sequence ofbits 1a’ may be processed using at least one of a channel encoder 101, a bit interleaver 102 and a bitscrambler 103 to generate a first subset of bits 1a comprising ^^bits, which may be coded bits due to theprocessing. The second sequence of bits 1b’ may be processed using at least one of a channel encoder101, a bit interleaver 102 and a bit scrambler 103 to generate a second subset of bits 1b comprising ^^bits, which may be coded bits due to the processing. One or more of these modules 101, 102 and 103 may take as input the second sequence of bits 1b’ in order to select a signature of a code (e.g., the sequence of frozen bits for Polar code).The aforementioned corresponds to the step S1000 of FIG.1, in which two subsets of bits 1a and 1b aregenerated by splitting the multiple bits 1, i.e., the ^ bits, of the message 2, i.e., message ^^. In case noprocessing of the first sequence of bits 1a’ is performed, the first subset of bits 1a is the first sequenceof bits 1a’ (i.e., ^^ = ^^ bits). In case no processing of the second sequence of bits 1b’ is performed,the second subset of bits 1b is the second sequence of bits 1b’ (i.e., ^^ = ^^ bits). The splitting of themultiple bits 1, i.e., ^ bits, of the message 2 by the splitter 100 may correspond to the method step 1100of FIG. 2. The optional processing of the first sequence of bits 1a’ using at least one of the channel encoder 101, the bit interleaver 102 and the bit scrambler 103 to generate the first subset of bits 1a corresponds to the optional method step 1100a of FIG.2. The optional processing of the second sequence of bits 1b’ using at least one of the channel encoder 101, the bit interleaver 102 and the bit scrambler 103 to generate the second subset of bits 1b corresponds to the optional method step 1100b of FIG.2. As shown in FIG. 12, the first subset of bits 1a may be mapped by a matrix mapper 105 to the block-partitioned spreading matrix ^ (labeled with reference sign “3”) that is not block-diagonal. The spread-ing matrix 3 may be a ^ × (^ + 1) spreading matrix, with ^ ≥ ^. In other words, the spreading matrix3 may be generated using the first subset of bits 1a. This corresponds to the method step 2000 of FIG. 1. As shown in FIG. 12, the second subset of bits 1b may be mapped by a vector mapper 106 to theinformation-bearing symbol vector ^ (labeled with the reference sign „4“), as defined in above equation(3). The symbol vector ^ comprises the modulated symbols ^^ , … , ^^, which result from mapping eachbit subsequence of ^^ / ^ into a scalar symbol ^^ with a scalar modulator with cardinality 2^^ / ^(e.g.,QAM, PSK, etc.). The symbol vector ^ may be a (^ + 1)-dimensional vector. This corresponds to themethod step 3000 of FIG. 1.In a bilinear combiner 107, the ^ × (^ + 1) spreading matrix 3, i.e., the matrix C, may be processed toobtain ^ × (^ + 1) matrix ^, which is combined with the (^ + 1)-dimensional symbol vector 4, i.e.,the vector ^, to provide the transmit vector 5, i.e., the vector ^^. An example of this is described in moredetail with regard to FIG. 16. In other words, the spreading matrix 3 and the information-bearing symbolvector 4 may be used to generate the transmit vector 5. This corresponds to the method step 4000 ofFIG.1.For transmitting the message 2, the transmit vector 5 may be provided to a resource mapping 108 thatmaps the transmit vector 5 to the ^ physical resources.The matrix mapper 105 may be configured to map the first subset of bits ^^into the spreading matrix ^of size ^ × (^ + 1) using the following general procedure. First, the ^^ input bits may be used to gener-ate 2^ + 1 spreading sequences, which are gathered in vector ^ of size ^^ + 2^^ with ^^ + ^^ = ^.The vector ^ has the following structure: where spreading sequence ^^ is a ^^-dimensional vector and the 2^ remaining spreading sequences, ^^and ^^ , for ^ = 1, … , ^, are ^-dimensional vectors designed such that ^^ and ^^ are orthogonal, i.e.,^^^ ^^ = 0, ^ = 1, … , ^. (7)Different ways of obtaining the spreading sequences in the vector ^ are described with regard to FIGs.13 to 15.Finally, the spreading matrix ^ may be obtained from the vector ^ using the following structure:where ^(⋅) denotes the mapping of the elements of the spreading vector ^ to the elements of the spread-ing matrix ^ following equation (8) and ^(. ) is a mapping defining a projection throughdefined for an arbitrary This mapping may be also referred to as “spreading combiner”. Scalar ρ is a parameter (real scalarcomprised between 0 and 1) balancing the power between the spreading sequences, and ^^is an ^- dimensional zero vector.Given the structure of the spreading vector ^ in equation (6), the spreading matrix ^ is entirely deter-mined from ^ through mapping ^(⋅) as specified in equation (8). Therefore, there are as many distinctspreading matrices ^ as sequences ^. As shown in the equation (8), the spreading combiner ^(⋅) is suchthat the spreading matrix ^ is not block-diagonal.FIG. 13 shows an example of an implementation form of step 2000 of generating the block-partitionedspreading matrix of the method of FIG.1.FIG. 13 shows an example of an implementation form of the matrix mapper 105 of FIG. 12. As shownin FIG. 13, the first subset of bits ^^(labeled with the reference sign “1a”) may be used to generatespreading sequence ^^ of length ^^ and the remaining 2^ spreading sequences ^^ and ^^^, for ^ =1, … , ^, which are gathered into vectors: ^^ = ^^^ ^^ … ^^^^^ ^(11)of size ^^ + ^^ and ^^, respectively. The spreading sequences ^^, ^^, … , ^^ are spreading sequencesfor reference symbols and are labeled with the reference sign “6a”. The spreading sequences ^^^, … , ^^^are spreading sequences for information symbols and are labeled with the reference sign “7a”. Thus, asshown in FIG. 13, the first subset of bits 1a may be transformed by a spreading sequence generator 109to spreading sequences 6a for reference symbols and spreading sequences 7a for information symbols.This corresponds to method step 2100 of FIG.3. Optionally, as indicated in FIG. 13 by a delay distortion and / or Doppler distortion block 110, a delaydistortion and / or Doppler distortion of the vector ^ and, thus, the spreading sequences 6a for the refer-ence symbols may be performed to obtain vector ^. Vector ^ comprises delay distorted and / or Dopplerdistorted spreading sequences for the reference symbols. These delay distorted and / or Doppler distorted spreading sequences for the reference symbols are labelled with the reference sign “6”. This correspondsto the optional method step 2400a of FIG. 4. In addition or alternatively, as indicated in FIG. 13 by adelay distortion and / or Doppler distortion block 110, a delay distortion and / or Doppler distortion of thevector ^^ and, thus, the spreading sequences 7a for the information symbols may be performed to obtainvector ^^. Vector ^^ comprises delay distorted and / or Doppler distorted spreading sequences for the in-formation symbols. These delay distorted and / or Doppler distorted spreading sequences for the infor-mation symbols are labelled with the reference sign “7b”. This corresponds to the optional method step2400b of FIG.4.For the following a generic vector ^ = (^ ^ ^^ … ^^ )^ comprising ^ spreading sequences of length^^, for ^ = 1, … , ^ is considered. Due to the specific structure of the disclosed spreading combiner ^(⋅),used in above equation (8) and indicated in FIG.13 by the block 113, each of these spreading sequences (or a function thereof) is later used in the bilinear combiner 107 of FIG.12 to spread one of the symbolscomprised in vector ^ over a subset of the ^ available physical resources.Assuming that the ^-th sequence is associated with a subset ^^ ⊆ {1,2, … , ^} of ^^ = |^^| physical re-sources being transmitted in time slots {^^}^∈^^and frequency slots {^^}^∈^^Then, given two parametersthat can be randomly drawn ^ and ^, the post-processed spreading sequence ^^ is obtained as^^ = ^^ ∘ ^(^, ^) (12)where ∘ denote the element-wise multiplication and the delay and / or Doppler distortion vector ^(^, ^)is given by Then, the output vector ^ is obtained by gathering again the delay and / or Doppler distorted spreadingsequences as ^ = (^ ^ ^^ … ^^)^. The optional delay and / or Doppler distortion, i.e., the blocks110 ofFIG. 13, may be skipped by setting ^ = 0 and ^ = 0, which results in ^ = ^. Accordingly, performingonly a delay distortion may be achieved by setting ^ = 0. Performing only a Doppler distortion may beachieved by setting ^ = 0.The spreading sequences 7a for the information symbols in the vector ^^ (in case no delay distortionand / or Doppler distortion is performed) or the delay distorted and / or Doppler distorted spreading se-quences 7b for the information symbols in the vector ^^ are further processed by performing an orthog-onalization 111 to guarantee the orthogonality conditions in equation (7). In the following it is assumedthat the delay distortion and / or Doppler distortion 110 of the spreading sequences 6a for the reference symbols and the spreading sequences 7a for the information symbols is performed. The description is correspondingly valid in case the delay distortion and / or Doppler distortion 110 of the spreading se- quences 6a for the reference symbols and / or the delay distortion and / or Doppler distortion 110 of the spreading sequences 7a for the information symbols is not done.The ^ orthogonal spreading sequences 7 for the information symbols of length ^, ^^, … , ^^ in vector may be obtained as^ ^ = ^^^^^ , ^ = 1, … , ^ (14)where ^^ is a ^ × (^ − 1) unitary matrix collecting a basis of vectors orthogonal to ^^. The orthogonalspreading sequences ^^, … , ^^ for the information symbols in vector ^ are labeled with the referencesign “7”. The procedure to obtain these basis vectors may be systematic and agreed on beforehand be-tween all transmitters and the receiver. For instance, the Gram-Schmidt process could be applied. Theabove described orthogonalization for generating the orthogonal corresponds to method step 2200 of FIG.3. The spreading sequences 6a for the reference symbols (optionally the delay distorted and / or Dopplerdistorted spreading sequences 6 for the reference symbols) and the orthogonal spreading sequences 7for the information symbols may be combined in the vector ^ = (^^^^^^ … ^^^ ^^^ … using a vector combiner 112. The vector ^ is labelled with the reference sign “8”.The spreading matrix ^ may be obtained from vector ^ = (^^^^^^ … ^^^^^^ … ^^^)^throughspreading combiner ^(⋅) as specified in equation (8). The spreading combiner ^(⋅) is indicated in FIG.13 by block 113. The blocks 112 and 113 of FIG.13 correspond to method step 2300 of FIG.3.FIG. 14 shows an example of the spreading sequence generator used in the implementation form ofFIG.13. According to the example of FIG. 14, the first subset of bits 1a may be transformed to the spreading sequences 6a for the reference symbols and the spreading sequences 7a for the information symbols by performing a discrete mapping of the first subset of bits 1a to the spreading sequences 6a for the refer-ence symbols and the spreading sequences 7a for the information symbols. For this, discrete set mappers115 and 116 may be used in the spreading sequence generator 109 of the implementation form of FIG. 13.For example, an integer index ^ may be obtained from the ^^ bits of the first subset of bits 1a by applyinga bijective mapping ℐ: {0,1}^^ → {0, … , 2^^ − 1}. The integer index ^ is labeled in FIG. 14 by the refer-ence sign “9”. The bijective mapping may be referred to as “binary-to-integer mapping” and is presentedin FIG.14 by the block 114, which may be referred to as “binary-to-integer mapping block”. The index^ is subsequently used to generate the spreading sequences 6a for the reference symbols that are com-prised in the ^-dimensional vector ^ = ^[^] and the spreading sequences 7a for the information symbolsthat are comprised in the (^ − ^^)-dimensional vector ^^ = ^[^] as the (^ + 1)-th element of the discretecodebooks ^ = {^[0], … , ^[2^^ − 1]} and ℬ = {^[0], … , ^[2^^ − 1]}, respectively. This correspondsto method steps 2120 and 2121 of FIG. 6 (b), respectively. That is, this corresponds to generating thespreading sequences 6a for the reference symbols by selecting the spreading sequences 6a for the refer-ence symbols from a first discrete codebook ^ using the first subset of bits 1a. This may be performedusing a discrete set mapper ^ presented by the block 115 in FIG. 14. Further, this corresponds to gen-erating the spreading sequences 7a for the information symbols by selecting the spreading sequences 7afor the information symbols from a second discrete codebook ℬ using the first subset of bits 1a. Thismay be performed using a discrete set mapper ℬ presented by the block 116 in FIG. 14.The discrete codebooks ^ and ℬ can be, for example, chosen from the following list of sets of vectors:Galois sequences, Hadamard sequences, random Gaussian sequences, Grassmannian sequences, Zadoff-Chu sequences, standard legacy preamble sequences, demodulation reference signal (DMRS) se-quences, and arbitrary permutations and rotations of any of the previous sequencesFIG. 15 shows an example of the spreading sequence generator used in the implementation form ofFIG.13. According to the example of FIG. 15, the first subset of bits 1a may be transformed to the spreadingsequences 6a for the reference symbols and the spreading sequences 7a for the information symbols byperforming a continuous mapping of the first subset of bits 1a to the spreading sequences 6a for thereference symbols and the spreading sequences 7a for the information symbols. Thus, FIG. 15 showsanother example of an implementation form of the spreading sequence generator 109 of the implemen- tation form of FIG.13.For example, the JC bits of the first subset of bits 1a may be split by a bit splitter 117 into ^ disjointsequences 10 of ^ bits each. In other words, the first subset of bits 1a may be split into multiple se-quences 10 of bits of a common length ^ (i.e., the length is ^ bits). This corresponds to the method step2140 of FIG. 8. Each one of these sequences 10 of ^ bits may be mapped to corresponding complex-valued symbols ^^, ^^, … , ^^ by using scalar modulators 118 using constellations of size 2^such asQAM, PSK, etc. The complex-valued symbols ^^, ^^, … , ^^ are labeled with the reference sign “11”.In other words, the multiple sequences 10 of bits of the common length ^ may be mapped to the com-plex-valued symbols 11 using scalar modulators 118 of cardinality two to the power of the commonlength ^ (i.e., scalar modulation of cardinality 2^). This corresponds to method step 2141 of FIG. 8.Next all ^ complex-valued symbols 11 may be concatenated or combined by a vector combiner 119 invector ^ = (^^ ^^ … ^^)^, which is labeled with the reference sign “12”. This corresponds tomethod step 2142 of FIG. 8. The vector 12 may further be processed by a continuous mapper ^(∙) togenerate a ^^ + 2^^ − dimensional vector ^ as^ = ^(^^^) (15)where ^ is a scalar sca ^ ^^^^^^^ le parameter and ^: ℂ → ℂ is a continuous map. The continuous mapper^(∙) is represented in FIG. 15 by the block 120 and the ^^ + 2^^ − dimensional vector ^ is labeled withthe reference sign „13“. This corresponds to method step 2143 of FIG.8, wherein the vector 12 of FIG.15 is the first vector and the vector 13 is the second vector. The vector 13 may then be split by a vector splitter 121 into the spreading sequences 6a for the reference symbols and the spreading sequences 7a for the information symbols. This corresponds to the method step 2144 of FIG.8. According to a first example, the continuous mapping 120 is such that the following is true with ^^ denoting the scalar constellation set comprising 2^elements and ^with ^(^) = 4[Re(^) (1-Re(^)) + jIm(^) (1-Im(^))] where Re(⋅) and Im(⋅) denote the real part andimaginary parts, respectively, and ^(^) denotes the mapping resulting from ^ iterate compositions of ^.This corresponds to the method steps 2143a and 2143b of FIG.9. According to a second example, the continuous mapping 120 is such that the following is true with ^^denoting the scalar constellation set and 0.5 + ^0.5⋮^ (19) 0.5 + ^0.5^for a fixed ^ where ^ is a fixed sequence and with ^^(^^, ^^)^^^^ ^^^^ a ^(⋅) being a chaotic map, for instance given by This corresponds to the method steps 2143c and 2143d of FIG.10, wherein represents the thirdvector.FIG. 16 shows an example of the bilinear combiner used in the implementation form of FIG.12.According to the example of FIG. 16, in the bilinear combiner 107 of FIG. 12, a ^ × (^ + 1) matrix ^may be obtained by performing a spreading matrix processing of the spreading matrix C using the firstsubset of bits JC. The spreading matrix C, the first subset of bits ^^ and the matrix ^ are labelled withthe reference signs „3“, „1a“ and „14“, respectively. The spreading matrix processing is represented bythe block 122 in FIG. 16. For instance, the matrix ^ being a block-partitioned matrix may be generatedby acting on the (^ + 1) columns of the spreading matrix ^ = (^ ^^ ⋯ ^^) as a function of the ^^bits of the first subset of bits 1a (used to generate ^).For example, assuming that ^ denote the set of 2^^ possibly different truncated permutations taken frompossibly different subsets of ^ integers selected from the set {1,2, … ,^ = {^[0], ^[1], … , ^[2^^ − 1]} with ^[^] = (^^[^] … An example of choice of ^ may be to generate all possible permuta-tions of {1,2, … , ^}, keep only the first ^ elements of each one, and randomly select a set of 2^^ distinctones.Assuming that ^ is an integer index obtained from the ^^ bits of the first subset of bits 1a by applying abijective mapping ^: {0,1}^^ → {0, … , 2^^ − 1}. Then, the ^ × (^ + 1) matrix ^ is obtained as ^ =(^ ^^ ⋯ ^^) with the columns ^^, … , ^^ selected as a function of ^[^] as^^ = ^^^[^] (23)that is, the [^] + 1^-th column of ^. In other words, ^[^] provides an injective map between {1, … , ^}and {1, … , ^}, which selects and reorders the spreading sequences comprised in the ^ last columns of ^as a function of the ^^ bits of the first subset of bits 1a. Given the spreading matrix structure in equation(8), the spreading sequence comprised in the (^ + 1)-th column of ^, denoted by ^^, is associated withthe ^ physical resources ^^ + (^ − 1)^ + 1, … , ^^ + ^^ out of the ^ available physical resources. Thisallows controlling the resource mapping as a function of the ^^ bits of the first subset of bits 1a. Gener-ating the matrix ^ as described above corresponds to the method step 4100 of FIG. 11.In case of ^ = ^, then the ^ × (^ + 1) matrix ^ may be directly obtained from the spreading matrix ^,as ^ = ^. This corresponds to the case with set ^ = {^[0], ^[1], … , ^[2^^ − 1]} and ^[^] =(1 … ^)^ for ^ = 0, … , 2^^ − 1.Next the the transmit vector ^^ may be computed by a matrix / vector product between the matrix ^ andsymbol vector ^, as specified in equation (2). This corresponds to the method step 4200 of FIG.11.The matrix / vector product is represented in FIG. 16 by the block 123 and the symbol vector ^ is la-beled with the reference sign „4“.Thus, the bilinear combiner 107 may obtain the ^ × (^ + 1) matrix ^ by acting on the (^ + 1) col-umns of spreading matrix ^ as a function of the ^^ bits of the first subset of bits 1a (used to generate^) and, then, may generate signal vector ^^ by computing the product between the matrix ^ and thesymbol vector ^, as specified in equation (2).FIG. 17 shows an example of a receiver-side processing of the ^-dimensional transmit vector gener-ated by one of the methods of FIGs.1 to 16 and 18, after the ^-dimensional transmit vector has beenreceived, e.g., by a communication device.FIG. 17 shows an example of a receiver side for unsourced massive grant-free random access schemes.In the considered scenario, even after assuming that the set of active users ^ is known, the optimumjoint maximum likelihood (ML) multi-user detection and channel estimation problem is: given the received signal in equation (1) is intractable. Hence, a suboptimal receiver may be adopted. A possible approach is to perform user separation followed by single-user decoding within the context ofa successive interference cancellation (SIC) strategy. That is, once a set of active users (i.e., a set ofactive transmitters) is detected in the received signal and the corresponding messages are correctly de-coded, they are encoded again and subtracted from the received signal in a SIC module 124. This process is repeated until no new message can be decoded from the (residual) received signal. The user separationfunctionality may be decoupled as follows:As indicated in FIG. 17 by the activity detection block 125, the number of active users (i.e., number ofactive transmitters) is estimated by checking the presence of the spreading sequences in the (residual)received signal ^ (labelled in FIG. 17 by the reference sign „15“) and the corresponding spreading ma-trices ^^^^^ are provided. In FIG. 17, the corresponding spreading matrices ^^^^^ are labeled with thereference sign “3a”. As indicated in FIG.17 by the channel estimation block 126, the detected spreadingmatrices ^^^^^ may be used as pilot signals to estimate the channels ^^^^^ , which are labeled in FIG. 17by the reference sign “16”. As indicated in FIG.17 by the equalization block 127, the estimated channels^^^^^ may be equalized to obtain the corresponding symbol vectors {^^} , which are labeled in FIG. 17by the reference sign “4a”.Then, given the spreading matrix ^^^^^ and the symbol vector {^^} for each one of the active users (i.e.,active transmitters) in the estimated active set ^, single-user decoding is performed by reverting thedisclosed transmitter-side processing. This is indicated in FIG. 17 by the matrix demapper blocks 128,vector demapper blocks 129 and the combiners 130. Finally, as indicated by the CRC check blocks 131in FIG. 17, the decoded messages are accepted as valid messages if a valid cyclic redundancy check(CRC) is obtained. Only valid messages are re-encoded and subtracted from the received signal in theSIC module 124. In FIG.17, valid messages are labelled by the reference sign “2”. FIG.18 shows an example of a computer-implemented method according to an embodiment of this disclosure for transforming a message of multiple bits to a ^-dimensional transmit vector for transmis-sion via ^ physical resources, wherein ^ is an integer greater than one. The method of FIG. 18 is anexample of the computer-implemented method according to the third aspect of this disclosure. Thus, the description of the method according to the third aspect is correspondingly valid for the method of FIG.18.As shown in FIG. 18, in a step S1 the method comprises generating two subsets of bits by splitting themultiple bits. In a next step S2, the method comprises performing a continuous mapping of a first sub- set of bits of the two subsets of bits to spreading sequences for reference symbols and spreading se- quences for information symbols. In a next step S3, the method comprises generating orthogonal spreading sequences for the information symbols that are orthogonal to the spreading sequences for the reference symbols by performing an orthogonalization of the spreading sequences for the infor- mation symbols using the spreading sequences for the reference symbols. In a next step S4, the method comprises mapping the spreading sequences for the reference symbols and the orthogonal spreading sequences for the information symbols to blocks of a block-partitioned spreading matrix. In a next step S5, the method comprises generating, using a second subset of bits of the two subsets ofbits, an information-bearing symbol vector. In contrast to FIG.18, the step S5 may be performed be-fore any one of steps S2, S3 and S4 or simultaneously with at least one of steps S2, S3 and S4. In astep S6 following the steps S1 to S5, the method comprises generating the transmit vector using thespreading matrix and the information-bearing symbol vector. The block-partitioned spreading matrix may be block-diagonal or not. In case the block-partitioned spreading matrix is block-diagonal, the description of the FIGs.1 to 17 may be correspondingly valid with regard to the method of FIG.18, wherein the method steps of FIGs.1 to 17 with regard to the spreading matrix not being block-diagonal are adapted accordingly.FIG. 19 shows an example of a communication device for wirelessly transmitting a message of multi-ple bits via ^ physical resources, wherein ^ is an integer greater than one. The communication devicemay be an example of the communication device of the second aspect or the communication device ofthe fourth aspect. The description of the communication device of the second aspect and the descrip-tion of the communication device of the fourth aspect is correspondingly valid for the communication device of FIG.19. The communication device of FIG.19 is a communication device for wirelessly transmitting a mes-sage 2 of multiple bits 1 via ^ physical resources, wherein ^ is an integer greater than one. The com-munication device 200 is configured to transform the message 2 to a ^-dimensional transmit vector 5by performing the method according to the first aspect, e.g., the method of any one of FIGs. 1 to 16.Additionally or alternatively, the communication device 200 is configured to transform the message 2to a ^-dimensional transmit vector 5 by performing the method according to the third aspect, e.g., themethod of FIG.18. The communication device 200 may be referred to as transmitter device. It optionally may be config- ured to receive messages. In this case, it may be referred to as transceiver device. The communication device 200 may be configured to perform the processing described with regard to FIG.17 for receiv-ing messages. Optionally, the communication device 200 may comprise a single antenna. That is, itmay be a single antenna communication device. Alternatively, the communication device 200 may comprise multiple antennas. The communication device 200 may be configured to transmit the message 2 using the transmit vector5. For example, the communication device 200 may be configured to transmit to a communication de-vice with ^ antennas the message 2 using the transmit vector 5, wherein ^ is an integer greater thanone.The communication device 200 may comprise a processor or processing circuitry (not shown) config-ured to perform, conduct or initiate the various operations of the communication device 200 describedherein. The processing circuitry may comprise hardware and / or the processing circuitry may be con-trolled by software. The hardware may comprise analog circuitry or digital circuitry, or both analog and digital circuitry. The digital circuitry may comprise components such as application-specific inte- grated circuits (ASICs), field-programmable arrays (FPGAs), digital signal processors (DSPs), or multi-purpose processors. The communication device 200 may further comprise memory circuitry, which stores one or more instruction(s) that can be executed by the processor or by the processing cir- cuitry, in particular under control of the software. For instance, the memory circuitry may comprise a non-transitory storage medium storing executable software code which, when executed by the proces- sor or the processing circuitry, causes the various operations of the communication device 200 to be performed. In one embodiment, the processing circuitry comprises one or more processors and a non- transitory memory connected to the one or more processors. The non-transitory memory may carry ex-ecutable program code which, when executed by the one or more processors, causes the communica-tion device 200 to perform, conduct or initiate the operations or methods described herein. The computer-implemented methods of this disclosure, such as the method of the first aspect and the method of the third aspect, as well as the communication devices of this disclosure, such as the device of the second aspect and the device of the fourth aspect, may be applied to the New Radio (NR) Air Interface defined in 3GPP Release 15 (and further enhanced in Release 16 and 17). This NR Air Inter- face provides support to ultra-reliable ultra-low latency communication (URLLC) and massive ma- chine-type communication (mMTC) services in addition to the “legacy” mobile broadband communication, now termed enhanced mobile broadband (eMBB) service. Furthermore, 3GPP Re- lease 16 considers a new 2-step grant-free transmission to coexist with the “legacy” four-step random access channel (RACH) [3GPP TS 38.321] to cope with more stringent delay constraints. Further pro- tocol enhancements are expected to support a massive grant-free random access scheme in future 3GPP releases. The computer-implemented methods and communication devices of this disclosure may be applied to emerging services in the context of massive IoT or massive MTC. Such emergency services will gen- erate data traffic types and will require quality of service indicators that are not efficiently supportedby conventional multiple access protocols. The computer-implemented methods and communicationdevices of this disclosure provide a novel protocol to support the requirements of emerging services.The computer-implemented methods of this disclosure, such as the method of the first aspect and the method of the third aspect, as well as the communication devices of this disclosure, such as the deviceof the second aspect and the device of the fourth aspect, may be used in any system that requires mul-tiple transmitters to transmit a message (e.g., payload) through random access channels, such as 5Gsystems, 6G systems, Internet-of-things (IoT) systems, Wi-Fi communications systems etc.The transmitter-side processing provided by the computer-implemented methods according to the first aspect and third aspect may be a scheme in the category of spreading-based non-orthogonal multiple access (NOMA) schemes for new radio (NR). The present disclosure has been described in conjunction with various embodiments as examples as well as implementations. However, other variations can be understood and effected by those persons skilled in the art and practicing the claimed matter, from the studies of the drawings, this disclosure and the independent claims. In the claims as well as in the description the word “comprising” does not exclude other elements or steps and the indefinite article “a” or “an” does not exclude a plurality. A single element or other unit may fulfill the functions of several entities or items recited in the claims. The mere fact that certain measures are recited in the mutual different dependent claims does not indi- cate that a combination of these measures cannot be used in an advantageous implementation.

Claims

CLAIMS1. A computer-implemented method for transforming a message (2) of multiple bits (1) to a T-dimensional transmit vector (5) for transmission via T physical resources, T being an integergreater than one, the method comprises- generating (1000) two subsets of bits (1a, 1b) by splitting the multiple bits (1),- generating (2000), using a first subset of bits (1a) of the two subsets of bits (1a, 1b), a block-partitioned spreading matrix (3) that is not a block-diagonal matrix,- generating (3000), using a second subset of bits (1b) of the two subsets of bits (1a, 1b), an in-formation-bearing symbol vector (4), and- generating (4000) the transmit vector (5) using the spreading matrix (3) and the information-bearing symbol vector (4).

2. The computer implemented method according to claim 1 comprises- generating (1100a) the two subset of bits (1a, 1b) by splitting the multiple bits (1) into two se-quences of bits (1a’, 1b’) and- generating (1100a) the first subset of bits (1a) by processing a first sequence of bits (1a’) ofthe two sequences of bits (1a’, 1b’) using at least one of a channel encoder (101), a bit inter-leaver (102) and a bit scrambler (103), and / or- generating (1100b) the second subset of bits (1b) by processing a second sequence of bits (1b’)of the two sequences of bits (1a’, 1b’) using at least one of a channel encoder (101), a bit inter-leaver (102) and a bit scrambler (103).

3. The computer-implemented method according to claim 1 or 2, wherein generating (2000) thespreading matrix (3) comprises- transforming (2100) the first subset of bits (1a) to spreading sequences (6a) for reference sym-bols and spreading sequences (7a) for information symbols,- generating (2200) orthogonal spreading sequences (7) for the information symbols that are or-thogonal to the spreading sequences (6a) for the reference symbols by performing an orthogo-nalization (111) of the spreading sequences (7a) for the information symbols using thespreading sequences (6a) for the reference symbols, and- mapping (2300) the spreading sequences (6a) for the reference symbols and the orthogonalspreading sequences (7) for the information symbols to blocks of the spreading matrix (3).

4. The computer-implemented method according to claim 3, wherein generating (2000) thespreading matrix comprises- performing (2400a) a delay distortion and / or Doppler distortion (110) of the spreading se-quences (6a) for the reference symbols and using for the orthogonalization (111) the delay dis-torted and / or Doppler distorted spreading sequences (6) for the reference symbols as thespreading sequences (6a) for the reference symbols, and / or- performing (2400b) a delay distortion and / or Doppler distortion (110) of the spreading se-quences (7a) for the information symbols and using for the orthogonalization (111) the delaydistorted and / or Doppler distorted spreading sequences (7b) for the information symbols as thespreading sequences (7a) for the information symbols.

5. The computer-implemented method according to claim 3 or 4, wherein mapping (2300) thespreading sequences (6a) for the reference symbols and the orthogonal spreading sequences(7) for the information symbols to the blocks of the spreading matrix (3) comprises- mapping (2300a) the spreading sequences (6a) for the reference symbols to blocks of the firstcolumn of the spreading matrix (3), and- mapping (2300b) the orthogonal spreading sequences (7) for the information symbols toblocks in the main diagonal of the spreading matrix (3) starting from the second block.

6. The computer-implemented method according to any one of claims 3 to 5, wherein transform-ing (2100) the first subset of bits (1a) to the spreading sequences (6a) for the reference sym-bols and the spreading sequences (7a) for the information symbols comprises- performing (2110) a discrete mapping of the first subset of bits (1a) to the spreading sequences(6a) for the reference symbols and the spreading sequences (7a) for the information symbols.

7. The computer-implemented method according to any one of claims 3 to 6, wherein transform-ing (2100) the first subset of bits (1a) to the spreading sequences (6a) for the reference sym-bols and the spreading sequences (7a) for the information symbols comprises- generating (2120) the spreading sequences (6a) for the reference symbols by selecting thespreading sequences (6a) for the reference symbols from a first discrete codebook (115) usingthe first subset of bits (1a), and- generating (2121) the spreading sequences (7a) for the information symbols by selecting thespreading sequences (7a) for the information symbols from a second discrete codebook (116)using the first subset of bits (1a).

8. The computer-implemented method according to claim 7, wherein- the first discrete codebook (115) comprises at least one of Galois sequences, Hadamard se-quences, random Gaussian sequences, Grassmannian sequences, Zadoff-Chu sequences, stand-ard legacy preamble sequences, demodulation reference signal, DMRS, sequences, andarbitrary permutations and rotations of any of the previous sequences; and / or- the second discrete codebook (116) comprises at least one of Galois sequences, Hadamard se-quences, random Gaussian sequences, Grassmannian sequences, Zadoff-Chu sequences, stand- ard legacy preamble sequences, demodulation reference signal, DMRS, sequences, and arbitrary permutations and rotations of any of the previous sequences.

9. The computer-implemented method according to any one of claims 3 to 5, wherein transform-ing (2100) the first subset of bits (1a) to the spreading sequences (6a) for the reference sym-bols and the spreading sequences (7a) for the information symbols comprises- performing (2130) a continuous mapping of the first subset (1a) of bits to the spreading se-quences (6a) for the reference symbols and the spreading sequences (7a) for the informationsymbols.

10. The computer-implemented method according to any one of claims 3 to 5 and 9, whereintransforming (2100) the first subset of bits (1a) to the spreading sequences (6a) for the refer-ence symbols and the spreading sequences (7a) for the information symbols comprises- splitting (2140) the first subset of bits (1a) into multiple sequences of bits (10) of a commonlength (D),- generating (2141) multiple complex-valued symbols (11) by mapping the multiple sequencesof bits (10) of the common length (D) to the multiple complex-valued symbols (11) using sca-lar modulators (118) of cardinality two to the power of the common length (D),- generating (2142) a first vector (12) by combining the multiple complex-valued symbols (11),- continuously mapping (2143) the first vector (12) to a second vector (13) that has a greater di-mension compared to the first vector (12), and- splitting (2144) the second vector (13) into the spreading sequences (6a) for the referencesymbols and the spreading sequences (7a) for the information symbols.

11. The computer-implemented method according to claim 10, wherein continuously mapping(2143) the first vector (12) to the second vector (13) comprises- duplicating (2143a) information of the first vector (12), and- transforming (2143b) each duplicate of the duplicated information of the first vector (12) to atransformed version of the first vector (12) using a chaotic function, the second vector (13) be-ing the transformed version of the first vector (12).

12. The computer-implemented method according to claim 10, wherein continuously mapping(2143) the first vector (12) to the second vector (13) comprises- generating (2143c) a third vector by combining the first vector (12) with a fixed reference se-quence, and- transforming (2143d) the third vector using a chaotic function.

13. The computer-implemented method according to any one of claims 1 to 12, wherein generat-ing (4000) the transmit vector (5) using the spreading matrix (3) and the information-bearingsymbol vector (4) comprises- generating (4100) a block-partitioned matrix (14) comprising, as a first column, a vector ofspreading sequences (6) for reference symbols and, as further columns, columns of the spread-ing matrix (3) selected using the first subset of bits (1a), and- computing (4200) the transmit vector (5) by vector multiplying the information-bearing sym-bol vector (4) and the generated block-partitioned matrix (14).

14. A communication device (200) for wirelessly transmitting a message (2) of multiple bits (1)via T physical resources, T being an integer greater than one, wherein- the communication device (200) is configured to transform the message (2) to a T-dimensionaltransmit vector (5) by performing the method according to any one of the previous claims.

15. A computer-implemented method for transforming a message (2) of multiple bits (1) to a T-dimensional transmit vector (5) for transmission via T physical resources, T being an integergreater than one, the method comprises- generating (S1) two subsets of bits (1a, 1b) by splitting the multiple bits (1),- performing (S2) a continuous mapping of a first subset of bits (1a) of the two subsets of bits(1a, 1b) to spreading sequences (6a) for reference symbols and spreading sequences (7a) forinformation symbols,- generating (S3) orthogonal spreading sequences (7) for the information symbols that are or-thogonal to the spreading sequences (6a) for the reference symbols by performing an orthogo-nalization of the spreading sequences (7a) for the information symbols using the spreadingsequences (6a) for the reference symbols,- mapping (S4) the spreading sequences (6a) for the reference symbols and the orthogonalspreading sequences (7) for the information symbols to blocks of a block-partitioned spreadingmatrix,- generating (S5), using a second subset of bits (1b) of the two subsets of bits (1a, 1b), an infor-mation-bearing symbol vector (4), and- generating (S6) the transmit vector (5) using the spreading matrix and the information-bearingsymbol vector (4).

16. The computer-implemented method according to claim 15, wherein performing (S2) the con-tinuous mapping of the first subset of bits (1a) to the spreading sequences (6a) for the refer-ence symbols and the spreading sequences (7a) for the information symbols comprises- splitting (2140) the first subset of bits (1a) into multiple sequences of bits (10) of a commonlength (D),- generating (2141) multiple complex-valued symbols (11) by mapping the multiple sequencesof bits (10) of the common length (D) to the multiple complex-valued symbols (11) using sca-lar modulators (118) of cardinality two to the power of the common length (D),- generating (2142) a first vector (12) by combining the multiple complex-valued symbols (11),- continuously mapping (2143) the first vector (12) to a second vector (13) that has a greater di-mension compared to the first vector (12), and- splitting (2144) the second vector (13) into the spreading sequences (6a) for the referencesymbols and the spreading sequences (7a) for the information symbols.

17. The computer-implemented method according to claim 16, wherein continuously mapping(2143) the first vector (12) to the second vector (13) comprises- duplicating (2143a) information of the first vector (12), and- transforming (2143b) each duplicate of the duplicated information of the first vector (12) to atransformed version of the first vector (12) using a chaotic function, the second vector (13) be- ing the transformed version of the first vector (12).

18. The computer-implemented method according to claim 16, wherein continuously mapping(2143) the first vector (12) to the second vector (13) comprises- generating (2143c) a third vector by combining the first vector (12) with a fixed reference se-quence, and- transforming (2143d) the third vector using a chaotic function.

19. A communication device (200) for wirelessly transmitting a message (2) of multiple bits (1)via T physical resources, T being an integer greater than one, wherein- the communication device (200) is configured to transform the message (2) to a T-dimensionaltransmit vector (5) by performing the method according to any one of claims 15 to 18.

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