Orthogonal multiplexing of signals for wakeup sequence incoherent detection

Abstract

The embodiment of the invention relates to multiplexing of signals in a communication system. A first communication device (100) acquires a vector b including M integer value information symbols in a set {0, 1,..., q-1], where q = 2Q, and Q is a positive integer, and acquires an N * M matrix C including symbols in the set {0, 1,..., q-1}, where N is a positive integer, satisfying M < = N. And multiplying the matrix C by the vector b, and performing modulus q to obtain a vector y comprising N transmission symbols, each transmission symbol in the vector y being associated with one of q signals. An association signal for each transmission symbol in the vector y is transmitted to one or more receivers (510). A second communication device (300) receives N signals (510), where each signal is associated with a symbol in a set [0, 1,..., q-1], where q = 2Q, and Q is a positive integer. The second communication device (300) determines M integer value information symbols from N association symbols based on an N * M matrix C or a modulo inverse thereof, where the matrix C and the modulo inverse thereof comprise symbols in the set [0, 1,..., q-1], where N is a positive integer, satisfying M < = N. The invention further relates to a corresponding method and to a computer program.

Description

Technical Field

[0001] Embodiments of the present invention relate to a first communication device and a second communication device for multiplexing signals in a communication system. In addition, embodiments of the present invention also relate to corresponding methods and computer programs. Background Art

[0002] A solution to reduce the power consumption of a user equipment (UE) is to put the UE in a sleep mode and then use a mechanism that can wake up the UE. In 3GPP Long Term Evolution (LTE) and New Radio (NR), this is mainly achieved through the discontinuous reception (DRX) feature, which wakes up the UE at configured periodic moments to monitor the physical downlink control channel (PDCCH) in order to read the paging channel.

[0003] As an additional feature of DRX, a wake-up signal (WUS) is defined in LTE, which is sent from the base station. Only when the UE detects the WUS will the UE be woken up at the periodic moments given by the DRX configuration to monitor the PDCCH, otherwise the UE can remain in the sleep mode. The WUS in LTE is based on the orthogonal frequency division multiplexing (OFDM) waveform and consists of a complex-valued sequence that the UE attempts to detect. Summary of the Invention

[0004] The objective of embodiments of the present invention is to provide a solution to reduce or solve the drawbacks and problems of traditional solutions.

[0005] The above and other objectives are achieved by the subject matter claimed in the independent claims. Other embodiments of the present invention can be found in the dependent claims.

[0006] According to a first aspect of the present invention, the above and other objectives are achieved by a first communication device for a communication system, the first communication device being configured to:

[0007] Obtain a vector b including M integer-valued information symbols in the set {0, 1,..., q - 1}, where q = 2 Q , and Q is a positive integer;

[0008] Obtain an N × M matrix C including symbols in the set {0, 1,..., q - 1}, where N is a positive integer and M ≤ N;

[0009] Multiply the matrix C by the vector b and then take the modulo q to obtain a vector y including N transmission symbols, where each transmission symbol in the vector y is associated with one of q signals;

[0010] Send the associated signal of each transmission symbol in the vector y to one or more receivers.

[0011] The first communication device can also be referred to as a transmitter.

[0012] The advantage of the first communication device described in the first aspect is that signals that can be non-coherently detected by the receiver can be used to send information symbols for different receivers.

[0013] In an implementation of the first communication device described in the first aspect, the k-th component in the vector y is associated with the time-frequency resource k, where the component k satisfies 1 ≤ k ≤ N.

[0014] The advantage of this implementation is that signals such as frequency shift keying (FSK) or on-off keying (OOK) can be used for sending information symbols.

[0015] In an implementation of the first communication device described in the first aspect, for any positive integer value of n, N = 12n, or N = 14n.

[0016] The advantage of this implementation is that the transmission of signals is suitable for the time-frequency resource structure of 3GPP LTE and NR systems.

[0017] In an implementation of the first communication device described in the first aspect, the vector b includes information symbols for different receivers.

[0018] The advantage of this implementation is that information symbols for different receivers can be sent on the same time-frequency resource.

[0019] In an implementation of the first communication device described in the first aspect, the vector b includes S u information symbols for receiver u, such that

[0020]

[0021] where U is the number of receivers, 1 ≤ U ≤ M.

[0022] The advantage of this implementation is that multiple information symbols can be sent to different receivers on the same time-frequency resource.

[0023] In an implementation of the first communication device according to the first aspect, the associated signal is any one of the following:

[0024] On - Off Keying signal;

[0025] Frequency - Shift Keying signal;

[0026] Orthogonal Frequency Division Multiplexing signal; or

[0027] Discrete Fourier Transform - Precoded Orthogonal Frequency Division Multiplexing signal.

[0028] The advantage of this implementation is that a low - complexity receiver using non - coherent detection can be used.

[0029] In an implementation of the first communication device according to the first aspect, at least one information symbol represents any one of the following:

[0030] An indicator for waking up one or a group of receivers;

[0031] The identity of one or a group of receivers; or

[0032] Paging information associated with one or a group of receivers.

[0033] The advantage of this implementation is that the information represented by the information symbol can be used to achieve power saving in the receiver.

[0034] In an implementation of the first communication device according to the first aspect, M = N, and C and C –1 comprise integer - valued symbols from the set {0, 1, …, q – 1} and satisfy

[0035] C –1 C = I (mod q),

[0036] where C –1 is the modular inverse of C, I is the identity matrix, and mod q is the modulo - q operator.

[0037] The advantage of this implementation is that the information symbol can be perfectly retrieved by the receiver.

[0038] In an implementation of the first communication device according to the first aspect, C is an N×N matrix and the rank is equal to N, where q = 2 and C –1 satisfies at least one of the following:

[0039] C –1 is a matrix with one element equal to 1 in each row and each column;

[0040] C –1is a matrix in which at least one row has an even Hamming weight;

[0041] C –1 is a matrix in which N–1 rows have an even Hamming weight;

[0042] C –1 is a matrix in which the rows have an odd Hamming weight;

[0043] C –1 is a matrix whose total Hamming weight is equal to N 2 –N+1 such that the Hamming weight of N–1 rows is equal to N–1 and the Hamming weight of 1 row is equal to N; and / or

[0044] C –1 is a matrix in which each row has the same odd-valued Hamming weight.

[0045] The Hamming weight w(x) of a matrix or vector x is defined as the number of positive elements in x.

[0046] An advantage of this implementation is that C can be constructed to minimize the probability of error-detecting information symbols.

[0047] In one implementation of the first communication device described in the first aspect, C is an N×N matrix and the rank is equal to N, where Q>1, and C is a version obtained by permuting any row or column of the matrix The matrix is given as

[0048]

[0049] where c ii is an odd integer in the set {0,1,…,q–1}, and for at least one i, 1≤i≤N, each symbol in the set {0,1,…,q–1} is associated with a bit label such that the Hamming weight difference between the symbol X and the bit label of is at most 1.

[0050] The rank of matrix C can be defined as the maximum number of linearly independent columns of C.

[0051] An advantage of this implementation is that q = 2 Q >2 bits can be processed simultaneously, which can reduce the implementation complexity in the transmitter and receiver.

[0052] In one implementation of the first communication device described in the first aspect, M = N, where t is the smallest positive integer such that C t = I (mod q), and up to t–1 matrices are generated for the communication system (500) as follows:

[0053] {C, C 2 , …, C t–1}.

[0054] The advantage of this implementation is that different multiplexing matrices can be used in the communication system. For example, different matrices can be used in different cells, and different matrices can be obtained from C.

[0055] In an implementation of the first communication device described in the first aspect, C is an N×M matrix and its rank is equal to M, where M < N, q = 2, and C satisfies at least one of the following:

[0056] C is obtained by performing any row or column permutation on the matrix , and the matrix is given as

[0057]

[0058] where P is an M×M matrix with different rows and columns, and each row and each column contains a non-zero element,

[0059] and A is an (N–M)×M matrix;

[0060] C ′ The rank of the product of C and C' is equal to M, where C' is the transpose of C; and / or

[0061] C includes orthogonal column vectors with odd Hamming weights.

[0062] The advantage of this implementation is that the probability of signal detection can be increased because N signals are used to transmit M information symbols, where M < N.

[0063] According to the second aspect of the present invention, the above and other objects are achieved by a second communication device for a communication system, and the second communication device is configured to:

[0064] Receive N signals, where each signal is associated with a symbol in the set {0, 1, …, q–1}, where q = 2 Q , and Q is a positive integer;

[0065] Determine M integer-valued information symbols from the N associated symbols based on the N×M matrix C or its modular inverse, where the matrix C and its modular inverse include symbols in the set {0, 1, …, q–1}, where N is a positive integer and satisfies M ≤ N.

[0066] The second communication device can also be represented as a receiver.

[0067] An advantage of the second communication device described in the second aspect is that information symbols can be transmitted from a transmitter using signals that can be non-coherently detected by the second communication device.

[0068] In one implementation of the second communication device described in the second aspect, the signal is any one of the following:

[0069] On-off keying signal;

[0070] Frequency shift keying signal;

[0071] Orthogonal frequency division multiplexing signal; or

[0072] Discrete Fourier transform precoded orthogonal frequency division multiplexing signal.

[0073] An advantage of this implementation is that the second communication device can perform non-coherent detection using a low-complexity receiver.

[0074] In one implementation of the second communication device described in the second aspect, at least one information symbol represents any one of the following:

[0075] An indicator for waking up one or a group of receivers;

[0076] The identity of one or a group of receivers; or

[0077] Paging information associated with one or a group of receivers.

[0078] An advantage of this implementation is that the information represented by the information symbols can be used to achieve power savings in the second communication device.

[0079] In one implementation of the second communication device described in the second aspect, M = N, and C and C –1 Comprise integer-valued symbols from the set {0, 1, …, q – 1} and satisfy

[0080] C –1 C = I (mod q),

[0081] where C –1 is the modular inverse of C, I is the identity matrix, and mod q is the modulo-q operator.

[0082] An advantage of this implementation is that the information symbols can be perfectly retrieved by the second communication device.

[0083] In one implementation of the second communication device described in the second aspect, C is an N×N matrix and has a rank equal to N, where q = 2, and C –1 Satisfies at least one of the following:

[0084] C –1is a matrix in which each row and each column has one element equal to 1;

[0085] C –1 is a matrix in which at least one row has an even Hamming weight;

[0086] C –1 is a matrix in which N–1 rows have an even Hamming weight;

[0087] C –1 is a matrix in which the rows have an odd Hamming weight;

[0088] C –1 is a matrix whose total Hamming weight is equal to N 2 –N+1 such that the Hamming weight of N–1 rows is equal to N–1 and the Hamming weight of 1 row is equal to N; and / or

[0089] C –1 is a matrix in which each row has the same odd-valued Hamming weight.

[0090] An advantage of this implementation is that C can be constructed to minimize the probability of error detection information symbols.

[0091] In one implementation of the second communication device described in the second aspect, C is an N×N matrix and has a rank equal to N, where Q>1, and C is a version obtained by permuting any row or column of the matrix and the matrix is given as

[0092]

[0093] where c ii is an odd integer in the set {0,1,…,q–1}, and for at least one i, 1≤i≤N, each symbol in the set {0,1,…,q–1} is associated with a bit label such that the Hamming weight difference between the symbol X and is at most 1.

[0094] An advantage of this implementation is that q = 2 Q >2 bits can be processed simultaneously, which can reduce the implementation complexity in the transmitter and receiver.

[0095] In one implementation of the second communication device described in the second aspect, C is an N×M matrix and has a rank equal to M, where M<N, q = 2, and C satisfies at least one of the following:

[0096] C is obtained by performing any row or column permutation on the matrix and the matrix is given as

[0097]

[0098] Wherein, P is an M×M matrix with different rows and columns, and each row and each column contains a non-zero element.

[0099] And A is an (N–M)×M matrix;

[0100] The rank of the product of C′ and C is equal to M, where C′ is the transpose of C; and / or

[0101] C includes orthogonal column vectors with odd Hamming weights.

[0102] The advantage of this implementation is that the probability of signal detection can be increased because N signals are used to transmit M information symbols, where M < N.

[0103] According to a third aspect of the present invention, the above and other objects are achieved by a method for a first communication device, the method comprising:

[0104] Obtaining a vector b including M integer-valued information symbols in the set {0, 1, …, q–1}, where q = 2 Q , and Q is a positive integer;

[0105] Obtaining an N×M matrix C including symbols in the set {0, 1, …, q–1}, where N is a positive integer and satisfies M ≤ N;

[0106] Multiplying the matrix C by the vector b and then taking the modulus q to obtain a vector y including N transmission symbols, where each transmission symbol in the vector y is associated with one of q signals;

[0107] Sending the associated signal of each transmission symbol in the vector y to one or more receivers.

[0108] The method provided by the third aspect can be extended to an implementation corresponding to the implementation of the first communication device provided by the first aspect. Therefore, an implementation of the method includes one or more features of the corresponding implementation of the first communication device.

[0109] The advantages of the method provided by the third aspect are the same as those of the corresponding implementation of the first communication device provided by the first aspect.

[0110] According to a fourth aspect of the present invention, the above and other objects are achieved by a method for a second communication device, the method comprising:

[0111] Receiving N signals, where each signal is associated with a symbol in the set {0, 1, …, q–1}, where q = 2Q and Q is a positive integer;

[0112] Determine M integer-valued information symbols from N associated symbols based on the N×M matrix C or its modulo inverse, where the matrix C and its modulo inverse include symbols from the set {0, 1, …, q–1}, where N is a positive integer and satisfies M≤N.

[0113] The method according to the fourth aspect can be extended to an implementation corresponding to the implementation of the second communication device according to the second aspect. Accordingly, one implementation of the method includes one or more features of the corresponding implementation of the second communication device.

[0114] The advantages of the method according to the fourth aspect are the same as those of the corresponding implementation of the second communication device according to the second aspect.

[0115] An embodiment of the present invention also relates to a computer program, characterized by program code that, when run by at least one processor, causes the at least one processor to execute any of the methods provided by the embodiments of the present invention. In addition, an embodiment of the present invention also relates to a computer program product that includes a computer-readable medium and the computer program, where the computer program is included in the computer-readable medium and includes one or more of the following groups: read-only memory (ROM), programmable ROM (PROM), erasable PROM (EPROM), flash memory, electrically erasable PROM (EEPROM), and hard disk drive, etc.

[0116] Based on the following detailed description, other applications and advantages of the embodiments of the present invention will be apparent. BRIEF DESCRIPTION OF THE DRAWINGS

[0117] The drawings are intended to illustrate and explain different embodiments of the present invention, in which:

[0118] Figure 1 A first communication device provided by an embodiment of the present invention is shown;

[0119] Figure 2 A flowchart of a method for a first communication device provided by an embodiment of the present invention is shown;

[0120] Figure 3 A second communication device provided by an embodiment of the present invention is shown;

[0121] Figure 4Shows a flowchart of the method for a second communication device provided by an embodiment of the present invention;

[0122] Figure 5 Shows a communication system provided by an embodiment of the present invention;

[0123] Figure 6 Shows a block diagram of a transmitter provided by an embodiment of the present invention;

[0124] Figure 7 Shows a block diagram of a receiver provided by an embodiment of the present invention;

[0125] Figure 8 Shows the bit error probability of a Gilbert - Elliot channel using the C matrix of (51) and the Hamming code of (46);

[0126] Figure 9 Shows the bit error probability of a Gilbert - Elliot channel using the C matrix of (51) and the Hamming code of (46);

[0127] Figure 10 Shows a comparison of the bit error probabilities of Gilbert - Elliot channels using different demultiplexing algorithms;

[0128] Figure 11 Shows block diagrams of a transmitter and a receiver with q - ary signaling;

[0129] Figure 12 Shows the BER as a function of the BSC error probability when the input symbol is zero;

[0130] Figure 13 Shows the bit error rate as a function of the BSC error probability for optimized mapping, natural mapping, and Gray mapping. Detailed implementation

[0131] Compared with OFDM - based WUS in LTE, a complex WUS can be designed by using a separate radio unit for WUS, with a specific waveform highly optimized for low - complexity detection and low power consumption. This includes waveforms that can be non - coherently detected (i.e., by energy detection), such as frequency - shift keying (FSK), pulse - position modulation (PPM), and on - off keying (OOK). However, if energy detection is performed at the receiver, the phase of the signal cannot be detected. Therefore, it is impossible to transmit a bipolar or complex - valued sequence on WUS.

[0132] If WUS uses different waveforms, the time-frequency resources of WUS must be separated from other signals / channels in the system, which makes it very important to use as few resources as possible for WUS. For WUS in LTE, since it is coherently detected, a complex-valued sequence can be constructed to be orthogonal, which makes it possible to multiplex the WUS of different UEs on the same time-frequency resources. Therefore, multiplexing is performed by the superposition of the corresponding WUS. However, for non-coherent detection such as energy detection, the receiver output is usually binary, that is, indicating whether WUS is received, which makes it an unsolved problem of how to multiplex WUS.

[0133] Assume that LTE WUS has no dedicated radio unit and the UE can maintain time-frequency synchronization so that it can coherently detect the sequence. In LTE Rel-15, WUS addresses all UEs configured with a specific time slot, where the UE monitors the paging channel. This means that the UE can receive WUS even though the WUS is for another UE, which may cause unnecessary wake-up. In LTE Rel-16, this problem is alleviated and a more refined scheme is introduced through the concept of group WUS, and the UE can be configured as a UE group. The sequences of different groups can be orthogonal, so WUS can be multiplexed. Up to 8 groups can be configured.

[0134] Generally, if the multiplexing of WUS can be performed on shared time-frequency resources, the spectrum efficiency can be improved. Since the number of transmitted WUS will vary over time, the shared resources provide a statistical multiplexing gain. On the other hand, using dedicated orthogonal resources, for example, through frequency division multiplexing (FDM) or time division multiplexing (TDM), may require more resources to be allocated for WUS, and moreover, the spectrum utilization rate on each dedicated resource is on average smaller.

[0135] Therefore, the object of the embodiments of the present invention is to improve the spectrum efficiency of a communication system by multiplexing signals such as WUS sent from a base station to different UEs on the same time-frequency resources, especially for waveforms of non-coherent detection. The waveforms of non-coherent detection usually have only a limited set of transmission states. For example, one signal represents "0" and one signal represents "1". Therefore, the multiplexing with a non-coherent detection receiver cannot use an orthogonal sequence complex-valued sequence as assumed in LTE WUS. In addition, the superposition of signals produces a signal different from any original signal, such as a signal representing "0" or "1". The embodiments of the present invention solve the multiplexing problem of WUS and other types of signals, where the transmission waveform of the multiplexed signal is the same as the waveform of the corresponding signal. That is to say, the multiplexing is performed in such a way that the corresponding signals in different multiplexed signals do not directly superpose.

[0136] Figure 1 shows the first communication device 100 provided by an embodiment of the present invention. In Figure 1 the embodiment shown, the first communication device 100 includes a processor 102, a transceiver 104, and a memory 106. The processor 102 is coupled to the transceiver 104 and the memory 106 through a communication device 108 known in the art. The first communication device 100 can be used for wireless and / or wired communication in a communication system. The wireless communication capability can be provided by an antenna or an antenna array 110 coupled to the transceiver 104.

[0137] The processor 102 can be referred to as one or more general-purpose central processing units (CPUs), one or more digital signal processors (DSPs), one or more application-specific integrated circuits (ASICs), one or more field programmable gate arrays (FPGAs), one or more programmable logic devices, one or more discrete gates, one or more transistor logic devices, one or more discrete hardware components, or one or more chip sets. The memory 106 can be a read-only memory, a random access memory (RAM), or a non-volatile RAM (NVRAM). The transceiver 304 can be a transceiver circuit, a power controller, or an interface providing the ability to communicate with other communication modules or communication devices (such as network nodes and network servers). The transceiver 104, the memory 106, and / or the processor 102 can be implemented in separate chip sets or can be implemented in a common chip set.

[0138] In the present disclosure, that the first communication device 100 is used to perform some actions can be understood as that the first communication device 100 includes appropriate means for performing the actions, such as the processor 102 and the transceiver 104, etc.

[0139] According to an embodiment of the present invention, the first communication device 100 is used to obtain a vector b including M integer-valued information symbols in the set {0, 1, …, q – 1}, where q = 2 Q, and Q is a positive integer. The first communication device 100 is configured to obtain an N×M matrix C including symbols in the set {0, 1, …, q–1}, where N is a positive integer and satisfies M≤N. The first communication device 100 is configured to multiply the matrix C by the vector b and then take the modulo q to obtain a vector y including N transmission symbols, where each transmission symbol in the vector y is associated with one of q signals. The first communication device 100 is configured to send the association signal 510 of each transmission symbol in the vector y to one or more receivers.

[0140] The information symbol can, for example, represent the information required to wake up the receiver. The information symbol can also be obtained from the output of a forward error correcting (FEC) encoder. The first communication device 100 can arrange the information symbols into a vector b. In addition, the matrix C can be predefined according to a communication standard or determined from a set of matrices that can be defined by the communication standard.

[0141] In addition, in an embodiment of the present invention, the first communication device 100 includes a processor, and the processor is configured to: obtain a vector b including M integer-valued information symbols in the set {0, 1, …, q–1}, where q = 2 Q , and Q is a positive integer; obtain an N×M matrix C including symbols in the set {0, 1, …, q–1}, where N is a positive integer and satisfies M≤N; multiply the matrix C by the vector b and then take the modulo q to obtain a vector y including N transmission symbols, where each transmission symbol in the vector y is associated with one of q signals. The first communication device 100 includes a transceiver, and the transceiver is configured to send the association signal 510 of each transmission symbol in the vector y to one or more receivers.

[0142] In addition, in another embodiment of the present invention, the first communication 100 for the communication system 500 includes a processor and a memory having computer-readable instructions stored thereon, and the computer-readable instructions, when executed by the processor, cause the processor to perform the following operations: obtain a vector b including M integer-valued information symbols in the set {0, 1, …, q–1}, where q = 2 Q , and Q is a positive integer; obtain an N×M matrix C including symbols in the set {0, 1, …, q–1}, where N is a positive integer and satisfies M≤N; multiply the matrix C by the vector b and then take the modulo q to obtain a vector y including N transmission symbols, where each transmission symbol in the vector y is associated with one of q signals; send the association signal 510 of each transmission symbol in the vector y to one or more receivers.

[0143] Figure 2 shows that it can be in the first communication device 100 (such as Figure 1Flowchart of the corresponding method 200 executed in the first communication device shown. Method 200 includes: obtaining (202) a vector b including M integer-valued information symbols in the set {0, 1, …, q–1}, where q = 2 Q , and Q is a positive integer; Method 200 includes: obtaining (204) an N×M matrix C including symbols in the set {0, 1, …, q–1}, where N is a positive integer and satisfies M≤N. Method 200 includes: multiplying (206) the matrix C by the vector b and then taking the modulo q to obtain a vector y including N transmission symbols, where each transmission symbol in the vector y is associated with one of q signals. Method 200 includes: sending (208) the associated signal 510 of each transmission symbol in the vector y to one or more receivers.

[0144] Figure 3 Shows the second communication device 300 provided by an embodiment of the present invention. In Figure 3 the embodiment shown, the second communication device 300 includes a processor 302, a transceiver 304, and a memory 306. The processor 302 is coupled to the transceiver 304 and the memory 306 through a communication device 308 known in the art. The second communication device 300 also includes an antenna or antenna array 310 coupled to the transceiver 304, which means that the second communication device 300 is configured for wireless communication in a communication system.

[0145] The processor 302 may be referred to as one or more general-purpose CPUs, one or more DSPs, one or more ASICs, one or more FPGAs, one or more programmable logic devices, one or more discrete gates, one or more transistor logic devices, one or more discrete hardware components, and one or more chip sets. The memory 306 may be a read-only memory, RAM, or NVRAM. The transceiver 104 may be a transceiver circuit, a power controller, or an interface providing the ability to communicate with other communication modules or communication devices. The transceiver 304, the memory 306, and / or the processor 302 may be implemented in separate chip sets or in a common chip set.

[0146] In the present disclosure, the second communication device 300 can be used to perform some actions, which can be understood as that the second communication device 300 includes suitable means for performing the actions, such as the processor 302 and the transceiver 304, etc.

[0147] According to an embodiment of the present invention, the second communication device 300 is used to receive N signals 510, where each signal is associated with a symbol in the set {0, 1, …, q–1}, where q = 2 Qand Q is a positive integer. The second communication device 300 is configured to determine M integer-valued information symbols from N associated symbols based on the N×M matrix C or its modular inverse, where the matrix C and its modular inverse include symbols from the set {0, 1, …, q–1}, where N is a positive integer and M ≤ N.

[0148] In addition, in one embodiment of the present invention, the second communication device 300 includes a transceiver configured to receive N signals (510), where each signal is associated with a symbol from the set {0, 1, …, q–1}, where q = 2 Q and Q is a positive integer. The second communication device 300 includes a processor configured to determine M integer-valued information symbols from N associated symbols based on the N×M matrix C or its modular inverse, where the matrix C and its modular inverse include symbols from the set {0, 1, …, q–1}, where N is a positive integer and M ≤ N.

[0149] In addition, in another embodiment of the present invention, the second communication device 300 includes a processor and a memory having computer-readable instructions stored thereon that, when executed by the processor, cause the processor to perform the following operations: receive N signals 510, where each signal is associated with a symbol from the set {0, 1, …, q–1}, where q = 2 Q and Q is a positive integer; determine M integer-valued information symbols from N associated symbols based on the N×M matrix C or its modular inverse, where the matrix C and its modular inverse include symbols from the set {0, 1, …, q–1}, where N is a positive integer and M ≤ N.

[0150] Figure 4 shows a flowchart of a corresponding method 400 that may be performed in the second communication device 300 (such as Figure 3 the second communication device 300 shown). The method 400 includes: receiving (402) N signals 510, where each signal is associated with a symbol from the set {0, 1, …, q–1}, where q = 2 Q and Q is a positive integer. The method 400 includes: determining (404) M integer-valued information symbols from N associated symbols based on the N×M matrix C or its modular inverse, where the matrix C and its modular inverse include symbols from the set {0, 1, …, q–1}, where N is a positive integer and M ≤ N.

[0151] Figure 5The communication system 500 of an embodiment of the present invention is shown. The communication system 500 in the disclosed embodiment includes a first communication device 100 and one or more second communication devices 300 for communicating and operating in the communication system 500. The first communication device 100 may be represented as a transmitter device or simply a transmitter, and the second communication device 300 may be represented as a receiver device or simply a receiver, and sometimes may also be represented as a user. However, the first communication device 100 may also have receiving capabilities, and the second communication device may have transmitting capabilities. In Figure 5 In the non-limiting example shown, the first communication device 100 acts as a network access node (e.g., gNB) and communicates with one or more second communication devices 300 acting as client devices (e.g., UEs). The network access node may be connected to a network (NW) of a communication system such as a core network through a communication interface. However, it should be noted that the opposite situation is also possible, that is, the first communication device 100 is a client device and the second communication device 300 is a network access node. When the communication system is a 3GPP LTE or NR system, communication between the first communication device 100 and the second communication device 300 may be performed in the downlink (DL) and the uplink (UL).

[0152] As described above, the vector b includes M integer-valued information symbols in the set {0, 1, …, q – 1}, where q = 2 Q , and Q is a positive integer. The vector b can be represented as

[0153] b = (b 1 , b 2 , …, b M )′ (1)

[0154] where (.)′ represents transpose, and the symbol b i in the vector b represents which one of the q signals should be sent from the transmitter to the receiver i or a group of receivers i.

[0155] For 1 ≤ i ≤ M, where M ≤ N, the multiplexing code is given by a vector with symbols:

[0156]

[0157] An N × M (M ≤ N) multiplexing code matrix C, where the columns contain the multiplexing codes:

[0158] C = [c (1) , c (2) , …, c (M) (3)

[0159] The rank of C is equal to M, where the rank is determined based on modulo-q addition of vectors under the assumption.

[0160] The integer-valued information symbols in vector b are multiplexed with the multiplexing code matrix C, thereby generating the transmission symbol y through an N×1 vector

[0161] y = Cb (mod q) (4)

[0162] where (mod q) is the modulo-q operator. Thus, a multiplexing scheme is disclosed herein

[0163] In an embodiment of the present invention, for the multiplexing code matrix C, M = N, where t is the smallest positive integer satisfying C t = I (mod q), the communication system 500 can generate at most t–1 matrices according to the following formula

[0164] {C, C 2 , …, C t–1} (5)

[0165] Thus, at most t–1 orthogonal multiplexing code sets can be generated. Each set of orthogonal sets can be used in different cells of the cellular system, but is not limited thereto

[0166] In addition, when vector b includes information symbols for different receivers or users, vector b in an embodiment of the present invention can include S u information symbols for receiver u, such that

[0167]

[0168] where U is the number of receivers, 1 ≤ U ≤ M, and where

[0169]

[0170] According to an embodiment of the present invention, different conditions can be applied, depending on whether N = M or N > M for the matrix C. Some of these conditions are summarized below and will be described in more detail in the following disclosure

[0171] In an embodiment of the present invention, when for the multiplexing code matrix C, M = N, and C and C –1 include integer-valued symbols in the set {0, 1, …, q–1}, the following conditions are satisfied

[0172] C –1 C = I (mod q),

[0173] where C –1 is the modulo inverse of C, I is the identity matrix, and mod q is the modulo-q operator

[0174] In an embodiment of the present invention, when the multiplexing code matrix C is an N×N matrix and the rank is equal to N, where q = 2, the modulo inverse C –1 satisfies at least one of the following:

[0175] C –1 is a matrix in which each row and each column has one element equal to 1;

[0176] C –1 is a matrix in which at least one row has an even Hamming weight;

[0177] C –1 is a matrix in which N–1 rows have an even Hamming weight;

[0178] C –1 is a matrix in which the rows have an odd Hamming weight;

[0179] C –1 is a matrix in which the total Hamming weight is equal to N 2 –N + 1, such that the Hamming weight of N–1 rows is equal to N–1 and the Hamming weight of 1 row is equal to N; and / or

[0180] C –1 is a matrix in which each row has the same odd-valued Hamming weight.

[0181] In an embodiment of the present invention, when the multiplexing code matrix C is an N×N matrix and the rank is equal to N, where Q > 1, the multiplexing code matrix C is a version obtained by permuting any row or column of the matrix C, and the matrix is given as

[0182]

[0183] where c ii is an odd integer in the set {0, 1, …, q–1}, and for at least one i, 1 ≤ i ≤ N, each symbol in the set {0, 1, …, q–1} is associated with a bit label such that the Hamming weight difference between the symbol X and is at most 1.

[0184] In an embodiment of the present invention, when the multiplexing code matrix C is an N×M matrix and the rank is equal to M, where M < N and q = 2, the multiplexing code matrix C satisfies at least one of the following:

[0185] C is obtained by performing any row or column permutation on the matrix and the matrix is given as

[0186]

[0187] Among them, P is an M×M matrix with different rows and columns, where each row and each column contains a non-zero element, and A is an (N–M)×M matrix;

[0188] The rank of the product of C′ and C is equal to M, where C′ is the transpose of C; and / or

[0189] C includes orthogonal column vectors with odd Hamming weights.

[0190] In addition, other embodiments of the present invention relate to signal aspects, time-frequency resources for multiplexing signal transmission, and the application of multiplexed signals in different implementation manners and scenarios.

[0191] Therefore, in the embodiments of the present invention, the associated signal 510 is at least one of the following:

[0192] On-off keying signal;

[0193] Frequency shift keying signal;

[0194] Orthogonal frequency division multiplexing signal; or

[0195] Discrete Fourier transform precoded orthogonal frequency division multiplexing signal.

[0196] For the transmission of the associated signal 510, the first communication device 100 may transmit the associated signal 510 corresponding to the symbol y on the time-frequency resource k. k In other words, the component k (1≤k≤N) in the vector y is associated with the time-frequency resource k. The time-frequency resource may represent, for example, a time slot, an OFDM symbol, a subcarrier, a set of subcarriers, where a signal can be transmitted. In addition, for any positive integer value of n, N = 12n or N = 14n.

[0197] In addition, in the embodiments of the present invention, the associated signal 510 can be used for many different applications, which means that at least one information symbol represents at least one of the following:

[0198] An indicator for waking up one or a group of receivers;

[0199] The identity of one or a group of receivers; or

[0200] Paging information associated with one or a group of receivers.

[0201] Figure 6 Shows a block diagram of a part of the first communication device 100 acting as a transmitter provided by the embodiments of the present invention. The block diagram shows the vectorization block 120 connected to the multiplexing block 130.

[0202] Consider that the symbol set includes q symbols {0, 1, …, q–1}, where q = 2 Q, where Q is a positive integer, and the associated N-dimensional vector space Perform modulo-q on addition and multiplication. Assume that the symbols representing the signals of M different receivers are received by the vectorization block 120 and arranged into a vector b, where the symbols are given by the vector,

[0203] b = (b 1 , b 2 , …, b M )′ (8)

[0204] where (.)′ represents the transpose. The symbol b i represents which one of the q associated signals 510 sent from the transmitter to the receiver i. The receiver i can be a single user or represent a group of users. For 1 ≤ i ≤ M, M ≤ N, define the multiplexing code, which is given by the vector:

[0205]

[0206] The condition M ≤ N means that orthogonal multiplexing is possible, that is, the vector b can be perfectly detected. In addition, define the N×M multiplexing code matrix, where the columns contain the multiplexing codes:

[0207] C = [c (1) , c (2) , …, c (M) (10)

[0208] The transmitter multiplexes the symbols in the multiplexing block 130 by generating a linear combination of the components in the vector b, and generates the transmitted symbol output by the N×1 vector

[0209] y = Cb (mod q) (11)

[0210] where (mod q) represents the modulo-q operator. Therefore, the values in y come from the set {0, 1, …, q–1}. Therefore, q signals can be used to multiplex M information symbols.

[0211] The components in y can correspond to time-frequency resources, such as N time slots or frequencies, where each time slot or frequency k transmits one of the q signals (FSK frequency, PPM pulse, etc.), which is determined by the entry y k . Therefore, according to (11), multiplexing is performed in the symbol domain using q signals, and there is no superposition of any q signals.

[0212] As mentioned before, the vector b can be generalized to represent sending S symbols to U receivers (i.e., users or a group of users), where M = SU and 1 ≤ U ≤ M, such that:

[0213] b = (b 11 , b12 ,…,b 1S ,b 21 ,b 22 ,…,b 2S ,…,b U1 ,b U2 ,…,b US )′ (12)

[0214] In this case, the signal will transmit information corresponding to S·log 2 q bits to each receiver. A further generalization is to send S u symbols to user u, where

[0215]

[0216] and

[0217]

[0218] The information symbol can represent an indicator for waking up one receiver or a group of receivers. For example, if U = M and q = 2, the information symbol b i can indicate whether receiver i or receivers i in the group should be woken up. In addition, in a cellular network, a network identifier is assigned to a receiver (i.e., UE), such as a radio network temporary identifier (RNTI). Therefore, the information symbol can represent the identity of one receiver or a group of receivers. If the detected identity is the same as the identity of one receiver or a group of receivers, these receivers should be woken up. In addition, the information symbol can relate to information associated with the monitoring of a paging channel for one receiver or a group of receivers. This information can include paging occasions or other information required to receive the paging channel.

[0219] Therefore, an object of the present invention is to construct C such that, assuming the receiver knows C, the error probability of detecting b is minimized. For example, in the NR WUS scenario, if q = 2, misdetecting "0" as "1" means that the UE will perform an unnecessary wake-up, while misdetecting "1" as "0" means that the UE will not be woken up when it should be.

[0220] Figure 7A block diagram showing a part of a second communication device 300 acting as a receiver provided by an embodiment of the present invention is shown. The block diagram shows a signal detector 320 connected to a demultiplexing block 330. The signal detector 320 is used to receive radio signals and generate N outputs fed to the demultiplexing block 330, where each output represents which one of the q detected signals. In an embodiment of the present invention, the signal detector 320 may include non-coherent detection. The demultiplexing block 330 is used to detect information symbols sent for the receiver.

[0221] For the case M = N, well-known matrix properties imply the following equivalent statements:

[0222] i. The rank of C is N.

[0223] ii. There exists an inverse C –1 , such that C –1 C = CC –1 = I, where I is the identity matrix.

[0224] iii. The rank of C –1 is N.

[0225] iv. There exists a unique solution to y = Cb, given by b = C –1 y.

[0226] When the matrix elements are constrained to come from a set of q symbols, these properties also hold, but it should be noted that all calculations should be taken modulo q, and the matrix C –1 is called the matrix modulo inverse. When calculating the rank, all arithmetic operations should be taken modulo q. Therefore, condition (i.) is equivalent to the columns (or rows) of C being linearly independent in . Thus, for orthogonal multiplexing, it is required that:

[0227]

[0228] Consider transmitting an associated signal 510 corresponding to the transmission symbols in the vector y over the channel, and representing the received vector r = (r 1 , r 2 , …, r N )′ as r i ∈ {0, 1, …, q – 1}, and representing the error vector e = (e 1 , e 2 , …, e N )′ as e i ∈ {0, 1, …, q – 1}, such that

[0229] r = Cb + e (mod q) (15)

[0230] Based on this, demultiplexing can be performed linearly as:

[0231]

[0232] For example, r can be the output of a non-coherent detector, which, if q = 2, has components '0' or '1' indicating whether the energy of the WUS is higher than a predefined detection threshold, which is set to achieve a certain false alarm rate. It can be assumed that the matrix C is known to all receivers, and the i-th receiver or one of the i-th group of receivers extracts the i-th element in To extract the i-th element in –1 r is multiplied by the i-th row of C –1 Thus, in one example, the i-th receiver only needs to perform the multiplication with the i-th row of C

[0233] Construction of multiplexing codes when N = M

[0234] Based on mathematical group theory, the general linear group N is defined as the set of N×N invertible matrices, which, over the symbol set {0, 1, …, q–1}, is denoted as GL(N,q). The order of GL(N,q) (i.e., the number of matrices in the group) has been shown to be given by the following formula and the order of the elements of the group

[0235]

[0236] That is, if the matrix C is the smallest integer satisfying the following condition, then the matrix C has order t:

[0237] C t = I (18)

[0238] It is further known that all elements of a finite group have a finite order t, and t is a divisor of O N,q The order t can be determined by finding the minimal polynomial of the matrix C, i.e., the lowest-degree polynomial g(X) over the Galois field GF(q) that satisfies

[0239] g(C) = 0 (19)

[0240] where 0 is the zero matrix. The minimal polynomial will divide

[0241] g(X) = X t – 1 (20)

[0242] Based on this, t can be found. From (18), it can be derived that:

[0243] C –1 = C t–1 (21)

[0244] Thus, in the embodiments of the present invention, for any matrix C of order t, t - 1 sets of orthogonal multiplexing codes can be generated as:

[0245] {C, C 2 , …, C t–1}(22)

[0246] For example, different sets of orthogonal multiplexing codes can be used in different cells of the communication system 500. The exponent k of C k can be a function of the cell identity (ID) and / or can be configured by higher layer signaling.

[0247] Generate the multiplexing code matrix

[0248] Error probability depends on e and the i-th row of C –1 and can be constructed according to the desired characteristics as long as the rank of C –1 is equal to N, because this means that the rank of C is also equal to N. The best construction of C –1 depends on the assumption of e, i.e., the error model.

[0249] Example: Consider binary signaling (q = 2) and N = M = 3, with two different channels; one is an uncorrelated binary symmetric channel (BSC) (BSCρ = 0) and one is a fully correlated binary symmetric channel (BSCρ = 1). If the receivers are close to each other and experience similar propagation channels, it may be a fully correlated binary symmetric channel. For BSCρ = 0, the errors are independent and characterized by:

[0250] Pr[e i = 1] = p 0

[0251] = 1 – Pr[e i = 0] (23)

[0252] For BSCρ = 1, the errors are fully correlated, e 1 = e 2 = e 3 and are characterized by:

[0253] Pr[e = 1] = p 1

[0254] = 1 – Pr[e = 0] (24)

[0255] where 0 and 1 are vectors consisting of 0s and 1s respectively. Additionally, assume

[0256]

[0257] Has a modular inverse:

[0258]

[0259] By using (16), it can be obtained that:

[0260]

[0261] Then, the error cases can be identified from (27), as shown in Table 1.

[0262] Table 1: Examples of BSC channels and the corresponding probabilities of the corresponding error cases.

[0263]

[0264] For BSC ρ = 0, after some simplifications, through the verification of Table 1, the following results are obtained

[0265]

[0266] And it can be shown (assuming p 0 ≤ 0.5):

[0267]

[0268] Therefore, by comparing (31) and (27), it can be concluded that the smaller the Hamming weight of the rows in C –1 , the smaller the bit error rate (BER), and for the rows with Hamming weight equal to 1, the BER is the smallest. The Hamming weight w(x) of a matrix or vector x is defined as the number of positive elements in x. For BSC ρ = 1, it can be observed that:

[0269]

[0270] Since the Hamming weight of the second row of C –1 is equal to 2, then e 1 + e 3 = 0. Based on these observations, the following Construction 1 is given.

[0271]

[0272] For Construction 1, it can be clearly shown that the columns of C –1 are orthogonal, so they are linearly independent. Therefore, the rank of C –1 is equal to N, and its inverse matrix is (C –1 ) –1 = C.

[0273] In addition, for C –1Rows with even Hamming weight in, for BSC ρ = 1, the error probability is Because if the number of terms e i is even, then the sum is ∑ i e i = 0. Unfortunately, when each row has an even Hamming weight, it is impossible to construct a C with rank equal to N –1 . This forms Construction 2.

[0274]

[0275] However, it is known that the maximum size of a set of binary vectors of length N with a minimum Hamming distance equal to 2 is equal to 2 N–1 . Therefore, a set of N – 1 vectors with Hamming weight equal to 2 can be found. For the purpose of constructing C –1 , it still needs to be shown that a set can be chosen such that the vectors are linearly independent. An example of N – 1 rows with even weights and one row with an odd weight proves to be

[0276]

[0277] where it can be directly verified that the columns are linearly independent. Therefore, the following construction is given.

[0278]

[0279] In addition, for BSC ρ = 0, considering the example in (16), it is obvious that if the Hamming weight w(e) = 2, then

[0280]

[0281] Therefore, as long as there are an even number of errors, the rows in C –1 with odd Hamming weight will be able to provide perfect demultiplexing. Therefore, the following Construction 4 is given.

[0282]

[0283] For example, N is even and all rows have Hamming weight w = N – 1. For example, for N = 4, the rows of the following

[0284]

[0285] are linearly independent and the rank of C –1 is equal to N.

[0286] If the receiver cannot determine which of the q symbols has been received, the receive diversity can be increased by maximizing the Hamming weight of the rows in C –1 , which is given by Construction 5 below.

[0287]

[0288] For N = 4, the example is given by

[0289]

[0290] where it can be directly verified that the rows are linearly independent.

[0291] To ensure that each symbol has the same error probability, the Hamming weight of each row in C –1 must be constant. For Construction 1, this is clearly true, for which the Hamming weight of the rows is equal to 1. However, the Hamming weight can be chosen as other odd values, which is given by Construction 6 below.

[0292]

[0293] An example is to let C –1 be a circulant matrix, which is determined as follows:

[0294] Let the first row include the vector v′ 1 with an odd Hamming weight w(v′ 1 ).

[0295] For 2 ≤ i ≤ N, let v′ i include row i, where v′ i is v′ 1 circularly shifted by i – 1 steps.

[0296] It has been shown that there does not exist a circulant matrix with rank equal to N and an even Hamming weight w(v′ 1 ). In addition, it has been shown that when N is a power of 2, or when N is a prime number with a primitive root 2, any vector v′ 1 with an odd Hamming weight can be used; a prime number s with a primitive root 2 such that 2 s–1 ≡ 1 (mod s), where s ∈ {3, 5, 11, 13, 19, 29, 37,...}. Here, let

[0297]

[0298] have an odd w (w < N), which makes C –1 form a Toeplitz matrix. For N = 7 and w = 3, the example is as follows:

[0299]

[0300] This form can provide flexibility for receiver implementation because multiplying r by the Toeplitz matrix C –1 can be equivalently represented as multiplying r by v1 The circular convolution between. Table 2 shows in which cases the parameters N (excluding the cases where N is a power of 2 or N is a prime number with a primitive root 2) and w will result in ToeplitzC –1 having a rank equal to N.

[0301] Table 2: For different lengths N and Hamming weights w, the cases where the rank of ToeplitzC –1 is equal to N (marked as yes) and the cases where the rank of construction (31) is not equal to N (marked as no).

[0302]

[0303]

[0304] Construction of the multiplexing code when M < N

[0305] (9) The set of vectors y will include linear combinations of the columns of C. Therefore, in order to be able to demultiplex M symbols b uniquely i (1 ≤ i ≤ M), the rank of C must be equal to M. Therefore, the following condition 2 is adopted, where condition 2 is more general than condition 1.

[0306]

[0307] Let P be an M×M matrix whose elements in {0, 1, …, q–1} have distinct rows and columns, where each row and each column contains a non-zero element. In addition, let A be an (N–M)×M matrix with elements and form an N×M matrix:

[0308]

[0309] Due to the properties of P, the columns of are linearly independent, so the rank of is equal to M. In addition, any row or column permutation of will still make the rank of equal to M. This is given by the following construction 7.

[0310]

[0311] Linear demultiplexing

[0312] If M < N, by definition there is no C –1 , but linear demultiplexing can be performed according to several embodiments.

[0313] Demultiplexing using the pseudo-inverse

[0314] When considering all real numbers (i.e., when computing without using the modulo-q operator), it can be shown that if C is N×M and has rank equal to M, then the M×M matrix C′C has rank equal to M. However, when the symbol set is constrained to {0, 1, …, q–1}, this property is not valid. Therefore, the following Construction 8 is adopted to achieve this property.

[0315]

[0316] Appendix B contains results on the Hamming weight and minimum distance of such binary multiplexing codes. For Construction 8, linear demultiplexing can be performed as:

[0317]

[0318] For N = 7 and M = 3, an example of Construction 8 is

[0319]

[0320] where

[0321]

[0322] which has rank equal to 3.

[0323] Another example of Construction 8 is that C consists of orthogonal column vectors with odd Hamming weight. In this case, it can be shown that I′C = C (mod q), which has rank equal to M.

[0324] Demultiplexing using the pseudo-inverse in the real number field and rounding

[0325] In general, for the matrix C + =(C′C) –1 C′ is called the pseudo-inverse of C, and b * =C + r is the solution of the least squares problem

[0326]

[0327] where, ‖.‖ 2 is the Euclidean norm. However, if C is computed by taking modulo-q, and the symbols are constrained to be in the set {0, 1, …, q–1}, then b + is not the solution of (43). However, for multiplexing codes that do not necessarily satisfy Structure 8, linear demultiplexing can also be performed. For example, assume * and C and C + are computed in the real number field (i.e., without modulo operation), then the estimate is

[0328]

[0329] Among them, the rounding function round(x,q) rounds each element of x to the nearest integer in {0,1,…,q–1}. The advantage of doing this is that (44) and (45) are valid for any C of rank M.

[0330] Generate an invertible matrix at the receiver

[0331] In addition, a method that is valid for any C of rank M is that the receiver generates an intermediate inverse as follows:

[0332] Append N–M columns to C to create an N×N matrix C TX , so that its rank is equal to N in

[0333] Determine in and set to form the first M rows;

[0334] Calculate in to demultiplex M symbols.

[0335] Theorem 1 in Appendix A guarantees that columns can be appended to linearly independent C.

[0336] Nonlinear demultiplexing

[0337] When M < N, there is redundancy, that is, more resources are used than the number of multiplexed signals, which can be used as coding gain. For example, (9) can be rewritten as y′ = b′C′, and it is identified that C′ = G is the generator matrix of a linear block code. Therefore, any block code that satisfies condition 2 of C = G′ can be used with the generator matrix G. Therefore, for any G of a linear block code, it can be shown that there exists a parity-check matrix H, which has the property that its rows are linearly independent. Therefore, C = H′ can be set for any linear block code. For example, the (N,M,d) = (7,4,3) Hamming code with minimum distance d is generated by

[0338]

[0339] and has a parity-check matrix

[0340]

[0341] Use the (N,M,d) = (7,3,4) generated code. Demultiplexing can be performed by any existing decoding algorithm (including non-linear algorithms) of the block code. It should be noted that for C = G′, it can be obtained that

[0342]

[0343] Its rank is equal to 1, and if C = H′,

[0344]

[0345] its rank is equal to 0. Therefore, the matrix (C′C) –1 C′ does not exist, and neither G nor H satisfies Construction 8.

[0346] Non-binary multiplexing code q > 2

[0347] Consider the case of q = 2 Q (for some integer Q > 1). This means that the bits in b can be processed in blocks of Q = log 2 q bits. If c is odd, then gcd(c, q) = 1, where gcd(x, y) is the greatest common divisor of x and y. It means that there exists a unique inverse c –1 , such that cc –1 ≡ 1 (mod q). Furthermore, this means that for x = 0, 1, …, q – 1, the product xc (mod q) produces q different values. Therefore, if c is odd, the addition in (9) can be taken modulo q. For a diagonal matrix, it can be concluded that:

[0348]

[0349] Therefore, any row or column permutation of C in (39) implies the existence of a modular inverse C –1 .

[0350]

[0351] Evaluation results - binary case (q = 2)

[0352] Consider the following example of a multiplexing code

[0353]

[0354] Using (16), the bit error probability is given by:

[0355]

[0356] Assume a BSC with error probability p and calculate the probabilities of all error vectors, which become:

[0357]

[0358]

[0359] The Gilbert - Elliot channel model is intended to capture the correlated behavior of the channel and is a two - state Markov model. A Binary Symmetric Channel (BSC) with error probability p g is used in the good state (G), and a BSC with error probability p b is used in the bad state (B). The transition probability from G to B is set to p gb = 0.1, and the transition probability from B to G is set to p bg = 0.3. The steady - state probabilities can be determined as

[0360]

[0361] and

[0362]

[0363] This means that the average bit - error probability of bit i becomes

[0364]

[0365] And insert expressions (56) to (59) into (62). The (7,4,3) Hamming code of (46) is also evaluated. The bit - error probability using maximum - likelihood (ML) detection on a BSC exists in a closed - form and has been shown to be given by

[0366]

[0367] where the Hamming weight distribution of the codeword is

[0368] A 0 = 1, A 3 = 7, A 4 = 7, A 7 = 1 (64)

[0369] and has been derived as

[0370] P(p,i)= ip i–1 (1 – p) N–i+1 + p i (1 – p) N–i +(N – i)p i+1 (1 – p) N–i–1 (65)

[0371] can be combined and inserted into (62). ML detection minimizes the codeword error probability but not necessarily the BER, so the maximum a posteriori (MAP) decoding algorithm must be used.

[0372] At Figure 8In it, the error probability is plotted as a function of p g (for p b = 0.5). Monte-Carlo simulations were also performed (results marked with 'x'), which are in perfect agreement with the derived expressions. Based on (52) to (55), it can be understood that the error probability increases with the increase in the Hamming weight of the rows of C –1 , that is The results of the Hamming code are also included in the figure, thus showing that the coding gain results in the lowest BER, up to p g ≈ 0.2. The cost of this is to use 7 resources to multiplex 4 signals. For larger p b , Figure 9 shows the multiplexing codes that produce the rows with even Hamming weights in C –1 (i.e., the 2nd and 4th rows) become relatively better at higher p b and may even be better than the Hamming code. In addition, it is also possible for the BER to be greater than 0.5.

[0373] To evaluate different demultiplexing algorithms, the following matrix is used for N = 7 and M = 4

[0374]

[0375] This will result in the pseudo-inverse:

[0376]

[0377] For the method of generating an invertible matrix at the receiver, 4 columns are added to C so that its rank is equal to 7.

[0378]

[0379] Since two rows in (67) have a Hamming weight equal to 2, the BER will be greater than the BER of (68) because all its rows have a Hamming weight equal to 1, which can be confirmed from Figure 9 and Figure 9 compares the average BER of different demultiplexing algorithms; ML on (66), matrix inverse (68), pseudo-inverse calculated on the symbol set {0, 1,..., q - 1} (67), and pseudo-inverse rounded to an integer. ML clearly performs better than the others.

[0380] Bit labeling - non-binary case q > 2

[0381] Consider the case of Q > 1 and process Q = log 2 q bits from each user, which are arranged in a vector as

[0382] b = (b 11 , b 12 , …, b1Q , b 21 , b 22 , …, b 2Q , …, b U1 , b U2 , …, b UQ )′ (69)

[0383] where M = UQ and

[0384]

[0385] represents the j-th bit of user i. q = 2 Q symbols can be signaled by a single transmission of a q-ary waveform (e.g., q-FSK or OOK with q pulses). Alternatively, q symbols can be signaled by Q transmissions of a binary waveform (e.g., 2-FSK or OOK with 2 pulses). Let the function f map a block of Q bits to a label L ∈ {0, 1, …, q – 1}, and the inverse function f –1 provides the bit representation in the label. Additionally, a binary error vector e 2 of length M is mapped to a q-ary error vector e q of length U, as shown in Figure 11 for the transmitter-receiver chain involving the first communication device 100 and the second communication device 300. In Figure 11 , the binary vector b is converted to a q-ary vector b q . Multiplexing and demultiplexing are performed by the q-ary matrices C and C –1 respectively. The entries in the vector b q can indicate which one of the q signals designated for the receiver.

[0386] An error occurs when the following equation holds

[0387] f –1 (b q + C –1 e q ) ≠ b (71)

[0388] And the function f is crucial in affecting the BER, as shown in the following example.

[0389] Example: Let M = N = 4, q = 16, and the following equation:

[0390]

[0391] will determine the error probability of the bits (b 31 , b 32 , b 33 , b 34 ), so C –1The third row of, and multiply e q by the third element of . Assume that the BSC and the mapping are defined as in Table 3, where e q = f(e 2 ), and the corresponding probabilities of the error vectors are shown.

[0392] Table 3: Examples of the function f and the corresponding probabilities.

[0393]

[0394]

[0395] Consider the special case where b q = 0, i.e., (b 31 , b 32 , b 33 , b 34 ) = (0, 0, 0, 0), then (71) simplifies and

[0396]

[0397] The error probability is

[0398]

[0399] From Table 3, it can be identified that:

[0400] P 1 = Pr[e q = 3, 4, 8, 9, 11, 12, 13, 15] = p(1 – p) 3 + 3p 2 (1 – p) 2 + 3p 3 (1 – p) + p 4 (75)

[0401] P 2 = Pr[e q = 1, 2, 3, 4, 6, 7, 9, 11] = 2p(1 – p) 3 + 3p 2 (1 – p) 2 + 3p 3 (1 – p) (76)

[0402] P 3 = Pr[e q = 1, 3, 5, 6, 9, 12, 13, 14] = 2p(1 – p) 3 + 4p 2 (1 – p) 2 + 2p 3 (1 – p) (77)

[0403] P 4 = Pr[e q = 1, 5, 7, 9, 10, 11, 13, 15] = 3p 2 (1–p) 2 + 4p 3 (1–p) + p 4 (78)

[0404] These are plotted in Figure 12 where it should be noted that P 4 < p, that is, even without any coding gain, it is possible to achieve a lower bit error rate than that given by the BSC channel because N = M.

[0405] According to Table 4, the optimized bit - label mapping is compared with the natural mapping and the Gray mapping.

[0406] Table 4: Mapping of bit - labels to integers for the optimized mapping, natural mapping, and Gray mapping.

[0407]

[0408]

[0409] For Figure 13 the results, the vector b q is randomly generated over GF(q), and the figure contains the minimum BER maximum BER and average BER It can be seen that the Gray mapping has no significant performance gain, while the optimized mapping provides the lowest maximum error probability among all the mappings.

[0410] It can be observed from Table 3 that vectors with large Hamming weights affect more bits. Therefore, the optimized bit - label assignment is to assign labels to states with large Hamming weights such that the corresponding probabilities become smaller. For example, is associated with the probability of state 9, i.e., p 3 (1–p). Assuming C is a diagonal matrix, the process can be summarized in the following steps:

[0411] 1. Select an index i ∈ {1,…,M}.

[0412] 2. Let X be the state that has not been assigned a label and whose Hamming weight is not less than the Hamming weight of any remaining unassigned state.

[0413] 3. Assign a label to the state X ∈ {0, 1,…,q–1}.

[0414] 4. Determine the corresponding tags And assign Y to the unassigned state with the maximum possible Hamming weight.

[0415] 5. If there are unassigned states, return to step 2.

[0416] This means that the Hamming weight difference between the bit tags of state X and is at most 1.

[0417]

[0418] Parameter selection

[0419] If the disclosed scheme is applied to a 3GPP NR system with a WUS mechanism, the number N of time-frequency resources should preferably be adapted to the existing time-domain and frequency-domain structures of the system. For example, if the WUS waveform is FSK, the subcarriers of the OFDM waveform can be used as frequencies. A resource block consists of 12 subcarriers. Therefore, if N = 12k, k = 1, 2, …, i.e., a multiple of 12, it is efficient.

[0420] If the WUS waveform is OOK, one OFDM symbol can be used as the time-domain resource for the OOK symbol. The NR time-domain structure includes time slots, and the length of a time slot depends on the subcarrier spacing. Each time slot contains 14 OFDM symbols. Therefore, if N = 14k, k = 1, 2, …, i.e., a multiple of 14, it is efficient.

[0421] For the case of N > M, the matrix C can be constructed from the generator matrix or parity-check matrix of a suitable block code of length N. An example is the binary Golay code with parameters (N, M, d) = (24, 12, 8). Another example is the Hadamard code with N = 12k, which is a non-linear code consisting of 2N codewords and a minimum distance d = N / 2. Therefore, such codes can be used to multiplex WUS, where is the floor operator. Various operations can be performed on the (N, M) code to obtain the desired length, i.e., rate matching:

[0422] Puncturing: By deleting p encoded bits, the (N, M) code becomes an (N – p, M) code.

[0423] Shortening: By deleting p message bits, the (N, M) code becomes an (N – p, M – p) code.

[0424] Extension: By adding additional p redundant bits, the (N, M) code becomes an (N + p, M) code.

[0425] Lengthening: By adding additional p message bits, the (N, M) code becomes an (N + p, M + p) code.

[0426] Specifically, 3GPP NR includes polar codes and Reed-Muller codes, which are linear block codes that can be used to generate C.

[0427] The network access node in this document may also be referred to as a wireless network access node, an access network access node, an access point (AP), or a base station (BS). For example, a radio base station (RBS) may be called a transmitter, "gNB", "gNodeB", "eNB", "eNodeB", "NodeB", or "B node" in some networks, depending on the standards, technologies, and terms used. Based on the transmission power and cell size, the wireless network access node may have different categories or types, such as a macro eNodeB, a home eNodeB, or a pico base station. The wireless network access node may be a station, which is any device that includes an IEEE 802.11-compliant media access control (MAC) and physical layer (PHY) interface connected to a wireless medium (WM). The wireless network access node may be used for communication in 3GPP-related long term evolution (LTE), LTE-Advanced, fifth-generation (5G) wireless systems (such as new radio (NR) and its evolution), as well as in IEEE-related Wi-Fi, worldwide interoperability for microwave access (WiMAX), and their evolution.

[0428] The client device in this document can be represented as a user equipment (UE / user device), a mobile station, an internet of things (IoT) device, a sensor device, a wireless terminal, and / or a mobile terminal, capable of performing wireless communication in a wireless communication system (sometimes also referred to as a cellular wireless system). The UE can also be referred to as a mobile phone with wireless capabilities, a cellular phone, a computer tablet, or a laptop computer. In this context, the UE can be, for example, a portable, pocket-sized, handheld, computer-constituted, or vehicle-mounted mobile device, capable of transmitting voice and / or data to another communication entity (such as another receiver or server) through a radio access network (RAN). The UE can also be a station, which is any device that includes an IEEE 802.11-compliant MAC and PHY interface connected to the WM. The UE can be used for communication in 3GPP-related LTE, advanced LTE, 5G wireless systems (such as NR) and their evolutions, as well as in IEEE-related Wi-Fi, WiMAX, and their evolutions.

[0429] In addition, any method provided by the embodiments of the present invention can be implemented in a computer program having an encoding and decoding module. When the computer program is run by a processing device, it causes the processing device to execute the method steps. The computer program is included in a computer-readable medium of a computer program product. The computer-readable medium can basically include any memory, such as the ROM, PROM, EPROM, flash memory, EEPROM, or hard disk drive mentioned above.

[0430] Furthermore, it should be recognized that the first communication device 100 and the second communication device 300 include the necessary communication capabilities in the form of functions, modules, units, elements, etc. for executing and implementing the embodiments of the present invention. Examples of other such modules, units, elements, and functions are: processors, memories, buffers, control logics, encoders, decoders, rate matchers, de-rate matchers, mapping units, multipliers, decision units, selection units, switches, interleavers, de-interleavers, modulators, demodulators, input terminals, output terminals, antennas, amplifiers, receiving units, transmitting units, DSPs, TCM encoders, TCM decoders, power supply units, power feeders, communication interfaces, communication protocols, etc., which are appropriately arranged together to execute the solution.

[0431] Thus, one or more processors of the first communication device 100 and the second communication device 300 may include, for example, one or more instances of a CPU, a processing unit, a processing circuit, a processor, an ASIC, a microprocessor, or other processing logic that can interpret and execute instructions. The expression "processor" may thus represent a processing circuitry system including a plurality of processing circuits, the plurality of processing circuits being, for example, any, some, or all of the above-listed items. The processing circuitry may also perform data processing functions for input, output, and processing of data, the data processing functions including data buffering and device control functions, such as call processing control, user interface control, and the like.

[0432] Finally, it should be understood that the present invention is not limited to the above-described embodiments, but also relates to and incorporates all embodiments within the scope of the appended independent claims.

[0433] Appendix A

[0434] Condition 1 makes it necessary to find a set of linearly independent vectors in F N (q). For the binary case, the following theorem (proved in Appendix A) gives a sufficient condition for the size of the candidate set of vectors to be selected. Thus, how to generate a set of linearly independent binary vectors will be described.

[0435] Theorem 1: Define a candidate set S consisting of any but distinct N-dimensional vectors over F N (2), where the set size is |S| ≥ 2 N–1 , then N linearly independent vectors can be selected from S.

[0436] This theorem describes a sufficient condition because if S is not arbitrary, a set of linearly independent vectors can be found even when |S| < 2 N–1 . For example, if the candidate set consists of N orthogonal unit vectors, then they are also linearly independent.

[0437] Proof of Theorem 1: Define the empty set candidate set S 0 and process according to the following steps.

[0438] Step 1: Take the vector v 1 ∈ S 0 , define the set Q 1 = Q 0 ∪ v 1 and S 1 = S 0 \ v 1 . Thus, |Q 1 | = 1 and |S 1 | = |S 0 | – 1.

[0439] Step 2: Take vector v 2 ∈ S 1 , and define set Q 2 = Q 1 ∪ v 2 and S 2 = S 1 \ v 2 . Furthermore, if v 1 + v 2 ∈ S 1 , then S 1 = S 0 \(v 1 + v 2 ). Thus, |Q 2 | = 2 and |S 2 | ≥ |S 1 | – 1 – 1 = |S 0 | – 3.

[0440] Step 3: Take vector v 3 ∈ S 2 , and define set Q 3 = Q 2 ∪ v 2 and S 3 = S 2 \ v 3 . Furthermore,

[0441] if v 3 + v 1 ∈ S 2 , then S 2 = S 2 \(v 3 + v 1 ).

[0442] if v 3 + v 2 ∈ S 2 , then S 2 = S 2 \(v 3 + v 2 ).

[0443] if v 3 + v 1 + v 2 ∈ S 2 , then S 2 = S 2 \(v 3 + v 1 + v 2 ).

[0444] Thus, |Q 3 | = 3 and |S 3 | ≥ |S2 |–1–3=|S 0 |–7。

[0445] ……

[0446] Step p: Take vector v p ∈S p–1 , define set Q p =Q p–1 ∪v p and S p =S p–1 \v p 。

[0447] In addition, for each linear combination where α i ∈GF(2), if then

[0448] Therefore, |Q p |=p and

[0449] By recursion, for p=N–1, it is required that |S N–1 |≥1, which means |S 0 |≥2 N–1 。

[0450] Appendix B

[0451] Table 5 contains the minimum Hamming distance d min of all codewords of the multiplexing code generated by C of size N×M –1 and the Hamming weight w of (C′C) min C′. These matrices C are obtained by exhaustive search. A large d

[0452] Table 5: Minimum Hamming distance d min of the multiplexing code generated by C –1 and the Hamming weight w of (C′C)

[0453]

Claims

1. A first communication device (100) for a communication system (500), the first communication device (100) being configured to: Obtain a vector b comprising M integer-valued information symbols from the set {0, 1, …, q–1}, wherein, q = 2 Q , and Q is a positive integer; Obtain an N×M matrix C comprising symbols from the set {0, 1, …, q–1}, where N is a positive integer and M ≤ N; Multiply the matrix C with the vector b and then take the modulo q to obtain a vector y comprising N transmission symbols, wherein each transmission symbol in the vector y is associated with one of q signals; Send the associated signal (510) of each transmission symbol in the vector y to one or more receivers.

2. The first communication device (100) according to claim 1, wherein, Component k in the vector y is associated with time-frequency resource k, where the component k satisfies 1 ≤ k ≤ N.

3. The first communication device (100) according to claim 1 or 2, wherein, For any positive integer value of n, N = 12n, or N = 14n.

4. The first communication device (100) according to any one of the above claims, wherein, The vector b comprises information symbols for different receivers.

5. The first communication device (100) according to claim 4, wherein, The vector b includes S u information symbols for the receiver u, such that where U is the number of receivers and 1 ≤ U ≤ M.

6. The first communication device (100) according to any one of claims 1 to 5, wherein, The associated signal (510) is any one of the following: On-off keying signal; Frequency shift keying signal; Orthogonal frequency division multiplexing signal; or Discrete Fourier transform precoded orthogonal frequency division multiplexing signal.

7. The first communication device (100) according to any one of the above claims, wherein, At least one information symbol represents any one of the following: An indicator for waking up one or a group of receivers; The identity of one or a group of receivers; or Paging information associated with one or a group of receivers.

8. The first communication device (100) according to any one of the above claims, wherein, M = N, and C and C –1 include integer value symbols in the set {0, 1, …, q–1}, and satisfy C –1 C = I (mod q), where C –1 is the modular inverse of C, I is the identity matrix, and mod q is the modulo-q operator.

9. The first communication device (100) according to any one of claims 1 to 8, wherein, C is an N×N matrix and has a rank equal to N, where q = 2, and C –1 satisfies at least one of the following: C –1 is a matrix in which each row and each column has one element equal to 1; C –1 is a matrix in which at least one row has an even Hamming weight; C –1 is a matrix in which N–1 rows have an even Hamming weight; C –1 is a matrix in which the rows have odd Hamming weights; C –1 is a matrix whose total Hamming weight equals N 2 –N + 1 such that the Hamming weight of N–1 rows equals N–1 and the Hamming weight of 1 row equals N; and / or C –1 is a matrix in which each row has the same odd-valued Hamming weight.

10. The first communication device (100) according to any one of claims 1 to 8, wherein, C is an N×N matrix and has a rank equal to N, where Q > 1, and C is a version obtained by permuting any row or column of the matrix and the matrix is given as where c ii is an odd integer in the set {0, 1, …, q–1}, and for at least one i, 1 ≤ i ≤ N, each symbol in the set {0, 1, …, q–1} is associated with a bit label such that the Hamming weight difference between the bit label of symbol X and is at most 1.

11. The first communication device (100) according to any one of claims 1 to 8, wherein, M = N, where t is the smallest positive integer such that C t = I (mod q), and up to t–1 matrices are generated for the communication system (500) as follows: {C, C 2 , …, C t–1}.

12. The first communication device (100) according to any one of claims 1 to 8, wherein, C is an N×M matrix and its rank is equal to M, where M < N, q = 2, and C satisfies at least one of the following: C is obtained by performing any row or column permutation on the matrix and the matrix is given as where P is an M×M matrix with different rows and columns, and each row and each column contains a non-zero element, and A is an (N–M)×M matrix; The rank of the product of C′ and C is equal to M, where C′ is the transpose of C; and / or C comprises orthogonal column vectors with odd Hamming weights.

13. A second communication device (300) for a communication system (500), the second communication device (300) being configured to: Receive N signals (510), wherein, Each signal is associated with a symbol in the set {0, 1, …, q–1}, where q = 2 Q , and Q is a positive integer; determine M integer-valued information symbols from N correlated symbols based on the N×M matrix C or the modulo inverse of the matrix C, wherein the matrix C and the modulo inverse of the matrix C include symbols from the set {0, 1, …, q–1}, wherein N is a positive integer and satisfies M≤N.

14. The second communication device (300) according to claim 13, wherein, the signal (510) is any one of the following: on-off keying signal; frequency shift keying signal; orthogonal frequency division multiplexing signal; or orthogonal frequency division multiplexing signal pre-coded with discrete Fourier transform.

15. The second communication device (300) according to claim 13 or 14, wherein, at least one information symbol represents any one of the following: an indicator for waking up one or a group of receivers; the identity of one or a group of receivers; or paging information associated with one or a group of receivers.

16. The second communication device (300) according to any one of claims 13 to 15, wherein, M = N, and C and C –1 include integer-valued symbols from the set {0, 1, …, q–1} and satisfy C –1 C = I (mod q), Among them, C –1 is the modular inverse of C, I is the identity matrix, and mod q is the modulo q operator.

17. The second communication device (300) according to any one of claims 13 to 15, wherein, C is an N×N matrix and has a rank equal to N, where q = 2, and C –1 satisfies at least one of the following: C –1 is a matrix in which each row and each column has one element equal to 1; C –1 is a matrix in which at least one row has an even Hamming weight; C –1 is a matrix in which N–1 rows have an even Hamming weight; C –1 is a matrix whose rows have odd Hamming weights; C –1 is a matrix whose total Hamming weight is equal to N 2 –N + 1, such that the Hamming weight of N – 1 rows is equal to N – 1 and the Hamming weight of 1 row is equal to N; and / or C –1 is a matrix in which each row has the same odd-valued Hamming weight.

18. The second communication device (300) according to any one of claims 13 to 15, wherein, C is an N×N matrix and has a rank equal to N, where Q > 1, and C is a version obtained by permuting any row or column of the matrix and the matrix is given as where c ii is an odd integer in the set {0, 1, …, q–1}, and for at least one i, 1 ≤ i ≤ N, each symbol in the set {0, 1, …, q–1} is associated with a bit label such that the Hamming weight difference between the bit label of symbol X and is at most 1.

19. The second communication device (300) according to any one of claims 13 to 15, wherein, C is an N×M matrix and has a rank equal to M, wherein M<N, q = 2, and C satisfies at least one of the following: C is obtained by performing any row or column permutation on the matrix and the matrix is given as wherein P is an M×M matrix with distinct rows and columns, and each row and each column contains a non-zero element, and A is an (N–M)×M matrix; the rank of the product of C′ and C is equal to M, wherein C′ is the transpose of C; and / or C includes orthogonal column vectors with odd Hamming weights.

20. A method (200) for a first communication device (100), the method (200) comprises: Obtain (202) a vector b of M integer-valued information symbols from the set {0, 1, …, q – 1}, where q = 2 Q , and Q is a positive integer; obtain (204) an N×M matrix C including symbols from the set {0, 1, …, q–1}, wherein N is a positive integer and satisfies M≤N; multiply (206) the matrix C with the vector b and then take the modulo q to obtain a vector y including N transmission symbols, wherein each transmission symbol in the vector y is associated with one of q signals; send (208) the associated signal (510) of each transmission symbol in the vector y to one or more receivers.

21. A method (400) for a second communication device (300), the method (400) comprises: Receive (402) N signals (510), where each signal is associated with a symbol in the set {0, 1, …, q – 1}, where q = 2 Q , and Q is a positive integer; determine (404) M integer-valued information symbols from N correlated symbols based on the N×M matrix C or its modulo inverse, wherein the matrix C and the modulo inverse of the matrix C include symbols from the set {0, 1, …, q–1}, wherein N is a positive integer and satisfies M≤N.

22. A computer program having program code for performing the method according to claim 20 or 21 when the computer program runs on a computer.

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