Interleaved constant amplitude zero autocorrelation sequences for communication or radar systems

Abstract

Embodiments of the invention relate to interleaved constant amplitude zero autocorrelation sequences for communication systems or radar systems. A transmitter device (100) transmits a communication signal or a radar signal (510) to a receiver device (300). The communication signal or a radar signal (510) is generated based on a complex-valued interleaved sequence which is a constant amplitude zero autocorrelation sequence interleaved by a permutation polynomial. The receiver device (300) receives the communication signal or the radar signal (510) and detects the complex-valued sequence based on the communication signal or the radar signal (510). Furthermore, the invention also relates to corresponding methods and a computer program.

Description

[0001]INTERLEAVED CONSTANT AMPLITUDE ZERO AUTOCORRELATION SEQUENCES FOR COMMUNICATION OR RADAR SYSTEMS TECHNICAL FIELD Embodiments of the invention relate to constant amplitude zero autocorrelation sequences for communication systems or radar systems. Furthermore, embodiments of the invention also relate to corresponding methods and a computer program. BACKGROUND Constant amplitude zero autocorrelation (CAZAC) sequences have ideal periodic autocorrelation function, i.e., the correlation value is zero for any non-zero time-shift. One example of a CAZAC sequence is the Zadoff-Chu sequence. Signals based on the CAZAC property are used in communication systems and radar systems as they can be reliably detected. In communication systems, CAZAC sequences are used as, e.g., reference signals for channel estimation, synchronization signals or used as random access preambles. The number of known CAZAC sequence constructions is fairly small and it is often required to define large sets of CAZAC sequences, preferably containing orthogonal sequences. Therefore, an open issue is to find sequence constructions which have the CAZAC property. SUMMARY An objective of embodiments of the invention is to provide a solution which mitigates or solves the drawbacks and problems of conventional solutions. The above and further objectives are solved by the subject matter of the independent claims. Further embodiments of the invention can be found in the dependent claims. According to a first aspect of the invention, the above mentioned and other objectives are achieved with a transmitter device for a communication system or a radar system, the transmitter device being configured to: interleave a complex-valued sequence by a permutation polynomial to obtain a complex- valued interleaved sequence, the complex-valued sequence being a constant amplitude zero autocorrelation sequence; and transmit a communication signal or a radar signal to a receiver device, the communication signal or the radar signal being generated based on the complex-valued interleaved sequence. An advantage of the transmitter device according to the first aspect is that CAZAC sequences can be produced by interleaving a complex-valued sequence. Thereby, a large set of CAZAC sequences can be produced from the complex-valued sequence. In an implementation form of a transmitter device according to the first aspect, the permutation polynomial is a linear permutation polynomial, a quadratic permutation polynomial, or a cubic permutation polynomial. An advantage with this implementation form is that the sequences can be generated with low- complexity since permutation polynomials provide a succinct and simple representation of a permutation. In an implementation form of a transmitter device according to the first aspect, the permutation polynomial has an associated inverse permutation polynomial which is a linear permutation polynomial or a quadratic permutation polynomial. An advantage with this implementation form is that permutation polynomials with degree larger than two may be used. In an implementation form of a transmitter device according to the first aspect, the complex- valued interleaved sequence is a Zadoff-Chu sequence, or a complex-valued constant amplitude zero autocorrelation sequence derived from a Zadoff-Chu sequence. An advantage with this implementation form is that permutation polynomial interleaved Zadoff- Chu sequences can be shown to have the CAZAC property. In an implementation form of a transmitter device according to the first aspect, deriving the complex-valued sequence from a Zadoff-Chu sequence comprises applying at least one operation on the Zadoff-Chu sequence in the group comprising: a rotation, a translation, a decimation, a linear frequency modulation, and a conjugation. An advantage with this implementation form is that a larger set of CAZAC sequences can be obtained. In an implementation form of a transmitter device according to the first aspect, the complex- valued interleaved sequence is represented as a Zadoff-Chu sequence multiplied by a complex-valued modulation sequence. An advantage with this implementation form is that the transmitter device and the receiver device can be simplified. In an implementation form of a transmitter device according to the first aspect, the communication signal or the radar signal is the complex-valued interleaved sequence, or the complex-valued interleaved sequence comprised in an OFDM signal, or the complex-valued interleaved sequence comprised in a DFT-s-OFDM signal, or the complex-valued interleaved sequence comprised in a radar signal. An advantage with this implementation form is that the sequence can be transmitted by waveforms which are used in communication systems or radar systems. In an implementation form of a transmitter device according to the first aspect, the transmitter device being configured to obtain a set of sequences, wherein each sequence in the set of sequences is obtained by at least one of: a unique cyclic shift of the complex-valued interleaved sequence, the cyclic shift comprising cyclically shifting the elements of the complex-valued interleaved sequence an integer number of steps; interleave the complex-valued sequence by a unique permutation polynomial from a set of permutation polynomials; and derive the complex-valued interleaved sequence based on a root index from a set of root indices, each root index in the set of root indices being a number which is relatively prime to a number corresponding to the length of a sequence in the set of sequences. An advantage with this implementation form is that a large set of CAZAC sequences can be obtained. In an implementation form of a transmitter device according to the first aspect, the set of sequences comprises a set of orthogonal sequences. An advantage with this implementation form is that there is no interference among signals which are generated from different sequences in the set. In an implementation form of a transmitter device according to the first aspect, the transmitter device being configured to: transmit a control signal to the receiver device, the control signal indicating one or more of: a configuration of at least one permutation polynomial, a configuration of the sequence length, a configuration of at least one root index, a configuration of at least one cyclic shift, and a configuration of an allocated time-frequency resource for transmission of the complex-valued interleaved sequence. An advantage with this implementation form is that the transmission of signals obtained from the complex-valued interleaved sequence could be flexibly configured. According to a second aspect of the invention, the above mentioned and other objectives are achieved with a receiver device for a communication system or a radar system, the receiver device being configured to: receive a communication signal or a radar signal from a transmitter device, the communication signal or the radar signal being generated based on a complex-valued interleaved sequence, wherein the complex-valued interleaved sequence is a complex-valued sequence interleaved by a permutation polynomial, and wherein the complex-valued sequence is a constant amplitude zero autocorrelation sequence; and detecting the complex-valued sequence based on the communication signal or the radar signal. In an implementation form of a receiver device according to the second aspect, the receiver device being configured to: receive a control signal from the transmitter device, the control signal indicating one or more of: a configuration of at least one permutation polynomial, a configuration of the sequence length, a configuration of at least one root index, a configuration of at least one cyclic shift, and a configuration of an allocated time-frequency resource for transmission of the complex-valued interleaved sequence; and detect the complex-valued sequence further based on the control signal. An advantage with this implementation form is that the transmission of signals obtained from the complex-valued interleaved sequence could be flexibly configured. In an implementation form of a receiver device according to the second aspect, detecting the complex-valued sequence comprises: deinterleave the communication signal or the radar signal; and / or correlating the received communication signal or the radar signal with a replica of the transmitted communication signal or radar signal. In an implementation form of a receiver device according to the second aspect, the permutation polynomial is a linear permutation polynomial, a quadratic permutation polynomial, or a cubic permutation polynomial. An advantage with this implementation form is that the sequences can be generated with low- complexity since permutation polynomials provide a succinct and simple representation of a permutation. In an implementation form of a receiver device according to the second aspect, the permutation polynomial has an associated inverse permutation polynomial which is a linear permutation polynomial or a quadratic permutation polynomial. An advantage with this implementation form is that permutation polynomials with degree larger than two may be used. In an implementation form of a receiver device according to the second aspect, the complex- valued interleaved sequence is a Zadoff-Chu sequence, or a complex-valued constant amplitude zero autocorrelation sequence derived from a Zadoff-Chu sequence. An advantage with this implementation form is that permutation polynomial interleaved Zadoff- Chu sequences can be shown to have the CAZAC property. In an implementation form of a receiver device according to the second aspect, the complex- valued interleaved sequence is represented as a Zadoff-Chu sequence multiplied by a complex-valued modulation sequence. An advantage with this implementation form is that the transmitter device and the receiver device can be simplified. In an implementation form of a receiver device according to the second aspect, the communication signal or the radar signal is the complex-valued interleaved sequence, or the complex-valued interleaved sequence comprised in an OFDM signal, or the complex-valued interleaved sequence comprised in a DFT-s-OFDM signal, or the complex-valued interleaved sequence comprised in a radar signal. An advantage with this implementation form is that the sequence can be transmitted by waveforms which are used in communication systems or radar systems. According to a third aspect of the invention, the above mentioned and other objectives are achieved with a method for a transmitter device, the method comprises: interleaving a complex-valued sequence by a permutation polynomial to obtain a complex-valued interleaved sequence, the complex-valued sequence being a constant amplitude zero autocorrelation sequence; and transmitting a communication signal or a radar signal to a receiver device, the communication signal or the radar signal being generated based on the complex-valued interleaved sequence. The method according to the third aspect can be extended into implementation forms corresponding to the implementation forms of the transmitter device according to the first aspect. Hence, an implementation form of the method comprises the feature(s) of the corresponding implementation form of the transmitter device. The advantages of the methods according to the third aspect are the same as those for the corresponding implementation forms of the transmitter device according to the first aspect. According to a fourth aspect of the invention, the above mentioned and other objectives are achieved with a method for a receiver device, the method comprises: receiving a communication signal or a radar signal from a transmitter device, the communication signal or the radar signal being generated based on a complex-valued interleaved sequence, wherein the complex-valued interleaved sequence is a complex-valued sequence interleaved by a permutation polynomial, and wherein the complex-valued sequence is a constant amplitude zero autocorrelation sequence; and detecting the complex-valued sequence based on the communication signal or the radar signal. The method according to the fourth aspect can be extended into implementation forms corresponding to the implementation forms of the receiver device according to the second aspect. Hence, an implementation form of the method comprises the feature(s) of the corresponding implementation form of the receiver device. The advantages of the methods according to the fourth aspect are the same as those for the corresponding implementation forms of the receiver device according to the second aspect. Embodiments of the invention also relate to a computer program, characterized in program code, which when run by at least one processor causes the at least one processor to execute any method according to embodiments of the invention. Further, embodiments of the invention also relate to a computer program product comprising a computer readable medium and the mentioned computer program, wherein the computer program is included in the computer readable medium, and may comprises one or more from the group of: read-only memory (ROM), programmable ROM (PROM), erasable PROM (EPROM), flash memory, electrically erasable PROM (EEPROM), hard disk drive, etc. Further applications and advantages of embodiments of the invention will be apparent from the following detailed description. BRIEF DESCRIPTION OF THE DRAWINGS The appended drawings are intended to clarify and explain different embodiments of the invention, in which: ^ Fig.1 shows a transmitter device according to an embodiment of the invention; ^ Fig. 2 shows a flow chart of a method for a transmitter device according to an embodiment of the invention; ^ Fig.3 shows a receiver device according to an embodiment of the invention; ^ Fig.4 shows a flow chart of a method for a receiver device according to an embodiment of the invention; ^ Fig. 5a and 5b shows a communication system and a radar system, respectively, according to embodiments of the invention; ^ Fig.6 shows maximum set size for QPP interleaved Zadoff-Chu sequences, for root index ^ = ^, where the set contains unique sequences obtained from different QPPs. The dash-dotted line represents the set size when Zadoff-Chu sequences with different root indices is used in conventional solutions; ^ Fig.7 shows possible values of the mutual cross-correlation between two sequences in a set obtained by using different QPPs according to embodiments of the invention; ^ Fig.8 shows possible values of the mutual cross-correlation between two sequences in a set obtained by using different root indices according to embodiments of the invention; ^ Fig.9a shows a block diagram of a transmitter device where the interleaved Zadoff- Chu sequence is used as modulation symbols in an OFDM signal and Fig.9b shows a block diagram of a receiver device corresponding to the block diagram of the transmitter device shown in Fig.9a; ^ Fig.10a shows a block diagram of a transmitter device where the DFT of the Zadoff- Chu sequence is interleaved and is used as modulation symbols in an DFT-s-OFDM signal and Fig.10b shows a block diagram of a receiver device corresponding to the block diagram of the transmitter device shown in Fig.10a; ^ Fig.11a shows a block diagram of a transmitter device where the interleaved Zadoff- Chu sequence is used as modulation symbols in an DFT-s-OFDM signal and Fig.11b shows a block diagram of a receiver device corresponding to the block diagram of the transmitter device shown in Fig.11a; and ^ Fig.12 illustrates signaling between the transmitter device 100 and the receiver device according to embodiments of the invention. DETAILED DESCRIPTION A constant amplitude zero autocorrelation (CAZAC) sequence, ^[^], ^ = 0,1, … , ^ − 1, is characterized by having constant amplitude, |^[^]|, where |∙| denotes absolute value, and having an ideal periodic autocorrelation function (PACF). The sequence elements may have real and / or imaginary parts and we refer to this as a complex-valued sequence. Ideal PACF implies that ^[^]is orthogonal to any cyclically shifted version of itself, i.e., (mod ^)]= 0(1) for delays ^ = 1,2, … , ^ − 1, where (∙)∗denotes complex conjugate and (mod ^) is the modulo- ^ operator. These properties make CAZAC sequences suitable for applications in wireless communications and for radar systems. The constant amplitude results in low peak-to-average ratio (PAPR) of the signal, which is beneficial for its coverage since higher transmit power could be used. The ideal PACF makes it possible to detect the received signal at distinct time delays in an orthogonal manner, which is beneficial for signal detection or for channel estimation. CAZAC sequences are used in 3GPP Long Term Evolution (LTE) and New Radio (NR) for physical random access channel (PRACH) preambles, sounding reference signal (SRS), demodulation reference signal (DMRS) and primary synchronization signal (PSS). Well-known families of CAZAC sequences include, e.g., Zadoff-Chu sequences, Frank sequences, generalized chirp-like (GCL) sequences, Björck sequences and biphase sequences. Moreover, exhaustive search by computers have been performed to find CAZAC sequences. It has been shown that if ^ is a prime number, then there are at most^^^^^ ^^^ ^ CAZAC sequences. If ^ is non-prime and divisible by a perfect square, then there are infinitely many CAZAC sequences. If ^ is non-prime and not divisible by a perfect square, it is unknown how many CAZAC sequences there are. Certain mathematical operations can be used to construct CAZAC sequences. It can be shown that if ^[^]is a CAZAC sequence then, ^[^] is also a CAZAC sequence: 1) (Rotation) ^[^] = ^^[^], for some |^| = 1. 2) (Translation) ^[^] = ^[^ + ^ (mod ^)], where ^ is an integer. 3) (Decimation) ^[^] = ^[^^ (mod ^)], where ^ is an integer relatively prime to ^. frequency modulation) ^[^] = ^ ^ ^^ 4) (Linear ^ ^ ^[^], where ^ is an integer and ^ ^^ ^ = ^ ^ with ^ =√−1. 5) (Conjugation) ^[^] = ^∗[^]. It has also been shown that ^[^] is a CAZAC sequence if and only if ^[^] is a CAZAC sequence, where the discrete Fourier transform (DFT) is defined by Another form of mathematical operation is permutation, i.e., the integers from the set {^: 0,1, … , ^ − 1} are ordered according to some function ^ . This results in the interleaved sequence ^[^]= There is, however, no general permutation property which would guarantee that ^[^]= ^[^[^]] is a CAZAC sequence for an arbitrary permutation ^[^]. On the contrary, it is possible to construct counter-examples where permutations do not preserve the CAZAC property for ^[^]. It is disclosed herein that new classes of CAZAC sequences may be obtained by certain permutations. We will particularly address the case of generating signals from interleaved Zadoff-Chu sequences. One of the most commonly used CAZAC sequences is the Zadoff-Chu sequence, which is defined by where ^ is an integer (aka. root index) which is relatively prime to ^ and ^ is an integer. A set of ^ orthogonal CAZAC sequences can be constructed by cyclically shifting the sequence {^^^[^ + ^(mod ^)], 0 ≤ ^ ≤ ^ − 1}. The set of CAZAC sequences can be enlarged by including sequences with different root indices and in that case, there is non-zero cross- correlation between sequences with different root indices. The largest such set is achieved when ^ is a prime number, since then ^ ∈ {1,2, … , ^ − 1}. Zadoff-Chu sequences are used in LTE and NR and are mapped to subcarriers of an OFDM signal. When a Zadoff-Chu sequence is used as a reference signal, it is allocated to the same subcarriers as the data transmission. Since the number of allocated subcarriers for data transmission in LTE and NR, ^, is not a prime number, ^ is chosen to be the largest prime fulfilling ^ < ^, and the sequence is cyclically extended to length ^. Due to this manipulation, the extended sequence is not a CAZAC sequence anymore. A related sequence family is the generalized chirp-like (GCL) sequences, which are modulated Zadoff-Chu sequences defined by ^^^^[^]= ^[^(mod ^)]^^^[^], ^ = 0,1, … , ^ − 1 (4) where ^ = ^^^, and ^ and ^ are integers. It has been shown that GCL sequences are CAZAC sequences, for any arbitrary unitary modulation sequence ^[^]. For creating sets of CAZAC sequences derived from a Zadoff-Chu sequence, conventional solutions have been limited to using cyclic shifts, using multiple root indices or applying modulation sequences. The CAZAC property of the sequence is not maintained if it is shortened or extended. While Zadoff-Chu sequences are common in many applications, interleaved Zadoff-Chu sequences have not been considered. Interleaved versions could provide a new family of CAZAC sequences and may be useful for generating sets of sequences. An objective of the invention is to enable a transmitter device, which includes an interleaver based on a permutation polynomial, to generate a signal from an interleaved complex-valued sequence and the interleaved complex-valued sequence should have the CAZAC property. Embodiments of the invention relates to generating a CAZAC sequence and / or a set of CAZAC sequences to be used as reference signals, radar signals, synchronization signals, for carrying data information, or any other suitable application. Fig. 1 shows a transmitter device 100 according to an embodiment of the invention. In the embodiment shown in Fig. 1, the transmitter device 100 comprises a processor 102, a transceiver 104 and a memory 106. The processor 102 is coupled to the transceiver 104 and the memory 106 by communication means 108 known in the art. The transmitter device 100 may be configured for wireless and / or wired communications in a communication system or a radar system. The wireless communication capability may be provided with an antenna or antenna array 110 coupled to the transceiver 104, while the wired communication capability may be provided with a wired communication interface 112 e.g., coupled to the transceiver 104. The processor 102 may 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 chipsets. The memory 106 may be a read-only memory, a random access memory (RAM), or a non-volatile RAM (NVRAM). The transceiver 304 may be a transceiver circuit, a power controller, or an interface providing capability to communicate with other communication modules or communication devices, such as network nodes and network servers. The transceiver 104, memory 106 and / or processor 102 may be implemented in separate chipsets or may be implemented in a common chipset. That the transmitter device 100 is configured to perform certain actions can in this disclosure be understood to mean that the transmitter device 100 comprises suitable means, such as e.g., the processor 102 and the transceiver 104, configured to perform the actions. According to embodiments of the invention the transmitter device 100 is configured to interleave a complex-valued sequence by a permutation polynomial to obtain a complex- valued interleaved sequence. The complex-valued sequence being a constant amplitude zero autocorrelation sequence. The transmitter device 100 is configured to transmit a communication signal or a radar signal 510 to a receiver device 300. The communication signal or the radar signal 510 is generated based on the complex-valued interleaved sequence. Furthermore, in an embodiment of the invention, the transmitter device 100 for a communication system or a radar system 500 comprises a processor configured to interleave a complex-valued sequence by a permutation polynomial to obtain a complex-valued interleaved sequence, the complex-valued sequence being a constant amplitude zero autocorrelation sequence. The transmitter device 100 further comprises a transceiver configured to transmit a communication signal or a radar signal 510 to a receiver device 300, the communication signal or the radar signal 510 being generated based on the complex- valued interleaved sequence. Moreover, in yet another embodiment of the invention, the transmitter device 100 for a communication system or a radar system 500 comprises a processor and a memory having computer readable instructions stored thereon which, when executed by the processor, cause the processor to: interleave a complex-valued sequence by a permutation polynomial to obtain a complex-valued interleaved sequence, the complex-valued sequence being a constant amplitude zero autocorrelation sequence; and transmit a communication signal or a radar signal 510 to a receiver device 300, the communication signal or the radar signal 510 being generated based on the complex-valued interleaved sequence. Fig. 2 shows a flow chart of a corresponding method 200 which may be executed in a transmitter device 100, such as the one shown in Fig. 1. The method 200 comprises: interleaving 202 a complex-valued sequence by a permutation polynomial to obtain a complex- valued interleaved sequence, the complex-valued sequence being a constant amplitude zero autocorrelation sequence; and transmitting 204 a communication signal or a radar signal 510 to a receiver device 300, the communication signal or the radar signal 510 being generated based on the complex-valued interleaved sequence. Fig. 3 shows a receiver device 300 according to an embodiment of the invention. In the embodiment shown in Fig.3, the receiver device 300 comprises a processor 302, a transceiver 304 and a memory 306. The processor 302 is coupled to the transceiver 304 and the memory 306 by communication means 308 known in the art. The receiver device 300 further comprises an antenna or antenna array 310 coupled to the transceiver 304, which means that the receiver device 300 is configured for wireless communications in a communication system. 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, one or more chipsets. The memory 306 may be a read-only memory, a RAM, or a NVRAM. The transceiver 104 may be a transceiver circuit, a power controller, or an interface providing capability 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 chipsets or may be implemented in a common chipset. That the receiver device 300 is configured to perform certain actions can in this disclosure be understood to mean that the receiver device 300 comprises suitable means, such as e.g., the processor 302 and the transceiver 304, configured to perform the actions. According to embodiments of the invention the receiver device 300 is configured to receive a communication signal or a radar signal 510 from a transmitter device 300. The communication signal or the radar signal 510 is generated based on a complex-valued interleaved sequence. The complex-valued interleaved sequence is a complex-valued sequence interleaved by a permutation polynomial, and the complex-valued sequence is a constant amplitude zero autocorrelation sequence. The receiver device 300 is configured to detect the complex-valued sequence based on the communication signal or the radar signal 510. Furthermore, in an embodiment of the invention, the receiver device 300 for a communication system or a radar system 500 comprises a transceiver configured to: receive a communication signal or a radar signal 510 from a transmitter device 300, the communication signal or the radar signal 510 being generated based on a complex-valued interleaved sequence, wherein the complex-valued interleaved sequence is a complex-valued sequence interleaved by a permutation polynomial, and wherein the complex-valued sequence is a constant amplitude zero autocorrelation sequence. The receiver device 300 further comprises a processor configured to detect the complex-valued sequence based on the communication signal or the radar signal 510. Moreover, in yet another embodiment of the invention, the receiver device 300 for a communication system or a radar system 500 comprises a processor and a memory having computer readable instructions stored thereon which, when executed by the processor, cause the processor to: receive a communication signal or a radar signal 510 from a transmitter device 300, the communication signal or the radar signal 510 being generated based on a complex-valued interleaved sequence, wherein the complex-valued interleaved sequence is a complex-valued sequence interleaved by a permutation polynomial, and wherein the complex- valued sequence is a constant amplitude zero autocorrelation sequence; and detect the complex-valued sequence based on the communication signal or the radar signal 510. Fig.4 shows a flow chart of a corresponding method 400 which may be executed in a device 300, such as the one shown in Fig. 3. The method 400 comprises: receiving 402 a communication signal or a radar signal 510 from a transmitter device 300, the communication signal or the radar signal 510 being generated based on a complex-valued interleaved sequence, wherein the complex-valued interleaved sequence is a complex-valued sequence interleaved by a permutation polynomial, and wherein the complex-valued sequence is a constant amplitude zero autocorrelation sequence; and detecting 404 the complex-valued sequence based on the communication signal or the radar signal 510. Fig.5a shows a communication system 500 and Fig.5b shows a radar system 500 according to embodiments of the invention. The communication system 500 in Fig. 5a comprises a transmitter device 100 and a receiver device 300 configured to communicate and operate in the communication system 500. For simplicity, the shown communication system 500 only comprises one transmitter device 100 and one receiver device 300. However, the communication system 500 may comprise any number of transmitter devices 100 and any number of receiver devices 300 without deviating from the scope of the invention. The communication system 500 may be a 3GPP system such as LTE or NR. In the exemplary illustration the transmitter device 100 act as a network access node, such as a base station, while the receiver device 300 act as a client device, such as a UE. The network access node may be part of a RAN and being connected to a core network via a suitable communication interface. The radar system 500 in Fig.5b comprises a transmitter device 100 configured to transmit a radar signal 510. The radar system 500 also comprises a receiver device 300 having a receiver antenna. In the following disclosure further embodiments of the invention will be presented. Complex-valued interleaved sequence In embodiments of the invention, interleaving is performed on a complex-valued CAZAC sequence, which is a Zadoff-Chu sequence, or a complex-valued CAZAC sequence derived from a Zadoff-Chu sequence. The complex-valued sequence may be derived from a Zadoff-Chu sequence by applying at least one operation on the Zadoff-Chu sequence in the group comprising: a rotation, a translation, a decimation, a linear frequency modulation, and a conjugation. Permutation polynomials A permutation can equivalently be understood of as an interleaver and hence a permutation can be implemented with an interleaver. There exist several types of interleavers, e.g., block interleaver, convolutional interleaver, pseudo-random interleaver, etc. The herein disclosed solution is using interleavers based on permutation polynomials of different types. In embodiments of the invention, the permutation polynomial is a linear permutation polynomial, a quadratic permutation polynomial, or a cubic permutation polynomial. These polynomials have an algebraic structure which allows for analytical treatment favorable for designing the interleaver. They also have benefits for low-complexity implementation due to that the permutation can be computed on the fly through a closed-form expression. The polynomial ^[^] = ^^^^+ ^^^^^^^^+... +^^(mod ^) (5) is a ^th degree permutation polynomial if it permutes the values in the set {0,1, … , ^ − 1}. The coefficients ^^are integer values and it can be assumed that ^^∈ {0,1, … , ^ − 1} since ^[^] is periodic in ^. It is known that there exists at least one inverse permutation polynomial, ^^^[^], to each permutation polynomial, such that ^^^[^[^]] = ^. The degree of may not be the same as for . A permutation polynomial based interleaver is fully characterized by its polynomial coefficients, which is favorable for low-complexity implementation, since it is possible to compute Eq. (5) directly instead of pre-computing and directly storing the ^ permuted values. A linear permutation polynomial (LPP) has degree ^ = 1, i.e., it is a first degree polynomial. It can be shown that a requirement for being a permutation is that gcd(^^, ^)= 1, where gcd(^, ^)denotes the greatest common divisor of the integers ^ and ^. Thus, ^^needs to be relatively prime to ^. A quadratic permutation polynomial (QPP) has degree ^ = 2, i.e., it is a second degree polynomial. Let ^ = ∙ … ∙ ^^^^be its prime factorization where ^^, ^ = 0,1, … , ^ are prime numbers and the multiplicities are positive integers. It has been shown that the conditions on ^^and ^^are: ^ If ^^= 2, ^^= 1, then (mod 2). ^ If ^^= 2, ^^> 1, then ^^≢ 0 (mod 2) and ^^≡ 0 (mod 2). ^ If ^^> 2, ^^≥ 1, then ^^≢ 0 (mod ^^) and ^^≡ 0 (mod ^^). These conditions may not be fulfilled for certain ^, thus QPPs do not necessarily exist for all ^. The values of ^ for which QPPs exist could be odd or even but QPPs do not exist when ^ is a prime number. It is known that two distinct QPPs (i.e., having different coefficients) can generate the same permutation. The number of unique QPPs that generate different permutations can be computed by derived formulas. Moreover, certain QPPs will produce the same permutation as an LPP, i.e., they are referred to as reducible QPPs. It has been shown that a QPP is irreducible if and only if ^ > gcd(2^^, ^). When the prime decomposition of ^ is such that ^^= 2, ^^= 0, or 1, or 2 and ^^= 1, ^ = 1,2, … , ^, then there are no irreducible QPPs. A cubic permutation polynomial (CPP) has degree ^ = 3, i.e., it is a third degree polynomial. Conditions on the coefficients of higher-order permutation polynomials, e.g., CPPs, have also been derived. CPPs exist for more values of ^ than QPPs. Interleaved Zadoff-Chu sequences For an LPP, ^^corresponds to the aforementioned decimation property and ^^corresponds to the translation property, which both preserve the CAZAC property for any CAZAC sequence. Therefore, it follows that a Zadoff-Chu sequence which is interleaved by an LPP becomes a CAZAC sequence. For a QPP, by inserting the permutation polynomial in Eq. (3), the interleaved sequence ^^^[^[^]]of Eq. (3) with ^ = 0 becomes for even for odd ^. It can be numerically verified by computing Eq. (1) with (6) or (7) for different QPPs, that a QPP interleaved Zadoff-Chu sequence is a CAZAC sequence. This can be shown and the mathematical proof of this theorem is not trivial. Theorem 1: If ^^^[^], ^ = 0,1, … , ^ − 1 is a Zadoff-Chu sequence and ^[^] is a QPP then ^^^[^[^]], ^ = 0,1, … , ^ − 1 is a CAZAC sequence. For QPP and higher order permutation polynomials, we can also prove the following theorem. Theorem 2: If ^^^[^], ^ = 0,1, … , ^ − 1 is a Zadoff-Chu sequence and ^[^] is a permutation polynomial with an inverse which is a QPP or LPP, then ^^^[^[^]], ^ = 0,1, … , ^ − 1 is a CAZAC sequence. Thus, the permutation polynomial has an associated inverse permutation polynomial which is a linear permutation polynomial or a quadratic permutation polynomial. The theorems hold for Zadoff-Chu sequences and other CAZAC sequences being interleaved by a QPP may not become a CAZAC sequence. Therefore, the disclosed solution is to apply a permutation polynomial to a Zadoff-Chu sequence, to produce the sequence ^^^[^[^]]. A signal is generated from ^^^[^[^]], either by transmitting the sequence or to use the sequence as modulation symbols in OFDM or DFT-s- OFDM transmission. A person skilled in the art will understand that permutation polynomials of degree larger than 2 may be used. An advantage of using higher-degree polynomials is that more values of ^ could be used. For example, there exist no QPPs when ^ = 5 but there exist CPPs. Table 1 shows an example of the number of CPPs which exist for a given ^, and the number of CPPs for which the interleaved Zadoff-Chu sequence is a CAZAC sequence. Table 1. Number of CPPs and number of CPPs which gives the CAZAC property. #CPPs #CPPs w. ^ CAZAC 4 4 4 5 20 4 6 20 20 7 0 0 8 48 48 9 90 90 10 88 24 11 110 0 12 40 40 13 0 0 14 12 12 15 136 40 16 448 448 17 272 0 18 396 396 19 0 0 20 176 48 21 24 24 22 460 20 23 506 0 24 352 352 25 400 400 26 24 24 27 2754 2754 28 24 24 29 812 0 30 560 176 31 0 0 32 3840 3840 33 700 40 34 1120 32 35 120 24 36 792 792 37 0 0 38 36 36 39 48 48 40 1472 448 41 1640 0 42 120 120 43 0 0 44 920 40 45 2520 792 46 2068 44 47 2162 0 48 2944 2944 49 1764 1764 50 1800 1800 It can be observed that when ^=4,6,8,9,12,14,16,18,21,24,25,26,27,28,32,36,39,42,48,49,50, then every CPP will provide the CAZAC property. If ^=5,10,15,20,22,30,33,34,35,40,44,45,46, only a subset of the CPPs will provide the CAZAC property. If ^=7,11,13,17,19,23,29,31,37,41,43,47, there are no CPPs which will provide the CAZAC property. These are the prime numbers which are larger than 5. If ^=5,10,11,15,17,20,22,23,29,30,33,34,35,40,41,44,45,46,47, there exist CPPs but it is not guaranteed that the CAZAC property is provided. This sequence of numbers of ^ can be obtained from 2^3^(6^ + 5), ^, ^, ^ ≥ 0. A person skilled in the art will be able to extend the above principles and find permutation polynomials of degree larger than 3 in order to provide the CAZAC property of an interleaved Zadoff-Chu sequence. Modulated Zadoff-Chu sequences An alternative representation of the interleaved Zadoff-Chu sequence is obtained by rewriting the interleaved sequence as ^^^^^[^]^ = ^[^]^^^[^](8)where the modulation sequence is ^[^]= ^^^^^[^]^^∗ ^^[^]. (9) Thus, Eq. (8) allows the transmitter and receiver to implement the interleaved sequence as a Zadoff-Chu sequence multiplied by a modulation sequence. If ^[^] has period ^, it is required that ^[^ + ^] = ^[^]. From Eq. (6) and (7) and using a QPP, we obtain for ^ > 0, ^[^ + ^]^^^^^ ^^^^^ ^ ^ ^^^ ^^^^^^^ ^^^^^ ^ ^^^^^^ ^ ^ ^ ^[^]^^ ^(^ ^)^ ^ ^ ^^^^^^^^^^^(^^^^)^ , ^ odd (10) =^ [ ]^ ^[^]^[^]^^^^^^^^^^^^^^(^^^^^^)^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ , ^ even. Thus, in embodiments of the invention, the complex-valued interleaved sequence may be represented as a Zadoff-Chu sequence multiplied by a complex-valued modulation sequence. In conventional solutions of GCL sequences, ^[^]has period ^ = ^, where ^ = ^^^, and ^ and ^ are integers. The modulation sequence in Eq. (8) based on permutation polynomials can have period ^ ≠ ^ and are thus not necessarily fulfilling the period of the construction of GCL sequence. For example, consider ^ = 2^^, then ^^= 2^, 0 < ^ < ^^and ^^= 1 are feasible coefficients of a QPP. Inserting ^ = ^ / ^^in (10), results in ^[^ + ^] = ^[^], i.e., the period is ^ = 2^^^^. For example, if ^^= 5, then ^ ∈ {2,4,8,16}, whereas the possible values of ^ are ^ ∈ {2,4} since ^ = 32 = 8 ∙ 2^= 2 ∙ 4^. Set of sequences Embodiments of the invention also relates to the transmitter device 100 being configured to generate a set of sequences according to the herein disclosed solution. The set of sequences thus comprises two or more sequences having the properties according to the present solution. The set of sequences generated comprises a set of orthogonal sequences. In general, to generate a set of sequences includes one or more of the following operations i.e., using multiple permutation polynomials, using unique cyclic shifts, and using multiple root indices. In other words, in embodiments of the invention the transmitter device 100 is configured to obtain a set of sequences and each sequence in the set of sequences is obtained by at least one of the following operations: ^ A unique cyclic shift of the complex-valued interleaved sequence, the cyclic shift comprising cyclically shifting the elements of the complex-valued interleaved sequence an integer number of steps; ^ Interleave the complex-valued sequence by a unique permutation polynomial from a set of permutation polynomials; and ^ Derive the complex-valued interleaved sequence based on a root index from a set of root indices, each root index in the set of root indices being a number which is relatively prime to a number corresponding to the length of a sequence in the set of sequences. In an embodiment, a set of orthogonal CAZAC sequences is obtained from a single Zadoff- Chu sequence and a single permutation polynomial by cyclically shifting the interleaved sequence, i.e., {^^^[^[^ + ^] (mod ^)]: ^ = 0,1, … , ^ − 1, ^ = 0,1, … , ^ − 1}. In an embodiment, a set of CAZAC sequences is obtained from a single Zadoff-Chu sequence by using different permutation polynomials {^^^,^^^^[^]^, ^ = 0,1, … , ^ − 1, ^ = 0,1, … , ^ − 1}. It should be noted that in order to obtain a set of unique sequences, it may not be sufficient to apply unique permutation polynomials. Two different QPPs which generate two different permutations could produce the same sequence ^^^[^[^]]. For example, when ^ = 8, the two different QPPs ^^[^]= 2^^+ ^ (mod 8) and ^^[^]= 2^^+ 3^ (mod 8) produce different permutations but give the same sequence ^^^[^^[^]] = ^^^[^^[^]]. This is due to the term ^^in the exponential function of the Zadoff-Chu sequence, which makes the two sequences equal if ^^ ^[^] ≡ ^^ ^[^](mod ^). Fig.6 shows the results of exhaustive search for the maximum number of unique sequences, ^, obtained from a single Zadoff-Chu sequence with all feasible QPPs of the given even length ^. As comparison, the dash-dotted line shows the maximum set size using different root indices and no QPPs. It can be seen that there exist lengths ^ for which a larger set is obtained from a single Zadoff-Chu sequence by using different QPPs than by using Zadoff-Chu sequences with different root indices but without QPPs. The possible values of the magnitude of the cross-correlation (11) between two unique sequences in the set is contained in Fig.7. For example, when ^ = 8, the mutual cross-correlation between two sequences in the set is either ^^^^^ = 0 or ^^^^^ = 0.5. In Table 2, the relative occurrence of the cross-correlation values is contained for ^ = 128. For example, 40% of the sequences are orthogonal. The possible values of the magnitude of the cross-correlation between two unique sequences in the set obtained by using different root indices is contained in Fig.8. Table 2. Relative occurrence for cross-correlation values when ^=128. Occurrence^0.4 0 0.008 0.047 0.004 0.140 0.008 0.148 0.44 0.234 0.008 0.250 0.047 0.320 0.008 0.383 0.004 0.391 0.008 0.438 0.008 0.477 0.04 0.500 0.004 0.586 0.004 0.586 0.04 0.695 0.002 0.711 In an embodiment (see above), a set of orthogonal CAZAC sequences is obtained from a single Zadoff-Chu sequence by using different permutation polynomials. For example, if ^ = 32, it can be confirmed by evaluating Eq. (11) that a set of orthogonal sequences can be formed from the QPPs ^^[^]= 2^^+ ^(mod ^), ^^[^]= 2^^+ 3^(mod ^), ^^[^]= 2^^+ 17^(mod ^)and ^^[^] = 2^^+ 19^(mod ^). It could be observed from Fig. 8 that orthogonal sequences according to Eq. (11) may not be found for certain values of ^, e.g., ^ = 98 is one such example where there exist irreducible QPPs while zero crosscorrelation according to Eq. (11) cannot be fulfilled. In an embodiment, a set of CAZAC sequences is obtained from a single Zadoff-Chu sequence by using different permutation polynomials and different cyclic shifts, {^^^,^^^^[^ + ^]^, ^ = 0,1, … , ^ − 1, ^ = 0,1, … , ^ − 1, ^ = 0,1, … , ^ − 1}. A person skilled in the art will understand that the set could be formed by using a subset of the cyclic shifts ^ = 0,1, … , ^ − 1. In an embodiment, a set of CAZAC sequences is obtained from multiple Zadoff-Chu sequences obtained from a set ^ containing at least two different root indices, 0,1, … , ^ − 1(12)by using at least one of different permutation polynomials and / or different cyclic shifts, 0,1, … , ^ − 1, ^ ∈ ^}. Signal generation The complex-valued interleaved sequence generated according to embodiments of the invention may be used to generate a communication signal or a radar signal depending on the application. In this respect the communication signal 510 may be the complex-valued interleaved sequence, or the complex-valued interleaved sequence comprised in an OFDM signal, or the complex-valued interleaved sequence comprised in a DFT-s-OFDM signal, or the complex-valued interleaved sequence comprised in a radar signal. In an embodiment, the interleaved Zadoff-Chu sequence can be used as the modulation symbols in an OFDM signal, as illustrated in the block diagram of Fig. 9a. The transmitter device 100 in Fig. 9a comprises an interleaver block 120 connected to an inverse discrete Fourier transform (IDFT) block 130. Thus, the interleaved Zadoff-Chu sequence is modulating the subcarriers though the IDFT block 130. It was shown that the DFT of a Zadoff-Chu sequence which is cyclically shifted ^ step is where ^^^is the modular multiplicative inverse, fulfilling ^^^^ ≡ 1 (mod ^), which exists since ^ is relatively prime to ^. Thus, the DFT version is obtained by the operations rotation (by translation (by ^) and decimation (by ^^^) on the original Zadoff-Chu sequence. The term ^^^^ + ^ can be regarded as an LPP, since ^^^is relatively prime to ^. Thus, the DFT of a Zadoff-Chu sequence is a CAZAC sequence. Fig.9b shows a block diagram of a receiver device 300 corresponding to the block diagram of the transmitter device 100 in Fig. 9a. The receiver device 300 comprises a DFT block 330 connected to a de-interleaver block 320. In an embodiment, the interleaved DFT of a Zadoff-Chu sequence is used the modulation symbols in an OFDM signal, as illustrated in Fig.10a. The transmitter device 100 comprises a DFT block 140 connected to an interleaver block 120 which in turn is connected to a IDFT block 130. The Zadoff-Chu sequence is precoded through the DFT block 140, and the output of the DFT block 140 is interleaved in the interleaver block 120 using a permutation polynomial and then used to modulate the subcarriers through the IDFT block 130. Fig.10b shows a block diagram of a receiver device 300 corresponding to the block diagram of the transmitter device 100 in Fig. 10a. The receiver device 300 comprises a DFT block 340 connected to a de- interleaver block 320 which in turn is connected to a IDFT block 330. Fig. 11a shows yet another embodiment of a block diagram of a transmitter device 100 comprising an interleaver block 120 connected to a DFT block 140 which in turn is connected to an IDFT block 130. Fig.11b shows a block diagram of a receiver device 300 corresponding to the block diagram of the transmitter device 100 in Fig. 11a. The receiver device 300 comprises a DFT block 340 connected to a IDFT block 330 which in turn is connected to a de- interleaver block 320. Fig.12 illustrates control signaling between the transmitter device 100 and the receiver device 300 according to embodiments of the invention. In step I in Fig. 12, the transmitter device 100 transmits a control signal 520 to the receiver device 300. The control signal 520 indicates one or more of: a configuration of at least one permutation polynomial, a configuration of the sequence length, a configuration of at least one root index, a configuration of at least one cyclic shift, and a configuration of an allocated time- frequency resource for transmission of the complex-valued interleaved sequence. In step II in Fig.12, the receiver device 300 receives the control signal 520 from the transmitter device 100. In step III in Fig.12, the transmitter device 100 transmits a communication signal or a radar signal 510 to the receiver device 300. As aforementioned, the communication signal 510 may be the complex-valued interleaved sequence, or the complex-valued interleaved sequence comprised in an OFDM signal, or the complex-valued interleaved sequence comprised in a DFT-s-OFDM signal, or the complex-valued interleaved sequence comprised in a radar signal. In step IV in Fig.12, the receiver device 300 receives the communication signal or the radar signal 510 and detects the complex-valued sequence of the communication signal or a radar signal 510 further based on the information indicated in the control signal 520. For detection the receiver device 300 may deinterleave the communication signal or the radar signal 510 and / or correlating the received communication signal or the radar signal 510 with a replica of the transmitted communication signal or radar signal 510. If deinterleaving is performed, the detection can be based on the replica signal generated from Zadoff-Chu sequence. If correlating is performed, the detection can be based on the replica signal generated from the interleaved Zadoff-Chu sequence. A network access node herein may also be denoted as a radio network access node, an access network access node, an access point (AP), or a base station (BS), e.g., a radio base station (RBS), which in some networks may be referred to as transmitter, “gNB”, “gNodeB”, “eNB”, “eNodeB”, “NodeB” or “B node”, depending on the standard, technology and terminology used. The radio network access node may be of different classes or types such as e.g., macro eNodeB, home eNodeB or pico base station, based on transmission power and thereby the cell size. The radio network access node may further be a station, which is any device that contains an IEEE 802.11-conformant media access control (MAC) and physical layer (PHY) interface to the wireless medium (WM). The radio network access node may be configured for communication in 3GPP related long term evolution (LTE), LTE-advanced, fifth generation (5G) wireless systems, such as new radio (NR) and their evolutions, as well as in IEEE related Wi-Fi, worldwide interoperability for microwave access (WiMAX) and their evolutions. A client device herein may be denoted as a user device, a user equipment (UE), a mobile station, an internet of things (IoT) device, a sensor device, a wireless terminal and / or a mobile terminal, and is enabled to communicate wirelessly in a wireless communication system, sometimes also referred to as a cellular radio system. The UEs may further be referred to as mobile telephones, cellular telephones, computer tablets or laptops with wireless capability. The UEs in this context may be, for example, portable, pocket-storable, hand-held, computer- comprised, or vehicle-mounted mobile devices, enabled to communicate voice and / or data, via a radio access network (RAN), with another communication entity, such as another receiver or a server. The UE may further be a station, which is any device that contains an IEEE 802.11- conformant MAC and PHY interface to the WM. The UE may be configured for communication in 3GPP related LTE, LTE-advanced, 5G wireless systems, such as NR, and their evolutions, as well as in IEEE related Wi-Fi, WiMAX and their evolutions. Furthermore, any method according to embodiments of the invention may be implemented in a computer program, having code means, which when run by processing means causes the processing means to execute the steps of the method. The computer program is included in a computer readable medium of a computer program product. The computer readable medium may comprise essentially any memory, such as previously mentioned a ROM, a PROM, an EPROM, a flash memory, an EEPROM, or a hard disk drive. Moreover, it should be realized that the transmitter device and the receiver device comprise the necessary communication capabilities in the form of e.g., functions, means, units, elements, etc., for performing or implementing embodiments of the invention. Examples of other such means, units, elements and functions are: processors, memory, buffers, control logic, encoders, decoders, rate matchers, de-rate matchers, mapping units, multipliers, decision units, selecting units, switches, interleavers, de-interleavers, modulators, demodulators, inputs, outputs, antennas, amplifiers, receiver units, transmitter units, DSPs, TCM encoder, TCM decoder, power supply units, power feeders, communication interfaces, communication protocols, etc. which are suitably arranged together for performing the solution. Therefore, the processor(s) of the transmitter device and the receiver device may comprise, e.g., one or more instances of a CPU, a processing unit, a processing circuit, a processor, an ASIC, a microprocessor, or other processing logic that may interpret and execute instructions. The expression “processor” may thus represent a processing circuitry comprising a plurality of processing circuits, such as e.g., any, some or all of the ones mentioned above. The processing circuitry may further perform data processing functions for inputting, outputting, and processing of data comprising data buffering and device control functions, such as call processing control, user interface control, or the like. Finally, it should be understood that the invention is not limited to the embodiments described above, but also relates to and incorporates all embodiments within the scope of the appended independent claims.

Claims

CLAIMS 1. A transmitter device (100) for a communication system or a radar system (500), the transmitter device (100) being configured to: interleave a complex-valued sequence by a permutation polynomial to obtain a complex- valued interleaved sequence, the complex-valued sequence being a constant amplitude zero autocorrelation sequence; and transmit a communication signal or a radar signal (510) to a receiver device (300), the communication signal or the radar signal (510) being generated based on the complex-valued interleaved sequence.

2. The transmitter device (100) according to claim 1, wherein the permutation polynomial is a linear permutation polynomial, a quadratic permutation polynomial, or a cubic permutation polynomial.

3. The transmitter device (100) according to claim 1 or 2, wherein the permutation polynomial has an associated inverse permutation polynomial which is a linear permutation polynomial or a quadratic permutation polynomial.

4. The transmitter device (100) according to any one of the preceding claims, wherein the complex-valued interleaved sequence is a Zadoff-Chu sequence, or a complex-valued constant amplitude zero autocorrelation sequence derived from a Zadoff-Chu sequence.

5. The transmitter device (100) according to claim 4, wherein deriving the complex-valued sequence from a Zadoff-Chu sequence comprises applying at least one operation on the Zadoff-Chu sequence in the group comprising: a rotation, a translation, a decimation, a linear frequency modulation, and a conjugation.

6. The transmitter device (100) according to any one of claims 3 to 5, wherein the complex- valued interleaved sequence is represented as a Zadoff-Chu sequence multiplied by a complex-valued modulation sequence.

7. The transmitter device (100) according to any one of the preceding claims, wherein the communication signal or the radar signal (510) is the complex-valued interleaved sequence, or the complex-valued interleaved sequence comprised in an OFDM signal, or the complex- valued interleaved sequence comprised in a DFT-s-OFDM signal, or the complex-valued interleaved sequence comprised in a radar signal.

8. The transmitter device (100) according to any one of claims 1 to 7, configured to obtain a set of sequences, wherein each sequence in the set of sequences is obtained by at least one of: a unique cyclic shift of the complex-valued interleaved sequence, the cyclic shift comprising cyclically shifting the elements of the complex-valued interleaved sequence an integer number of steps; interleave the complex-valued sequence by a unique permutation polynomial from a set of permutation polynomials; and derive the complex-valued interleaved sequence based on a root index from a set of root indices, each root index in the set of root indices being a number which is relatively prime to a number corresponding to the length of a sequence in the set of sequences.

9. The transmitter device (100) according to claim 8, wherein the set of sequences comprises a set of orthogonal sequences.

10. The transmitter device (100) according to any one of the preceding claims, configured to: transmit a control signal (520) to the receiver device (300), the control signal (520) indicating one or more of: a configuration of at least one permutation polynomial, a configuration of the sequence length, a configuration of at least one root index, a configuration of at least one cyclic shift, and a configuration of an allocated time-frequency resource for transmission of the complex-valued interleaved sequence.

11. A receiver device (300) for a communication system or a radar system (500), the receiver device (300) being configured to: receive a communication signal or a radar signal (510) from a transmitter device (300), the communication signal or the radar signal (510) being generated based on a complex- valued interleaved sequence, wherein the complex-valued interleaved sequence is a complex- valued sequence interleaved by a permutation polynomial, and wherein the complex-valued sequence is a constant amplitude zero autocorrelation sequence; and detect the complex-valued sequence based on the communication signal or the radar signal (510).

12. The receiver device (300) according to claim 11, configured to: receive a control signal (520) from the transmitter device (100), the control signal (520) indicating one or more of: a configuration of at least one permutation polynomial, a configuration of the sequence length, a configuration of at least one root index, a configurationof at least one cyclic shift, and a configuration of an allocated time-frequency resource for transmission of the complex-valued interleaved sequence; and detecting the complex-valued sequence further based on the control signal (520).

13. The receiver device (300) according to claim 11 or 12, wherein detecting the complex- valued sequence comprises: deinterleave the communication signal or the radar signal (510); and / or correlating the received communication signal or the radar signal (510) with a replica of the transmitted communication signal or radar signal (510).

14. The receiver device (300) according to any one of claims 11 to 13, wherein the permutation polynomial is a linear permutation polynomial, a quadratic permutation polynomial, or a cubic permutation polynomial.

15. The receiver device (300) according to any one of claims 11 to 14, wherein the permutation polynomial has an associated inverse permutation polynomial which is a linear permutation polynomial or a quadratic permutation polynomial.

16. The receiver device (300) according to any one of claims 11 to 15, wherein the complex- valued interleaved sequence is a Zadoff-Chu sequence, or a complex-valued constant amplitude zero autocorrelation sequence derived from a Zadoff-Chu sequence.

17. The receiver device (300) according to claim 15 or 16, wherein the complex-valued interleaved sequence is represented as a Zadoff-Chu sequence multiplied by a complex- valued modulation sequence.

18. The receiver device (300) according to any one of claims 11 to 17, wherein the communication signal or the radar signal (510) is the complex-valued interleaved sequence, or the complex-valued interleaved sequence comprised in an OFDM signal, or the complex- valued interleaved sequence comprised in a DFT-s-OFDM signal, or the complex-valued interleaved sequence comprised in a radar signal.

19. A method (200) for a transmitter device (100), the method (200) comprising: interleaving (202) a complex-valued sequence by a permutation polynomial to obtain a complex-valued interleaved sequence, the complex-valued sequence being a constant amplitude zero autocorrelation sequence; andtransmitting (204) a communication signal or a radar signal (510) to a receiver device (300), the communication signal or the radar signal (510) being generated based on the complex-valued interleaved sequence.

20. A method (400) for a receiver device (300), the method (400) comprising: receiving (402) a communication signal or a radar signal (510) from a transmitter device (300), the communication signal or the radar signal (510) being generated based on a complex- valued interleaved sequence, wherein the complex-valued interleaved sequence is a complex- valued sequence interleaved by a permutation polynomial, and wherein the complex-valued sequence is a constant amplitude zero autocorrelation sequence; and detecting (404) the complex-valued sequence based on the communication signal or the radar signal (510).

21. A computer program with a program code for performing a method according to claim 19 or 20 when the computer program runs on a computer.

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