A method of doubly selective channel estimation and sensing using repeated chirps for OFDM systems

Abstract

This innovation presents a novel method for both linear time-varying channel estimation and low complexity sensing in Orthogonal Frequency Division Multiplexing (OFDM) systems by leveraging repeated chirp signals (CS). By integrating chirps orthogonally within a single OFDM symbol in frequency domain, the method enables simultaneous estimation of channel coefficients, delay, and Doppler shifts while facilitating environmental sensing. The repetition of chirps in time creates a sparse distribution in the frequency domain, and the number of repeated chirps within each OFDM symbol determines the number of subcarriers allocated in the frequency domain, with the remaining subcarriers dedicated to OFDM data (D) which ensure seamless data (D) transmission, environmental sensing, and channel estimation.

Description

[0001] SPECIFICATION

[0002] A METHOD OF DOUBLY SELECTIVE CHANNEL ESTIMATION AND SENSING USING REPEATED CHIRPS FOR OFDM SYSTEMS

[0003] Technical Field:

[0004] This invention relates to a method of doubly selective channel estimation and sensing using repeated chirps for OFDM systems that can be applicable in dynamic communication environments, such as next-generation wireless networks, vehicular communication systems, and integrated sensing and communication (ISAC) scenarios, where accurate channel estimation, efficient spectral utilization, and low-complexity sensing are critical for ensuring reliable performance in rapidly changing conditions.

[0005] State of The Art:

[0006] In the case of knowledge of the technique, channel estimation in OFDM systems relied heavily on pilot symbols inserted periodically across time and frequency domains. Traditional methods employed strategies like uniform spacing, random distribution, or adaptive placement to strike a balance between accuracy and efficiency. For instance, the periodic transmission of training symbols, where an entire OFDM symbol is allocated for pilots, was effective in estimating the channel but caused significant spectral inefficiency due to reduced data throughput. Pilots aided channel estimation on the other hand, provided moderate channel estimation accuracy in frequency-selective channels but struggled in fast-fading or highly dynamic conditions due to limited time-domain resolution [1], Advanced techniques like scattered or adaptive pilots improved estimation in varying environments but added complexity.

[0007] An alternative approach proposed in [2] introduced the orthogonal coexistence of OFDM and chirps by combining K repeated chirps within an OFDM symbol, where the chirps were used as pilots for channel estimation and for sensing, with their duration matching the cyclic prefix (CP) duration. Although this method achieved orthogonality in frequency domain, it had notable limitations. Constraining the chirp duration to the CP reduced sensing performance, as longer chirp durations, which are essential for enhanced sensing capabilities, would compromise spectral efficiency. Additionally, the chirps were generated in the analog domain, necessitating two RF chains and precise synchronization between them, which posed challenges for both mono- and bi-static sensing scenarios. Moreover, channel estimation was only addressed for frequency-selective channels, neglecting dynamic channel conditions where time variations play a critical role.

[0008] OFDM-based sensing methods face additional challenges. Pilots used to estimate channel state information (CSI) for tracking environmental changes often reduce data throughput and require careful optimization. Multipath reflections in cluttered environments can distort the sensed information, complicating target detection and localization. Conventional approaches involve comb-like pilot placement for time-frequency interpolation, followed by 2D FFT processing to create range-Doppler maps that reveal object positions and velocities. However, this increases computational complexity compared to radar chirp-based sensing, which retrieves information from the IF band. Additionally, pilots designed in the frequency domain are not optimized to handle Doppler spread, where signal copies arrive with varying Doppler shifts, causing intercarrier interference (ICI). This interference degrades channel estimation and communication performance, especially when data and pilots coexist within the same OFDM symbol.

[0009] With the rapid advancement of wireless communication technologies and the increasing demands they impose, upcoming 6G networks will require innovative solutions to address evolving service requirements. Among these, one of the most promising approaches is joint sensing and communication (JSAC). By seamlessly integrating communication and sensing functionalities, JSAC enables network nodes to not only transmit data but also sense their surrounding environment, leading to enhanced system reliability, improved decision-making, and optimized resource efficiency. However, with the ever-growing congestion in the radio spectrum, designing a proper waveform that can efficiently manage resources, mitigate interference, and provide both communication and sensing functionalities is paramount. While OFDM has been a cornerstone of modern communication systems due to its spectral efficiency and robustness, it lacks the inherent capability to perform sensing tasks.

[0010] To address this limitation while maintaining backward compatibility with existing OFDM modulators, we propose to enhance OFDM communication by incorporating chirp signals. These chirps serve dual purposes: they facilitate accurate channel estimation in both static and dynamic environments in addition to a decreased complexity for high resolution sensing, thereby bridging the gap between traditional communication systems and the emerging JSAC paradigm.

[0011] As a result, a new method is needed that integrates repeated chirps as pilots within OFDM symbols to enable efficient channel estimation and sensing, mitigate Doppler spread effects, minimize spectral inefficiency, address dynamic channel conditions, and balance the trade-offs between complexity, accuracy, and performance in next generation 6G networks, ensuring robust communication and reliable environmental awareness in highly dynamic and cluttered scenarios.

[0012] References:

[0013] [1] M. a. A. H. Ozdemir, " Channel estimation for wireless OFDM systems," IEEE Communications Surveys and Tutorials, p. 9.2, 2007.

[0014] [2] E. a. S. M. M. a. A. H. Memisoglu, " Orthogonal coexistence of overlapped radar and communication waveforms," in 2022 IEEE Wireless Communications and Networking Conference (WCNC), 2022.

[0015] Description of The Invention:

[0016] The invention to realize all the objectives mentioned above and which will emerge from the detailed description below; aims to maintain backward compatibility with existing OFDM modulators while enhancing OFDM communication by integrating chirp signals. These chirps serve dual purposes: they facilitate accurate channel estimation in both static and dynamic environments in addition to a decreased complexity for high resolution sensing, thereby bridging the gap between traditional communication systems and the emerging JSAC paradigm.

[0017] The method of this invention builds upon the robust foundation of OFDM by integrating chirps in a way that not only preserves its established benefits but also unlocks new functionalities. This ensures a smooth transition toward 6G networks while maintaining compatibility with existing infrastructures, enabling efficient spectrum usage and supporting the dual requirements of communication and sensing in future wireless systems.

[0018] The proposed invention offers the following advantages:

[0019] 1. Channel Estimation in Doubly Selective Channels: Facilitates channel estimation in doubly selective channels by using repeated chirps as pilots in the frequency domain.

[0020] 2. Generating Repeated Chirps from OFDM: Allows to generate repeated chirps using OFDM transmitter.

[0021] 3. Joint Sensing and Communication: Enables simultaneous sensing and communication functionalities.

[0022] 4. Single RF Chain Implementation: Both OFDM and repeated chirps are generated using the same RF chain, reducing hardware complexity.

[0023] 5. Backward Compatibility: Ensures seamless integration with existing OFDM systems and no extra hardware is needed.

[0024] 6. Low-Complexity Sensing: Provides a low-complexity solution for sensing applications.

[0025] Societal Impact:

[0026] • Enhanced Disaster Management: The integration of chirp-based sensing and OFDM communication enables precise real-time location tracking and environmental monitoring, improving response times and coordination during natural disasters or emergencies. • Safer Transportation Systems: By combining sensing and communication, this technology enhances vehicle-to-everything (V2X) communication, supporting safer autonomous vehicles and efficient traffic management.

[0027] • Advanced Remote Monitoring: Enables robust and efficient remote health monitoring, where chirp-based sensing provides accurate data for critical healthcare applications, particularly in underserved or rural areas.

[0028] • Resource Optimization: Facilitates energy-efficient and spectrum-efficient 6G systems, reducing infrastructure and operational costs for widespread deployment.

[0029] • Smart City Applications: Supports integrated sensing and communication for smart infrastructure, such as adaptive traffic lights, waste management, and urban planning, leading to more efficient and sustainable cities.

[0030] The structural and characteristic features and all advantages of the method subject to the invention will be understood more clearly thanks to the figures given below and the detailed explanation written by referring to these figures, and therefore the evaluation should be made by taking these figures and detailed explanation into consideration.

[0031] Description of the Figures:

[0032] The invention will be described with reference to the accompanying figures, so that the features of the invention will be more clearly understood and appreciated, but the purpose of this is not to limit the invention to these certain regulations. On the contrary, it is intended to cover all alternatives, changes and equivalences that can be included in the area of the invention defined by the accompanying claims. The details shown should be understood that they are shown only for the purpose of describing the preferred embodiments of the present invention and are presented in order to provide the most convenient and easily understandable description of both the shaping of methods and the rules and conceptual features of the invention. In these drawings;

[0033] Figure 1 A schematic view of system models

[0034] Figure 2 A schematic view of an example of transceiver design Figure 3 A view of chirps before and after phase correction

[0035] The figures to help understand the present invention are numbered as indicated in the attached image and are given below along with their names.

[0036] Disclosure of References:

[0037] BS. Base Station

[0038] UE. User Device

[0039] CS. Chirp Signal

[0040] CP. Cyclic Prefix

[0041] CPI. Cyclic Prefix 1

[0042] CP2. Cyclic Prefix 2

[0043] 51. Symbol 1

[0044] 52. Symbol 2

[0045] FFT. Fast Fourier Transform

[0046] IFFT. Inverse Fast Fourier Transform

[0047] D. Data

[0048] NS. No Shift

[0049] WS. With Shift

[0050] C. Continuous

[0051] Pd. Phase Discontinuity

[0052] 10. ^-Samples

[0053] 20. Upsampling a

[0054] 30. Mapping

[0055] 40. Modulation

[0056] 50. Add CP

[0057] 60. Conjugation

[0058] 70. Radar Processing

[0059] 80. RF Front-End Detail Description of The Invention:

[0060] The system model considers an integrated sensing and communication (ISAC) scenario where a base station (BS) simultaneously serves multiple user devices (UE) while performing environmental sensing. The base station (BS) employs OFDM waveform with repeated chirps embedded in specific subcarriers within each OFDM symbol to enable sensing and channel estimation as they are used as pilots. Communication data (D) is transmitted to user devices (UE) using the remaining subcarriers. This coexistence ensures efficient resource utilization while meeting both communication and sensing requirements. An example representation of the system model described here is shown in Figure 1.

[0061] OFDM Signal Model:

[0062] Consider that N data (D) symbols are modulated using OFDM over a total bandwidth B at a carrier frequency fc. The OFDM modulator maps these symbols {X(m), ~m = 0,..., N — 1} in the frequency domain. If the bandwidth of each of the N subcarriers is B 1

[0063] defined as A = — then the time duration of OFDM symbol is T = —. Consequently, the

[0064]

[0065] frequency domain samples X(m) must be transformed into the time domain using the Inverse Fast Fourier Transform (IFFT). Therefore, the discrete output of the OFDM modulator is given by

[0066] s0FDM(n) = ^a; UOFDMM ej27r~,

[0067]

[0068] and it can also be defined in a matrix form as

[0069] SOFDM > pH^OFDM

[0070]

[0071] (CS) Model:

[0072] Consider a linear Chirp signal (CS) in discrete time domain, schirpwhich sweeps linearly across bandwidth Bcover a time duration Tc, and has the time-bandwidth product M = r / Tc is a nonzero integer where = Bc / Tcis the chirp rate. The discrete time domain representation of schiris expressed as

[0073] • p2

[0074] SchirP(p)= ejn- o < p < M.

[0075] Repeated Chirps Signal (CS):

[0076] Let the signal sK(n) be formed by repeating schir(p), K times where K is an integer power of two, resulting in N = M ■ K samples which can be written in vector form as

[0077] $K= l / < ® «chirp,

[0078] or equivalently in discrete time as

[0079] sK(n) = schirp([n]M), n = 0,1,...,1V — 1

[0080] Where [. ]Mis the modulo of M. The repeated chirps in frequency domain are given as

[0081] N — l

[0082] SK(tn) = schirp([n]M)e-727rmn / w, m = 0,1,...,1V — 1

[0083]

[0084] n=0

[0085] Since sK(n) is periodic with period M, we can set n = p + kM such that k = 0,..., K — 1, and p = 0,1,..., M — 1, therefore we can write

[0086] K-l M-l

[0087] SKO) -11scbirpQp^e-j2nm(j}+kM) / N

[0088] fc=0 p=0

[0089] which can be written as

[0090] K-l M-l

[0091] SK(m) = g-j2mrik / K schirp(p) g-j2n:mp / N

[0092]

[0093] fc=0 Taking the outer sum will give a discrete delta function such that

[0094] K—l

[0095] \ ' „-j2mnk / K > m mod K = 0

[0096]

[0097] Zu to, otherwise

[0098] fc=0

[0099] This implies that SKO71) is nonzero only for m = 0, K, 2K,..., (M — )K.

[0100] Setting m' = m / K where m' = 0,..., M — 1 we can write

[0101] M-l

[0102] schirp(p)e-j2rnn'p / M

[0103] p=0

[0104] Which can be written as

[0105] M-l M-l

[0106] • P2t ■ ^i2X-"1t n

[0107] \ eJn~Me-j^iri p / M _e-Jn~M \e-j2n(p-m )2 / M

[0108]

[0109] p=0 p=0

[0110] Analyzing the term of the summation we conclude that X

[0111]

[0112] p=o e~j2n(p~m'^2 / Mcan be approximated to a constant. Therefore, the discrete Fourier transformation of a repeated chirp is precisely the DFT of the single chirp schirpat frequency index m'. Finally, the discrete Fourier transformation of repeated chirps can be given as

[0113] . m2

[0114] SK(m) = K. e~J7l~M~, m mod K = 0

[0115]

[0116] 0, otherwise

[0117] SK(m) shows that repeated chirps can co-exist with OFDM in an orthogonal manner.

[0118] OFDM and Repeated Chirps:

[0119] An orthogonal co-existence between repeated chirps and OFDM in frequency domain where for OFDM symbol with N subcarriers used and a K times repeated chirps with number of samples of each chirp is M, both can co-existe as follows . m2

[0120] K.e~J71M, mmodK = 0

[0121]

[0122] Xdata(m), otherwise

[0123] In OFDM systems, Inverse Fast Fourier Transform (IFFT) is used to convert OFDM subcarriers to time domain symbols as described under the heading 'OFDM Signal Model', therefore we can write the transmitted chirp-based signal as

[0124] dmn

[0125]

[0126] CP Configuration:

[0127] In OFDM systems a cyclic prefix is added to the beginning of the symbol to combat the channel effect where an Lcpsamples are copied from the last part of the symbol and inserted in its begining. However, this cyclic prefix (CP) addition will introduce discontinuity to the chirp signal (CS) in time domain as depicted in Figure 3. which degrades the sensing performance. Therefore, proper manipulation is needed to make the chirps continuous (C) again where we will introduce a phase shift in frequency domain representation of the i-th chirp in case of the chirp is generated using OFDM directly and the phase needed can be written as

[0128] m(n-iLCp) S

[0129]

[0130] chirpfn -iLcv) = ej27r",

[0131] or simply by keeping the chirp subcarrier indices in frequency domain empty and generating a continuous (C) repeated chirp in time domain directly.

[0132] Channel:

[0133] The channel can be divided into two parts: one dedicated to radar sensing and the other to communication. Since radar processing (70) follows conventional techniques, where dechirping is employed to extract sensing information, this aspect will not be discussed here. Instead, the focus will be on communication channel estimation utilizing the embedded chirps in the frequency domain. Consider a -tap doubly selective channel, which can be expressed as

[0134] <2-i

[0135] h(n) = y hiej2N 8(n — If).

[0136]

[0137] i=0

[0138] where hLis the complex channel coefficient, It and f are the delay and Doppler shifts introduced by the channel, respectively.

[0139] Proposed Channel Estimation

[0140] The time domain received signal after passing through the defined channel can be written as

[0141] <2-1

[0142] y(n) = Y - IJ.

[0143]

[0144] i=0

[0145] After discarding the cyclic prefix (CP), the frequency domain received symbol can be extracted by the Fast Fourier Transform (FFT) as follows

[0146] <2-i

[0147] Y(m) = - ff).

[0148]

[0149] i=0

[0150] Where aL=

[0151]

[0152] e1« Note that for a static channel all ft = 0 for i = 0,..., Q — 1, which means that the channel can be directly estimated like any conventional pilot-based channel estimation and equalization method such as MMSE.

[0153] In case of mobile environment, OFDM subcarriers will be shifted by the amount (± ff) leading to distinct cases. However, in most cases after compensating for the frequency offset the first tap can be assumed to be f0= 0. Therefore, the channel delays can be estimated separately for each doppler which leads to simplifying the equation of the received signal and the novel channel estimation can be performed based on the subcarriers m' for the original chirp with different delays and the frequency shifted chirp with different delays also. The channel can be separated from taps coming with fa = 0 and taps coming with fa #= 0 thus it can be written as follows:

[0154] Z. (m r V— 1 h^a^K.e171M + y hi2ai2Xdata(Km' — for [Km' — ft]K= 0 L^=0 i2=0

[0155]

[0156] where Qi is the number of taps coming with f = 0 and Q2is the number of taps coming with [Km' — f ]K= 0. Dechirping Yj (m' with a conjugate of the original chirp can be given as

[0157] 9 / Ol 1 9 <22-I D^m') = ejn« y h^a^K.eJnM + hi2ai2Xdata[Km' - f)

[0158] \ <i=0 12 = 0

[0159]

[0160] for [Km' -fa]K= 0.

[0161] Simplifying the dechirped signal can give

[0162] Qi-1Q2-1,n2

[0163] — i IjKm — i. (m ) D1(m'>) = hilej2nN + y hi2ai2Xdata(Km' — fa eJ71«

[0164] — 0 12 — 0

[0165] Performing the Fourier transform on the output D will lead to the following

[0166] M Z-1 / <2i-l, <2z-lr,<z\ l X- 1-n ItKm ’. lm) \ y hiie,2n~N~ + y hi2ai2Xdata{Km' — \e-j27tmP / M m'=o \ ii = O <2=0 /

[0167]

[0168] After simplification it was gotten

[0169] ZV~ <. C<i1-p)m / ■v-1 ■v-1 C<i1 / i2) v2 2) hhe]2n— M - + 2_ 2_ ^2eJ~ Xdata(Km’ - fi2)e}2n- M

[0170]

[0171] mf=0 ii=0 mf=0 i2 = 0 Note that the first term

[0172]

[0173] h, ej2nM is a shift related to the channel delay, and the peak of each shift is the corresponding channel gain, and the second term is a quadratic shift which means the interference from OFDM data (D) will spread over the delay bins of the Fast Fourier Transform (FFT) output. Therefore, the interference is minimum and increasing the power assigned to the repeated chirps will enhance the channel estimation.

[0174] Sensing Receiver:

[0175] The sensing receiver can perform target detection using the reflected repeated chirps, similar to a conventional FMCW radar. In this process, the received chirps are dechirped by mixing them with the conjugate of the transmitted chirps, producing a beat frequency fb. This beat frequency is directly related to the distance between the transmitter and the reflector. Performing a Fast Fourier Transform (FFT) on the dechirped signal yields the range of information. However, the presence of coupled beat frequencies caused by Doppler shifts (due to mobility) necessitates using multiple chirps to accurately estimate both range and velocity.

[0176] The foregoing descriptions of specific embodiments of the present technology have been presented for the purposes of illustration and description. They are not intended to be exhaustive or to limit the present technology to the precise forms disclosed. Obviously, many modifications and variations are possible considering the above teachings. The embodiments were chosen and described to best explain the principles of the present technology and its practical applications, enabling others skilled in the art to utilize the present technology and its various embodiments with appropriate modifications as suited to the particular use contemplated. It is understood that various omissions and substitutions of equivalents are contemplated as circumstances may suggest or render expedient, but such changes are intended to cover the software or implementation without departing from the spirit or scope of the claims of the present technology.

[0177] In cases where no conflict occurs, the embodiments in the present disclosure and their features may be combined. The foregoing descriptions are merely specific implementations of the present disclosure and are not intended to limit its protection scope. Any variation or replacement readily determined by a person skilled in the art within the technical scope of the present disclosure shall fall within its protection scope. Therefore, the protection scope of the present disclosure shall be determined by the claims.

Claims

CLAIMS1- The invention relates to a method of doubly selective channel estimation and sensing using repeated chirps for OFDM systems, comprising;i. generating repeated chirp signals (CS) that sweep across a defined bandwidth and embedding them into specific subcarriers of an OFDM symbol,ii. ensuring orthogonal coexistence of the repeated chirp signals and OFDM data (D) subcarriers in the frequency domain,iii. utilizing the repeated chirp signals for estimating channel coefficients, delays, and Doppler shifts in dynamic environments, andiv. processing reflected repeated chirp signals to extract sensing information, including range and velocity of targets, by employing dechirping and Fourier Transform techniques.2- The method according to claim 1, wherein the repeated chirp signals are configured to occupy subcarrier indices that are periodic in the frequency domain, enabling sparse representation for improved sensing and channel estimation performance, the frequencydomain representation of the repeated chirps is given as:K—l M-lSK(m) =e-j2nmk / Kschiip^e-j2nmp / Nk=0 p=0where SK(m) represents the frequency-domain repeated chirp, K is the number of repetitions, M is the number of samples per chirp, p and m are time and frequency indices, respectively.3- The method according to claim 1, wherein a cyclic prefix (CP) is added to the OFDM symbol to combat channel effects, and a phase correction is applied to ensure timedomain continuity of the chirp signals, for time-domain continuity, the phase shift in the frequency domain for the i-th repeated chirps is given as:N-lz.1 v. mljn-iLcp)schirp(n -iLcp) = / , ^(m) eJ 71NWhere, Lcpis the cyclic prefix (CP) length, S^(m) is the frequency-domain representation of the i-th repeated chirps.4- The method according to claim 1, wherein the sensing receiver utilizes dechirping to generate a beat frequency proportional to the target distance and performs Fast Fourier Transform (FFT) to determine range and velocity.5- The method according to claim 1, wherein channel estimation is performed by separating subcarriers associated with dynamic channel taps and estimating delays for each Doppler shift independently, the doubly selective channel can be expressed as:<2-iy hte^—N—SCn - lii=0where, hLis the complex channel coefficient, fa is the Doppler shift, It is the delay, Q is the number of taps.6- The method according to claim 1, wherein the power allocated to the repeated chirps can be adaptively adjusted to minimize interference with the data (D) subcarriers and enhance channel estimation accuracy, the received signal after passing through the channel is given by:<2-iy(n) = Yi=0where; y(n) is the received signal,fa and It are the channel parameters, (n) is the transmitted OFDM-Chirp-based signal.7- A system for integrated sensing and communication (ISAC) in OFDM systems, comprising;i. an OFDM modulator configured to embed repeated chirp signals and communication data (D) into an OFDM symbol,ii. a cyclic prefix (CP) generator for improving resilience to channel, while a phase shift is applied to the repeated chirps accordingly.iii. a sensing receiver for processing reflected chirps to extract target information, andiv. a channel estimator configured to utilize the repeated chirps signal to estimate channel parameters in doubly selective environments.8- The system according to claim 7, wherein the system comprises a sensing receiver that compensates for Doppler shifts by processing multiple chirps to decouple range and velocity information.9- The system according to claim 7, wherein the system comprises an OFDM modulator that ensures orthogonal coexistence of chirp and data (D) subcarriers by mapping (30) chirp signals to periodic subcarrier indices in the frequency domain.10- The system according to claim 7, wherein the sensing and communication processes are configured to operate in an integrated manner to maximize spectral efficiency and minimize mutual interference.

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