Description:TECHNICAL FIELD: The present disclosure relates to the field of communication engineering and electronics. More particularly, the present disclosure relates to a method for joint estimation of multi-target state parameters in Orthogonal Frequency Division Multiplexing (OFDM) wireless systems using Slepian sequences.
BACKGROUND OF THE INVENTION
Wireless communication systems increasingly rely on OFDM for robust and efficient data transmission. Estimation of multi-target parameters such as range, velocity, and angle of arrival is critical in applications including radar, vehicle tracking, and wireless localization. Existing methods for parameter estimation often lack efficiency and precision, particularly in environments with multiple targets. Therefore, there is a need for a method and system that improves the accuracy and computational efficiency of multi-target parameter estimation.
SUMMARY
One or more of the problems of the conventional prior art may be overcome by various embodiments of the present disclosure.
In one aspect of the present disclosure, a method for joint estimation of multi-target state parameters in an Orthogonal Frequency Division Multiplexing (OFDM) wireless system includes receiving pilot symbols at the wireless communication equipment, projecting normalized sequences, performing Slepian cancellation, and repeating these steps for a predetermined number of iterations, thereby generating target estimates.
In another aspect of the present disclosure, the iterative estimation process in the aforementioned method is terminated based on a stopping criterion, which halts the iterations when the L2-norm of the residual signal, following Slepian cancellation, falls below a predefined threshold.
In another aspect of the present disclosure, the process of projecting the sequence obtained by dividing the received symbols by the known pilot symbols or residual signals onto an up-converted Kronecker Slepian sequences can be substituted with a method involving down-conversion of the received or residual signals and subsequent projection onto the Kronecker Slepian sequence.
In another aspect of the present disclosure, the base station transmits the OFDM pilot symbols, and the method is applied on the echo received at the base station due to multiple targets.
In another aspect of the present disclosure, the method can also be applied on the signal received at the user equipment having knowledge of the pilot symbols.
In another aspect of the present disclosure, the pilot symbols selected from the group consisting of position signals (PRS), demodulation signals (DMRS), synchronization signal blocks (SSB), channel state signals (CSI-RS), or any combination thereof.
In another aspect of the present disclosure, the sequences are projected onto one or more basis sequences, including Discrete Fourier Transform (DFT), oversampled DFT, Discrete Cosine Transform (DCT), or any other known basis sequences.
In another aspect of the present disclosure, joint estimation of two parameters selected from the group consisting of range, velocity, and angle of arrival can be performed where the estimation process of the two parameters is conducted iteratively in tandem until a predetermined number of iterations is completed, and subsequently, the remaining third parameter is separately estimated using a similar iterative approach.
In another aspect of the present disclosure, the method of estimating multiple target parameters is done by dividing the recovered wireless signals, generating sub-signals, computing multi-dimensional Discrete Fourier Transform (DFT), iteratively modifying the search space, and refining the estimation of the target parameters using Slepian sequences.
In yet another aspect of the present disclosure, a system comprises at least one transceiver module, at least one processor module, and at least one memory module configured to store instructions executable by the processor module which, when executed, cause the processor module to recover pilot symbols and data signals, generate Slepian sequences, and perform matrix and vector operations required for spectral estimation and target parameter computation.
In another aspect of the present disclosure, the matrix and vector operations in the system include computing a norm, dot product, executing matrix arithmetic operations, and identifying the maximum and minimum elements within a vector for refining parameter estimates.
DETAILED DESCRIPTION OF THE DRAWING.
The accompanying drawings, which are incorporated in and constitute a part of this specification, show certain aspects of the subject matter disclosed herein and, together with the description, help explain some of the principles associated with the disclosed implementations. In the drawing,
Fig. 1 depicts the modules in wireless communication equipment.
Fig. 2 depicts a method of target estimation as proposed.
Fig. 3A depicts simulation results, particularly the variation of RMSE of range estimation with SNR. We observe that the proposed method provides more accurate estimates closer to the root Cramer-Rao bound.
Fig. 3B depicts simulation results, particularly the variation of RMSE of velocity estimation with SNR. We have similar observations to the range estimates.
Fig. 3C depicts simulation results, particularly the variation of RMSE of angle estimation with SNR. Again, we have similar observations to the range and velocity estimates.
Fig. 4A depicts simulation results, particularly the increase in estimation error with target index for the proposed method. We observe that the RMSE does not increase significantly for the targets further away from the BS.
Fig. 4B depicts simulation results, particularly the comparison of target estimates with the ground truth. We observe that the estimates corresponding to the proposed method are closer to the actual parameter values even with closely spaced targets.
Fig. 5A depicts simulation results, particularly the target peak of the first target. The spectrum shows a peak at the frequency corresponding to the first target, and the peaks corresponding to the remaining targets are not visible.
Fig. 5B depicts simulation results, particularly the cancellation of the first peak and the resulting peak corresponding to the second target. Here the cancellation is applied as described in the steps of the proposed method. We observe that the effect of the previously estimated target is removed, and the peak corresponding to the next target is clearly visible.
Fig. 5C depicts simulation results, particularly the cancellation of the second peak and the resulting peak corresponding to the third target. We have similar observations, where the effect of the previous target is removed and the peak corresponding to the remaining target is visible
Figure 6 illustrates the proposed system in accordance with the present invention.
Figure 7 illustrates the flow diagram of the Method in accordance with the present disclosure.
DETAILED DESCRIPTION OF THE PRESENT INVENTION
Various embodiments of the present disclosure are discussed in detail below. While specific implementations and configurations of the system and method for joint estimation of multi-target state parameters in Orthogonal Frequency Division Multiplexing (OFDM) wireless systems are presented, these are provided for illustration purposes only. A person skilled in the relevant art will recognize that alternative components, methods, or configurations may be employed without departing from the spirit and scope of the invention. Therefore, the following description and accompanying figures should be viewed as illustrative rather than limiting.
Numerous specific details are provided to offer a comprehensive understanding of the disclosure. However, certain well-known details are omitted to avoid obscuring the description and to emphasize the novel aspects of the invention. References to "one embodiment," "an embodiment," “one aspect,” “some aspects,” or “an aspect” throughout this disclosure indicate that a specific feature, structure, or characteristic described is included in at least one embodiment. These references do not imply that all such features, structures, or characteristics are present in every embodiment, nor do they imply exclusivity between embodiments. Additionally, various features described herein may be combined across embodiments to create new configurations.
The terms used in this specification generally align with their ordinary meanings within the relevant art, unless specifically defined otherwise in the context of the disclosure. In cases where alternative language or synonyms are used, they should not be interpreted as limiting, but rather as broadening the scope of the invention. The examples provided, whether illustrative of terms, components, or configurations, are not intended to limit the scope of the disclosure or its claims. Moreover, the examples and use cases included in this specification, including any descriptive titles or subtitles, are provided for clarity and convenience, and should not be construed as restricting the scope of the invention.
Additional features and advantages of the invention will become apparent in the detailed description and accompanying claims. These features and advantages may arise from the specific configurations and combinations of components and methods discussed herein. The invention is further supported by the appended claims, which should be interpreted in light of the disclosed principles, while maintaining the flexibility to encompass variations, adaptations, and alternative embodiments that adhere to the inventive concepts set forth.
There is a need to overcome the limitations associated with existing methods of parameter estimation in Orthogonal Frequency Division Multiplexing (OFDM) wireless systems, which often lack efficiency and precision, particularly in environments with multiple targets. Conventional approaches struggle with high computational overhead, limited accuracy in estimating critical parameters such as range, velocity, and angle of arrival, and are often unable to mitigate interference effectively. These limitations hinder the performance of applications like radar, vehicle tracking, and wireless localization, necessitating a robust solution that enhances both computational efficiency and estimation accuracy.
Figure 6 illustrates a schematic representation of the system designed for joint estimation of multi-target state parameters in an Orthogonal Frequency Division Multiplexing (OFDM) wireless system. The system comprises the following key modules: a transceiver module, a processor module, a memory module, and a set of antennas. Each module performs specific functions essential to the accurate and efficient estimation of parameters such as range, velocity, and angle of arrival.
The transceiver module is responsible for transmitting and receiving signals, including OFDM pilot symbols and data signals. Acting as the primary interface with the wireless communication environment, it facilitates the acquisition of raw data required for subsequent processing. The antennas, integrated into the system, enable seamless signal transmission and reception, ensuring efficient communication and reliable data exchange.
The processor module includes multiple processing units (P1, P2, ..., Pp) that execute critical computational tasks. These tasks involve recovering pilot symbols and data signals from the OFDM grid, generating and processing Slepian sequences, and performing matrix and vector operations necessary for spectral estimation and target parameter computation. The iterative nature of these operations allows the processor module to refine estimates for multi-target parameters with high precision.
The memory module supports the processor by storing essential instructions and parameters. It contains multiple memory units (M1, M2, ..., Mm), which hold Kronecker Slepian sequences for spectral estimation, threshold values for stopping criteria, and transformation sequences used during the iterative estimation process. This seamless integration of the modules enhances the system's computational efficiency and scalability, as highlighted in Figure 1. The modular design effectively addresses conventional challenges such as computational overhead and interference, enabling robust performance in diverse wireless communication scenarios.
The method begins with the reception of pilot symbols at the wireless communication equipment, such as a base station or user equipment. The received signals are normalized by dividing them by the corresponding known pilot symbols, where this normalization facilitates the removal of potential errors and inconsistencies in the received data. Following normalization, the sequence is projected onto up-converted Kronecker Slepian sequences. This projection process involves generating high-resolution spectral estimates that form the basis for determining critical target parameters such as range, velocity, and angle of arrival. By iteratively refining these spectral estimates, the method narrows the search space for these parameters, enabling accurate detection even in scenarios with multiple targets.
Figure 7 illustrates the flow diagram of the method in accordance with the present disclosure for joint estimation of multi-target state parameters in OFDM wireless systems using Slepian sequences. The method (200) initiates with the reception of pilot symbols (210) at the wireless communication equipment, which serve as reference signals for estimating range, velocity, and angle of arrival of multiple targets. Following this, the received signal is normalized and projected onto Kronecker Slepian sequences (220), enhancing spectral energy concentration and reducing estimation errors associated with spectral leakage.
A stopping criterion is then evaluated based on the L2 norm threshold, ensuring that the iterative refinement process converges to an optimal estimation. If the threshold condition is met, the algorithm proceeds to the next step; otherwise, refinement continues. The method further includes a Slepian cancellation step (230), which iteratively removes the contribution of previously estimated targets, preventing interference in the detection of subsequent targets. Once cancellation is performed, the method enters an iterative loop (240) for handling multiple targets, progressively refining estimates for all detected targets within the observation window. Finally, the method generates target estimates (250), outputting precise values for range, velocity, and angle while ensuring minimal computational complexity. The structured approach of this method enhances estimation accuracy, computational efficiency, and robustness in multi-target environments, making it well-suited for applications in radar, wireless localization, and vehicular tracking
Slepian cancellation is performed at each step to mitigate the influence of the current target on the signal, thereby isolating the signals of interest for subsequent targets. This technique is particularly advantageous in environments with high interference, as it enhances the clarity and reliability of the parameter estimation process. The iterative nature of the method ensures that each step builds upon the results of the previous iteration, with the number of iterations being proportional to the number of detected targets. As each iteration progresses, target estimates are incrementally refined to achieve higher accuracy.
To prevent excessive computations, the iterative estimation process is governed by a stopping criterion based on the L2-norm of the residual signal. When the L2-norm falls below a predefined threshold, the process halts, signifying that the estimates have converged to a satisfactory level of precision. In an alternative embodiment, the method employs down-conversion of the received or residual signals, followed by projection onto the Kronecker Slepian sequence, as a substitute for the up-conversion process. This variation may provide computational advantages in certain applications.
The method is equally applicable to signals received at a base station or at user equipment with prior knowledge of the pilot symbols. For example, in a base station scenario, the OFDM pilot symbols transmitted by the base station are reflected by multiple targets and received as echoes. These echoes are processed to estimate the parameters of the targets. Alternatively, in the user equipment scenario, the received signals are processed directly to determine target characteristics. The versatility of the method extends to its compatibility with various types of OFDM pilot symbols, including but not limited to position signals (PRS), demodulation signals (DMRS), synchronization signal blocks (SSB), and channel state signals (CSI-RS). The inclusion of such diverse signal types broadens the applicability of the method across different communication standards and use cases.
The projection process incorporates one or more basis sequences, such as Discrete Fourier Transform (DFT), oversampled DFT, and Discrete Cosine Transform (DCT). These basis sequences are selected based on their ability to provide robust and efficient transformations for the spectral estimation process. By employing these sequences, the method ensures that the projections are computationally efficient while maintaining high accuracy in the derived estimates.
Joint estimation of parameters such as range, velocity, and angle of arrival is a core aspect of the method. This estimation is performed iteratively, with two parameters being estimated in tandem during each iteration. Once the iterations for the first two parameters are complete, the remaining parameter is estimated using a similar iterative approach. This staged estimation process minimizes computational complexity while ensuring that all parameters are accurately determined. Additionally, the method includes advanced refinement steps, such as dividing the recovered signals by pilot symbols to form a multi-dimensional parameter matrix, generating sub-signals, and performing coarse spectral estimates using multi-dimensional DFT. These refinement steps iteratively modify the search space and apply Slepian sequences to achieve precise target parameter estimates.
The system designed to implement this method comprises multiple modules that work in tandem to achieve the desired functionality. The transceiver module is responsible for transmitting and receiving OFDM pilot symbols and corresponding data signals. It acts as the interface between the wireless communication environment and the processing components of the system. The processor module is central to the system’s operation, performing tasks such as recovering pilot symbols and data signals from the OFDM grid, generating Slepian sequences, and executing matrix and vector operations required for spectral estimation and target parameter computation. These operations include norm computations, dot products, matrix arithmetic, and identifying extremum elements within vectors to refine parameter estimates.
The memory module complements the processor by storing instructions and parameters essential for the method’s execution. These include Kronecker Slepian sequences, thresholds for stopping criteria, and transformation sequences. The integration of these modules ensures that the system operates seamlessly, delivering high-precision parameter estimates with minimal computational overhead.
The iterative and modular design of the method and system addresses the limitations of conventional approaches, offering a robust solution for multi-target parameter estimation in wireless communication systems. By leveraging advanced techniques such as Slepian cancellation, basis sequence projection, and staged parameter estimation, the invention significantly enhances the accuracy, efficiency, and applicability of target parameter estimation processes.
We employ a generalized block reference signal to demonstrate our method’s efficacy in estimating target parameters in the following example.
EXAMPLE 1: Multi-Target Parameter Estimation in OFDM Wireless Systems Using Kronecker Slepian Sequence
In this example, we consider a base station (BS) with P receive antennas placed in a horizontal array with spacing d = 0.5λ. The pilot symbols are structured in a rectangular grid with N sub-carriers across M OFDM symbols.
The baseband OFDM transmits signal corresponding to the mth OFDM symbol is expressed as
s_m (t)=∑_(n=0)^(N-1)▒〖s_m (n) e^(j2πf_n t) rect((t-m¯T)/¯T) 〗.
Here,
s_m (n) represents the pilot symbol for the nth sub-carrier within the m OFDM symbol,
f_n represents the frequency of the nth sub-carrier, and
¯T=T+T_CP is the OFDM symbol duration, where T=1\/Δf defines the time without the cyclic prefix (CP), and T_CP is the CP duration.
The baseband transmit signal for M OFDM symbols is given as s(t)=∑_(m=0)^(M-1)▒〖s_m (t) 〗, which is then up-converted for transmission by the carrier frequency f_c using s ̃(t)=s(t) e^(j2πf_c t), and transmitted over the air.
The echo at the BS is down-converted and processed to obtain the signal of interest:
Z[n,m,p]=∑_(l=0)^(L-1)▒β_l e^(jp2π d/λ "sin" (θ_l ) ) e^(jm2πf_(d,l) ¯T) e^(-jn2πΔfτ_l )+V[n,m,p].
Here,
β_l is the attenuation,
n∈0,1,…,N-1 is the sub-carrier index, m∈0,1,…,M-1 is the symbol index representing time domain, and p∈0,1,…,P-1 is the antenna index,
V[n,m,p] is the AWGN with variance Nσ^2 that forms a tensor V∈C^(N×M×P).
We define Z∈C^(N×M×P) as the 3D tensor containing all values of Z[n,m,p], which represents our signal of interest.
The target parameter estimation involves extraction of the spectral content in Z associated with each target and use these estimates to determine the range, velocity, and azimuth angle of the lth target using (R_l ) ̂=((τ_l ) ̂c)/2, (v_l ) ̂=(c(f_(d,l) ) ̂)/(2f_c ), "and" (θ_l ) ̂=〖"sin" 〗^(-1) (((f_(θ,l) ) ̂λ)/d), respectively.
Here,c refers to the speed of light in free space, with (τ_l ) ̂ and (f_(d,l) ) ̂ as the delay and Doppler estimates for the lth target. We also define (f_(θ,l) ) ̂=d/λ "sin" ((θ_l ) ̂ ), the spectral estimate corresponding to angle.
The most commonly used technique to estimate target parameters is to compute the 3D-DFT of Z.
While DFT is a simpler method, it struggles with accuracy and resolution issues. In particular, the range, velocity, and angle resolutions in the DFT approach are given by ΔR=c/2N(Δf) , Δv=c/(2M¯T f_c ), "and" Δθ≈λ/Pd, respectively.
Moreover, since there is an inverse relationship between parameter resolution and the associated signal dimension, improving resolution requires a greater pilot occupancy, which creates a trade-off between estimation accuracy and pilot overhead. To overcome the drawbacks of the DFT-based estimation method, we introduce an estimation method that employs the Slepian sequences.
Slepian sequences:
Before we describe the proposed method, we discuss the Slepian sequences [3].
We consider the sequence x(n) along with its discrete-time Fourier transform (DTFT) X(f), which is given by X(f)=∑_(n=-∞)^∞▒〖x(n) e^(-j2πfn) 〗.
Here, we consider x(n) as the weights of an FIR filter of length N, aiming to determine the filter that minimizes energy leakage beyond the frequency band [-W,W], with W residing in the interval [0,1\/2]. Thus, we seek the filter that maximizes the ratio λ=(∫_(-W)^W▒〖|X(f)|^2 d〗 f)/(∫_(-0.5)^0.5▒〖|X(f)|^2 d〗 f), which indicates the fraction of energy in a band of interest, and the sequence x(n) thus obtained is referred to as the Slepian sequence.
In other words, Slepian sequence aims to maximize the ratio λ, and when we constrain the indices of the sequence x(n) from 0 to N-1, we get x∈R^N, with x=[x(0);x(1);…;x(N-1)]^T. Therefore, we seek x that maximizes λ=(x^H B_W x)/(x^H x), where B_W (m,n)=("sin" 2πW(m-n))/π(m-n) .
The Rayleigh-Ritz theorem indicates that the sequence maximizing λ is the dominant eigenvector of B_W. We refer to the N-length Slepian sequence as s_(N,W), where W represents the half-width parameter.
Modifying the Slepian sequences to model our signal of interest:
While Slepian sequences are effective for modeling band-limited signals, our signal of interest, Z, is a bandpass signal, specifically a multi-tone signal in scenarios with multiple targets. Additionally, it is a three-dimensional signal.
Therefore, we must adapt the Slepian sequence to accurately model three-dimensional multi-tone signals.
We define s_(N,W)^((f) )=[1 e^j2πf e^j2πf(2) … e^j2πf(N-1) ]^T⊙s_(N,W) as an upconverted Slepian sequence upconverted by f (⊙ here is the element-wise multiplation of vectors).
Further, to model the 3D- signal, we define the Kronecker Slepian sequence as
s ̅_NMP^((f_n,f_m,f_p ) )=(s_(P,W_p)^((f_p ) )⊗s_(P,W_m)^((f_m ) ) )⊗s_(P,W_n)^((f_n ) ).
Our method entails identifying the Kronecker Slepian sequence that exhibits the strongest correlation with z, in other words, to solve (f_n^*,f_m^*,f_p^* )=argmax_(〖 f〗_n,f_m,f_p∈[0,1] ) z^H s ̅_NMP^((f_n,f_m,f_p ) ).
Although the previous equation specifies the search space for f_m, f_n, and f_p as encompassing the full frequency range, we iteratively reduce this search space.
Proposed method:
This multi-target estimation method, built upon Slepian sequences, is presented here, using a 3D matrix, Z ∈ C^(N× M × P) , as input. The matrix is derived by dividing recovered wireless symbols by pilot symbols, where, N refers to the number of sub-carriers occupied by the pilot symbols, M is the number of OFDM slots, and P is the number of receive antennas. Alongside other parameters, Z is utilized, and the method involves the following steps:
Sub-signal creation: Here we create sub-signals of Z, where the (n, m, p)th sub-signal Z∈C^(N×M×P) is defined as Z ̃^((n,m,p) )=Z[nS_N:nS_N+N_s-1,mS_M:mS_M+M_s-1,pS_P:pS_P+P_s-1].
Here, n∈\{0,1,…,N-1\}, m∈\{0,1,…,M-1\}, and p∈\{0,1,…,P-1\} are the sub-signal indices.
The number of sub-signals is given by NMP, where N=⌊(N-N_s)/S_N ⌋+1, M=⌊(M-M_s)/S_M ⌋+1, and P=⌊(P-P_s)/S_P ⌋+1. Here, the terms S_N,S_M and S_P are the corresponding strides.
Finding the initial spectral estimates:
Here, we calculate the 3D-DFT of Z ̃^((n,m,p) ) denoted as (Z_DFT ) ̃^((n,m,p) ). The peak of (Z_DFT ) ̃^((n,m,p) ) corresponds to the coarse initial spectral estimate of the most dominant target, which is further refined in the upcoming steps.
Let k_(N,l)^((n,m,p) )∈\{0, 1, … , N_s-1\}, k_(M,l)^((n,m,p) )∈\{0, 1, … , M_s-1\}, and k_(P,l)^((n,m,p) )∈\{0, 1, … , P_s-1\} denote the DFT peak indices of the (n, m, p)th sub-signal corresponding to the lth target.
Next, based on the peak indices, we form the corresponding spectral ranges F_(N,l,r)^((n,m,p) )=[f_("min" ,N,l,r)^((n,m,p) ),f_("max" ,N,l,r)^((n,m,p) ) ], F_(M,l,r)^((n,m,p) )=[f_("min" ,M,l,r)^((n,m,p) ),f_("max" ,M,l,r)^((n,m,p) ) ], and F_(P,l,r)^((n,m,p) )=[f_("min" ,P,l,r)^((n,m,p) ),f_("max" ,p,l,r)^((n,m,p) ) ]. Here r ∈ {0, 1, . . . , R -1}, where R is the number of updates of the search space, narrowing the search space in each iteration.
The initial boundaries of the search spaces are given by f_("min" ,N,l,0)^((n,m,p) )=(k_(N,l)^((n,m,p) )-1)/N_s , f_("max" ,N,l,0)^((n,m,p) )=(k_(N,l)^((n,m,p) )+1)/N_s , f_("min" ,M,l,0)^((n,m,p) )=(k_(M,l)^((n,m,p) )-1)/M_s , f_("max" ,M,l,0)^((n,m,p) )=(k_(M,l)^((n,m,p) )+1)/M_s , f_("min" ,P,l,0)^((n,m,p) )=(k_(P,l)^((n,m,p) )-1)/P_s , and f_("max" ,P,l,0)^((n,m,p) )=(k_(P,l)^((n,m,p) )+1)/P_s .
Slepian projection and narrowing of the search space:
We form discrete sets S_(N,l,r)^((n,m,p) ), S_(M,l,r)^((n,m,p) ), and S_(P,l,r)^((n,m,p) ) by picking S equally spaced points in the corresponding search spaces described above.
Next, we form a set of modulated Slepian sequences D_(l,r)^((n,m,p) ) represented by D_(l,r)^((n,m,p) )=\{s ̅_(N_s M_s P_s)^((f_n,f_m,f_p ) ):f_n∈S_(N,l,r)^((n,m,p) ),f_m∈S_(M,l,r)^((n,m,p) ),f_p∈S_(P,l,r)^((n,m,p) ) \}, where s ̅_(N_s M_s P_s)^((f_n,f_m,f_p ) ) is a Kronecker Slepian sequence obtained using s ̅_NMP^((f_n,f_m,f_p ) )=(s_(P,W_p)^((f_p ) )⊗s_(P,W_m)^((f_m ) ) )⊗s_(P,W_n)^((f_n ) ).
Then, we project the Kronecker sequences in D_(l,r)^((n,m,p) ) on z ̃_l^((n,m,p) ) to obtain (f_(n,l,r)^*,f_(m,l,r)^*,f_(p,l,r)^* )=argmax_(s ̅∈D_(l,r)^((n,m,p) ) ) (z ̃_l^((n,m,p) ) )^H s ̅, where for the first target (l = 0), z ̃_0^((n,m,p) ) = z ̃^((n,m,p) ).
Next, each search space is updated using the following equations:
f_("min" ,N,l,r+1)^((n,m,p) )=S_(N,l,r)^((n,m,p) ) ("ind" (f_(n,l,r)^* )-1), f_("max" ,N,l,r+1)^((n,m,p) )=S_(N,l,r)^((n,m,p) ) ("ind" (f_(n,l,r)^* )+1),
f_("min" ,M,l,r+1)^((n,m,p) )=S_(M,l,r)^((n,m,p) ) ("ind" (f_(m,l,r)^* )-1), f_("max" ,M,l,r+1)^((n,m,p) )=S_(M,l,r)^((n,m,p) ) ("ind" (f_(m,l,r)^* )+1),
f_("min" ,P,l,r+1)^((n,m,p) )=S_(P,l,r)^((n,m,p) ) ("ind" (f_(p,l,r)^* )-1), and f_("max" ,P,l,r+1)^((n,m,p) )=S_(P,l,r)^((n,m,p) ) ("ind" (f_(p,l,r)^* )+1).
Here, ind(.) returns the index of the argument in the corresponding set.
The above equations do not cover the corner cases when "ind" (f_(m,l,r)^* )=0" or " S-1. In case "ind" (f_(m,l,r)^* )=0 then f_("min" ,M,l,r+1)^((n,m,p) ) is not updated, and when "ind" (f_(m,l,r)^* )=S-1, then f_("min" ,M,l,r+1)^((n,m,p) ) is not updated. Similar procedure is applied when "ind" (f_(n,l,r)^* )" or ind" (f_(p,l,r)^* )=0" or " S-1.
Iterative cancellation:
After R search space updates, we have f_(n,l,R-1)^*, f_(m,l,R-1)^*, and f_(p,l,R-1)^* as the spectral estimates of the lth target corresponding to range, velocity, and angle, respectively.
Before we estimate the next target, we remove the effect of the lth target using
z ̃_(l+1)^((n,m,p) )=z ̃_l^((n,m,p) )-s ̅^((l,r-1) ) (s ̅^((l,r-1) ) )^H z ̃_l^((n,m,p) ), where s ̅^((l,r-1) )=s ̅^((f_(n,l,r-1)^*,f_(m,l,r-1)^*,f_(p,l,r-1)^* ) ).
This filters out the effect of the lth target, and the Slepian sequence ensures that the spectral components corresponding to the other targets do not filter out to a maximum extent. The previous steps namely, i) finding the initial spectral estimates, ii) Slepian projection and search space narrowing, and iii) Iterative cancellation are applied iteratively on z ̃_(l+1)^((n,m,p) ) until all the targets are traversed.
Then the sub-signal estimates are averaged for the corresponding targets.
The performance of the proposed method is compared with the MUSIC method (2D-MUSIC for range and velocity estimates, and MUSIC-DOA for the angle estimates), and the 3D-DFT method. (in Fig 3A to 3C). The parameters used for simulation are shown in the below table 1:
Table 1
Parameter value
Carrier frequency (GHz) 28
Subcarrier spacing (kHz) 120
Sampling time (µs) 8.92
Number of subcarriers 32
Number of OFDM symbols 32
Number of receive antennas 32
Sub-signal size 28
Antenna spacing (m) 0.5λ

From the above, the present disclosure introduces a multi-target state parameter estimation method in OFDM wireless systems, leveraging Kronecker Slepian sequences to overcome the limitations of conventional DFT and MUSIC-based techniques. The method efficiently extracts range, velocity, and angle of arrival parameters by iteratively refining spectral estimates and performing interference cancellation through modulated Slepian sequences. By employing a structured search space narrowing approach, the method enhances estimation accuracy while maintaining computational efficiency, making it highly effective in multi-target detection scenarios. The simulation results confirm that the proposed method outperforms traditional techniques, achieving lower RMSE values and improved resolution, particularly in high-density target environments. This innovation enables precise multi-dimensional spectral analysis, ensuring robust performance in radar, vehicular tracking, and wireless communication applications.
Figure 1 illustrates a schematic representation of a system designed for joint estimation of multi-target state parameters in an Orthogonal Frequency Division Multiplexing (OFDM) wireless system. The system comprises a transceiver module, a processor module, and a memory module, each configured to execute computational operations essential for multi-target estimation. The transceiver module is responsible for transmitting and receiving OFDM pilot symbols, while the processor module processes these signals to perform spectral estimation and parameter extraction. The memory module stores Kronecker Slepian sequences, transformation matrices, and precomputed threshold values for iterative spectral refinement. The system architecture effectively enables high-accuracy estimation of parameters such as range, velocity, and angle of arrival through an iterative processing framework that enhances computational efficiency and robustness in multi-target environments.
Figure 2 illustrates the methodological flow diagram for joint estimation of multi-target state parameters using Slepian sequences. The process initiates with the reception of pilot symbols at the wireless communication equipment, such as a base station (BS) or user equipment (UE). The received symbols are then normalized by dividing them by known pilot symbols, thereby mitigating channel distortions and noise artifacts. Following this, the signal undergoes projection onto up-converted Kronecker Slepian sequences, enabling high-resolution spectral estimation. The method further involves iterative spectral refinement, where the search space is progressively narrowed based on spectral peaks detected in each iteration. Slepian cancellation is performed to mitigate interference from previously detected targets, ensuring that subsequent estimates remain unaffected by earlier detections.
Figure 3A presents a comparative analysis of Root Mean Square Error (RMSE) performance for range estimation across varying Signal-to-Noise Ratios (SNRs). The proposed Slepian sequence-based estimation method exhibits significantly lower RMSE values compared to conventional techniques such as 3D-DFT and MUSIC-based estimation methods. The results indicate that as SNR increases, the accuracy of range estimation improves, with the proposed method achieving performance closer to the root Cramer-Rao bound. The iterative refinement and projection onto optimized basis functions contribute to improved precision and reduced spectral leakage, enhancing estimation reliability in noisy environments.
Figure 3B presents the RMSE performance for velocity estimation, demonstrating a similar trend observed in range estimation. The proposed Kronecker Slepian sequence-based method maintains lower RMSE values across varying SNR levels, indicating superior velocity estimation accuracy. The method’s ability to adaptively refine spectral peaks through iterative processing results in minimized estimation error, especially at low SNRs where conventional DFT-based methods suffer from resolution limitations. Additionally, the use of Slepian sequences ensures optimal spectral concentration, mitigating the effects of spectral leakage and noise artifacts that commonly degrade performance in high-multipath environments.
Figure 3C showcases RMSE performance for angle estimation, further validating the effectiveness of the proposed estimation framework. The angle estimation accuracy is significantly improved due to the narrowed search space enabled by iterative spectral refinement. Unlike conventional techniques that exhibit fluctuating RMSE trends at low SNRs, the proposed method ensures consistent and stable estimation by leveraging high-resolution Slepian basis functions. The results confirm that the method effectively reduces angular uncertainty, enabling precise estimation of target directionality in cluttered environments where conventional techniques typically fail.
Figure 4A illustrates the estimation error variation with target index, analyzing the method’s accuracy across multiple targets in the field of view. The results indicate that the RMSE does not increase significantly for targets further from the base station, demonstrating the method’s ability to maintain consistent estimation performance across spatially distributed targets. The adaptive search space refinement ensures that later-estimated targets do not suffer from residual interference caused by previously detected targets, an issue that frequently affects DFT-based multi-target estimation approaches.
Figure 4B presents a comparison between estimated target parameters and the ground truth, confirming that the proposed method provides estimates that closely align with actual target values. Even in scenarios involving closely spaced targets, the proposed method maintains a clear separation between detected targets, ensuring that interference from neighboring targets does not distort parameter estimation. This performance improvement is attributed to iterative spectral refinement and the optimal energy concentration properties of Slepian sequences, which mitigate the effects of overlapping frequency components that often degrade multi-target estimation accuracy in dense environments.
Figure 5A illustrates the spectrum of the first detected target, showcasing a clear spectral peak corresponding to the target’s range, velocity, and angle estimates. The peak appears at the expected frequency bin, indicating that the search space refinement process successfully converged to the target’s actual parameters. The figure further confirms that the spectral leakage effect is minimal, owing to the high energy concentration of Slepian sequences, which prevents the spread of spectral energy across unrelated frequency bins.
Figure 5B depicts the effect of iterative cancellation on target estimation, showing how removing the influence of the first detected target reveals the second target’s spectral signature. The iterative cancellation step, applied as per the proposed method, eliminates interference from previously detected targets, ensuring that subsequent targets can be estimated with minimal spectral distortion. The results indicate that after cancellation, the second target’s spectral peak becomes more pronounced, confirming the method’s ability to successfully isolate multiple targets within the same observation window.
Figure 5C further extends the iterative cancellation process to a third target, demonstrating that as previously detected targets are progressively removed, the remaining spectral content corresponds exclusively to the next target in the sequence. The results confirm that the method effectively isolates individual target contributions, preventing spectral overlap and ensuring that each target’s parameters are estimated with high accuracy. This approach overcomes the fundamental limitations of conventional DFT-based methods, which suffer from interference accumulation and reduced estimation accuracy in multi-target scenarios. The performance improvements achieved through Slepian sequence projection and iterative cancellation position the proposed method as a highly effective solution for real-time multi-target estimation in OFDM-based wireless systems.
From Figures 1 to 5C, the present invention demonstrates a novel method and system for joint estimation of multi-target state parameters in Orthogonal Frequency Division Multiplexing (OFDM) wireless systems using Slepian sequences. The extraction of the invention, as observed from the detailed analysis of the figures, confirms several technical advancements and novel aspects over existing methods.
In a preferred embodiment of the present disclosure, a system and method for joint estimation of multi-target state parameters in OFDM wireless systems using Slepian sequences, significantly enhancing estimation accuracy and computational efficiency. By integrating signal normalization, projection onto Kronecker Slepian sequences, iterative spectral refinement, and interference mitigation through Slepian cancellation, the invention effectively isolates multiple targets while minimizing spectral leakage and estimation errors. The method ensures that range, velocity, and angle of arrival are estimated with high precision, overcoming the resolution limitations of traditional DFT and MUSIC-based methods. The system architecture, comprising a transceiver module, processor module, and memory module, enables real-time processing, allowing for high-resolution spectral estimation even in noisy and multi-target environments.
A key feature of the present disclosure is its iterative cancellation mechanism, which ensures that each detected target is sequentially removed, thereby preventing interference in the estimation of subsequent targets. This allows for clear separation between closely spaced targets and ensures that the accuracy of parameter estimation remains unaffected by residual spectral interference. Additionally, the proposed method achieves near-optimal performance relative to the Cramer-Rao bound, validating its effectiveness in real-world applications such as radar, vehicle tracking, and wireless localization. The combined advancements in multi-dimensional spectral estimation, adaptive search space narrowing, and interference suppression position the present invention as a highly robust and scalable solution for the next-generation OFDM-based wireless communication systems.
The implementations described in the foregoing description are not exhaustive and do not represent all possible implementations consistent with the subject matter disclosed herein. While certain variations have been detailed, other modifications, adaptations, or enhancements are possible within the scope of the invention. For instance, the disclosed features may be combined or sub-combined in various ways to achieve the intended functionality. Additionally, the logic flows described or depicted in the figures are not restricted to the specific sequences presented and may be executed in alternative orders to achieve similar results. The scope of the invention is defined solely by the appended claims and encompasses all such variations and equivalents.
, Claims:1. . A method (200) for joint estimation of multi-target state parameters in an Orthogonal Frequency Division Multiplexing (OFDM) wireless system, comprising:
receiving pilot symbols (210) at the wireless communication equipment;
projecting the normalized sequence (220) by dividing the received signals by the corresponding known pilot symbols onto up-converted Kronecker Slepian sequences to iteratively determine spectral estimates by narrowing the search space, adaptively refining frequency bins, and estimating target parameters including at least range, velocity, and angle;
performing Slepian cancellation (230) to mitigate the effect of the current target from the signal, ensuring residual spectral components do not interfere with subsequent target estimations;
repeating steps (220) to (230) for a predetermined number of iterations, where the number of iterations is equal to the number of detected targets, thereby generating target estimates (250).
2. The method (200) as claimed in claim 1, wherein the iterative estimation process is terminated based on a stopping criterion (220), which halts the iterations when the L2-norm of the residual signal, following Slepian cancellation (230), falls below a predefined threshold.
3. The method (200) as claimed in claim 1, wherein the process of projecting the received pilot symbols or residual signals onto an up-converted Kronecker Slepian sequence (220) is substituted with a method involving down-conversion of the received or residual signals and subsequent projection onto the Kronecker Slepian sequence.
4. The method (200) as claimed in claim 1, wherein the base station transmits the OFDM pilot symbols, and the method is applied on the echo received at the base station due to multiple targets.
5. The method (200) as claimed in claim 1, wherein the base station transmits the OFDM pilot symbols, and the method is applied on the signal received at the user equipment having knowledge of the pilot symbols.
6. The method (200) as claimed in claim 1, wherein the pilot symbols are selected from the group consisting of position signals (PRS), demodulation signals (DMRS), synchronization signal blocks (SSB), channel state signals (CSI-RS), or any combination thereof.
7. The method (200) as claimed in claim 1, wherein the sequences are projected onto one or more basis sequences (220), selected from the group consisting of Discrete Fourier Transform (DFT), oversampled DFT, Discrete Cosine Transform (DCT), up-converted Slepian sequences, or any other known basis sequences.
8. The method (200) as claimed in claim 1, wherein joint estimation of two parameters selected from the group consisting of range, velocity, and angle of arrival is performed, where the estimation process of the two parameters is conducted iteratively in tandem until a predetermined number of iterations is completed, and subsequently, the remaining third parameter is separately estimated using a similar iterative approach.
9. The method (200) of estimating multiple target parameters in a wireless communication system, as claimed in claim 1, further comprising the steps of:
dividing the recovered wireless signals by pilot symbols to form a multi-dimensional parameter matrix Z, where the dimensions correspond to the number of estimation parameters;
generating sub-signals from the multi-dimensional parameter matrix Z;
computing the multi-dimensional Discrete Fourier Transform (DFT) of each sub-signal to obtain coarse initial spectral estimates, which are subsequently refined using Kronecker Slepian sequences;
iteratively modifying the search space for the target parameters based on the spectral estimates derived in the previous step;
refining the estimation of the target parameters using Slepian sequences by projecting the residual parameter vector onto each iterative modification.
10. A system comprising:
at least one transceiver module;
at least one processor module;
at least one memory module configured to store instructions executable by the processor module,
wherein the instructions, when executed, cause the processor module to:
(a) recover pilot symbols and data signals from an Orthogonal Frequency Division Multiplexing (OFDM) grid;
(b) generate Slepian sequences;
(c) perform matrix and vector operations required for spectral estimation and target parameter computation;
(d) create sub-signals from the multi-dimensional parameter matrix and iteratively refine target spectral estimates using computationally efficient search space reduction.
11. The system as claimed in claim 10, wherein the processor module having the matrix and vector operations includes computing norm, dot product, and executing matrix arithmetic operations.