Deterministic pilot pattern allocation optimization for sparse channel estimation based on CS theory in OFDM system
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Abstract
Compressed sensing (CS)-based sparse channel estimation requires the sensing matrix with the minimum mutual coherence (MC), and its corresponding pilot pattern obtain optimal estimation performance. In order to minimize the MC of the sensing matrix, a deterministic optimized pilot pattern allocation scheme based on modified adaptive genetic algorithm (MAGA) is investigated in this paper. By adjusting the probability of mutation and crossover adaptively, the proposed scheme guides the search process to obtain the optimized pilot pattern. This method guarantees the convergence of the optimization process and prevents the process into local optimization to get the global optimization. Compared with the existing methods, simulation results prove that the proposed scheme obtain the sensing matrix with the smaller MC, whose corresponding deterministic pilot pattern effectively improve channel estimation performance.
Keywords
Sparse channel estimation Pilot pattern Mutual coherence Compressed sensingAbbreviations
- AGA
Adaptive genetic algorithm
- BER
Bit error rate
- CS
Compressed sensing
- CSI
Channel state information
- GA
Genetic algorithm
- MAGA
Modified adaptive genetic algorithm
- MC
Mutual coherence
- MSE
Mean square error
- OFDM
Orthogonal frequency division multiplexing
- OMP
Orthogonal matching pursuit
- RIP
Restricted isometry property
1 Introduction
Orthogonal frequency division multiplexing (OFDM) is utilized to resist multipath fading for good performance in wireless communication systems. The coherent demodulation and channel equalization of the receiver all need precise channel state information (CSI) and therefore the channel estimation plays a crucial role. In recent years, compressed sensing (CS) has become an innovative signal processing and acquiring theory by solving optimization problems [1, 2, 3]. Comparing the traditional scheme, CS-based sparse channel estimation gets the utmost out of the inherent sparse characteristics of the channel to perform the channel estimation. This method can obtain accurate CSI with much fewer pilots, and increase the spectrum utilization while improving the channel estimation performance [4].
To channel estimation scheme based on CS, the channel impulse response (CIS) is reconstructed by the orthogonal matching pursuit (OMP) algorithm, when pilots are randomly distributed in the subcarriers of the OFDM system [5]. If the position of the pilot pattern is randomly selected, the corresponding sensing matrix is a random structure and the restricted isometry property (RIP) is easy to be satisfied. If the pilot pattern location is fixed, the sensing matrix is deterministic and needs to be carefully designed to satisfy RIP. However, a direct and effective method to determine whether the sensing matrix satisfies RIP has not been proposed, and computing the mutual coherence (MC) of the sensing matrix is a good alternative [6]. We utilize the minimum MC as the criterion for optimizing the allocation of pilot patterns to perform channel estimation based on CS. However, it is unrealistic to blindly search the optimal pilot pattern in the actual communication system. Therefore, it is meaningful to establish an effective pilot pattern allocation optimization method.
Pilot pattern optimization allocation methods have been presented respectively to get the optimal pilot pattern for sparse channel estimation [7, 8, 9]. However, these methods are essentially random search. To overcome the disadvantages of random search, genetic algorithm (GA) was introduced to optimize the pilot pattern by updating the individual to find the suboptimal pilot pattern [10]. Nevertheless, this method requires the probability of mutation and crossover of being continuously verified to find a suitable value, and it is extremely difficult to select the best value for various optimization problems.
In this paper, modified adaptive genetic algorithm (MAGA)-based pilot pattern allocation optimization scheme is proposed for OFDM sparse channel estimation based on CS Theory. In MAGA, the probability of mutation and crossover is adjusted adaptively by individual fitness. If the solution set has a tendency to trap in local optimal, the probability of mutation and crossover is improved adaptively. If the solution set is scattered in the solution space, the probability of mutation and crossover is reduced adaptively. Therefore, the pilot pattern optimization scheme based on MAGA can greatly guarantee the convergence accuracy of the pilot pattern search process, and effectively avoid obtaining the local optimal solution.
The remainder of this paper is structured as follows. We establish the CS-based channel estimation model, and transform it into an optimization problem in Section 2. The innovative contribution of this work is detailed in Section 3, where MAGA-based pilot pattern allocation optimization scheme is presented and applied to solving the optimization problem. In Section 4, the numerical results of computer simulation are performed to verify the performance of the proposed scheme. Finally, Section 5 generalizes the main conclusion of this paper.
2 CS-based channel estimation optimization problem
Since the sampled interval is usually much smaller than the channel delay propagation, the channel coefficients are either zero or nearly zero, which implies that h is a sparse vector. According to the CS theory, the matrix A can be regarded as the sensing matrix, and it is essentially the weight of the transmitted pilot signal to the partial Fourier matrix. If the placement of the pilot pattern is randomly selected, the matrix A is a structured random matrix weighted by the transmitted pilot. Correspondingly, if the placement of the pilot pattern is deterministic, it is a deterministic sensing matrix. Therefore, the process of channel estimation based on CS is explained that the transmitted pilot is compressed to measure the impulse response h, and then h is reconstructed by the reconstruction algorithm with the received pilots. Moreover, it can clearly be seen from (3) that the pilot pattern decides the extraction of those rows of the standard Fourier transform matrix, and then determines the structure of the sensing matrix, and ultimately affects the performance of OFDM channel estimation. If the allocation of the pilot pattern is random, the corresponding sensing matrix is the structured random matrix. However, the pilot subcarrier with random distribution is not easy to be realized in the actual communication system. Therefore, it is necessary to study the deterministic sensing matrix with optimizing pilot pattern allocation so as to ensure the channel estimation performance.
It can be seen from (7) that the MC of matrix A is determined by the pilot pattern K, when the number of subcarrier and pilot has been determined.
3 Method: MAGA-based pilot pattern optimization
If the enumeration method is selected for searching the optimal pilot pattern, the computation complexity is huge. Therefore, a new pilot pattern optimization method is of great necessity. This method can quickly solve the combinatorial optimization problem (8) by adaptive adjustment of genetic operators, and then the optimized pilot pattern is acquired for efficient detection of sparse channels.
3.1 MAGA
Genetic algorithm (GA) is an intelligent optimization algorithm inspired by natural evolution. This algorithm applies the selection, mutation, and crossover to obtain the new population, which gradually evolves to get the optimal solution. Mutation probability and crossover probability largely determine the accuracy and convergence speed in the optimization process. If the value of the crossover probability is larger, the production rate of new individuals in the population will be accelerated, and the destruction possibility of individuals with high fitness will be increased. If the crossover probability is smaller, the search time of the algorithm will become longer or even pause. Furthermore, if the mutation probability is larger, the algorithm becomes random search. If the value is smaller, the new population is not easy to generate. Therefore, how to determine mutation probability and crossover probability is very important in the GA. On the other hand, mutation probability and crossover probability often need to be repeatedly verified by manual experience. Therefore, it is hard to select the appropriate value for different optimization problems.
Adaptive genetic algorithm (AGA) was proposed in order to perfect genetic algorithm [11]. In the AGA, mutation probability and crossover probability are adaptively obtained by the individual fitness. If the solution has the local optimal tendency, mutation probability and crossover probability will be increased adaptively. For excellent individuals, we should reduce the probability of crossover and the probability of mutation to protect them. For inferior individuals, we should increase the probability of crossover and the probability of mutation to change them. Therefore, for the optimization problem based on adaptive genetic algorithm, mutation probability, and crossover probability are obtained adaptively, which effectively ensures the convergence of the optimization and enlarges the population diversity. However, the AGA is suitable for later evolution of population. This is because the individual performance of the population is excellent, so we should protect the chromosomal structure from being destroyed [12]. In the early stage of evolution, the individuals with good performance will hardly change. This will not be conducive to the evolution process, and will easily cause the solution to trap in local optimum [13].
3.2 MAGA-based pilot pattern optimization method
Then, the genetic operators are adaptive to complete mutation and crossover to get the new population based on the MAGA. The whole optimization process is repeatedly iterated until the stop condition is satisfied. Finally, the individual with the greatest fitness is selected for the output of the optimization process, which is the suboptimal deterministic pilot pattern.
4 Results and discussion
System-related parameters
Parameters | Value |
---|---|
OFDM sample period | T = 83.3 μs |
OFDM symbol period | T_{u} = 21.33 ms |
Guard interval | T_{g} = 5.3 ms |
FFT length | N = 256 |
Number of channel multipath | S = 4 |
Modulation | 4QAM |
Number of pilot | M = 26 |
SNR | 0–30 dB |
Optimized pilot patterns by MAGA, GA, and random
Type | MC | Running time (s) | Optimized pilot pattern |
---|---|---|---|
Random | 0.2045 | 570.65 | 4, 9, 20, 25, 34, 38, 65, 70, 75, 83, 91, 104, 125, 130, 135, 149, 171, 178, 187, 188, 194, 202, 211, 219, 226, 248 |
GA | 0.1812 | 140.53 | 20, 26, 42, 53, 56, 64, 72, 77, 79, 85, 101, 107, 114, 119, 128, 146, 151, 156, 160, 173, 197, 208, 216, 223, 228, 244 |
MAGA | 0.1399 | 310.41 | 4, 16, 31, 39, 46, 54, 61, 75, 92, 100, 107, 113, 135, 142, 160, 168, 176, 183, 191, 197, 205, 211, 221, 229, 246, 253 |
5 Conclusion
CS is an innovative theory for efficiently processing and acquiring data by solving an underdetermined linear equation. CS-based sparse channel estimation can reconstruct channel impulse response with less pilot signals to solve the optimization problem, which are far fewer than those required by the sampling theory. This method has shown the advantages of increasing the estimation performance and reducing the pilot number by taking advantage of the inherent sparse characteristics of wireless channels. According to the CS theory, the smaller MC of the sensing matrix is beneficial to enhance estimation performance. An optimal scheme of deterministic pilot pattern allocation based on MAGA is proposed in this paper, which aims at minimizing the MC of the sensing matrix to pilot pattern. The proposed scheme can adaptively acquire the mutation probability and the crossover probability, and guide the optimization process to generate a near-optimal deterministic pilot pattern. The results of computer simulation prove that the proposed method is able to obtain a smaller MC sensing matrix compared with the existing schemes, and the estimation performance with the optimized pilot pattern is substantially improved for the OFDM sparse channel estimation based on CS theory.
Notes
Acknowledgements
Engineering Research Centre of Digital Audio and Video Ministry of Education, Communication University of China and Key Laboratory of High Speed Signal Processing and Internet of Things Technology Application, Jining Normal University.
Funding
This work was supported by Fundamental Research Funds for the Central Universities (Grant: 3132017XNG17), National Key Technology Research and Development Program of the Ministry of Science and Technology of China (Grant:2015BAK05B01),Research Program of Science and Technology at Universities of Inner Mongolia Autonomous Region (Grant: NJZY18232), and Research Fund for the Doctoral Program of Jining Normal University (Grant: jsbsjj1801).
Availability of data and materials
Not applicable.
Authors’ contributions
YN is the main contributor and author of this paper. He presented the main idea, formulated the model of channel estimation, accomplished simulation experiment, and analyzed the experimental result. XY completed the OMP algorithm. ZY proposed some meaningful suggestions for sparse channel estimation. All authors read and approved the final manuscript.
Competing interests
The authors declare that they have no competing interests.
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
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