Journal of information and communication convergence engineering 2022; 20(2): 73-78
Published online June 30, 2022
https://doi.org/10.6109/jicce.2022.20.2.73
© Korea Institute of Information and Communication Engineering
Correspondence to : Rong Ran (E-mail: sunnyran@ajou.ac.kr, Tel: +82-31-217-2375)
Department of Electrical and Computer Engineering, Ajou University, Suwon 16499, Republic of Korea.
This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0/) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
Based on experimental measurements conducted on many different practical wireless communication systems, ambient noise has been shown to be decidedly non-Gaussian owing to impulsive phenomena. However, most multiuser detection techniques proposed thus far have considered Gaussian noise only. They may therefore suffer from a considerable performance loss in the presence of impulsive ambient noise. In this paper, we consider a large-scale multiuser multiple-input multiple-output system in the presence of non-Gaussian noise and propose a genetic algorithm (GA) based detector for large-dimensional multiuser signal detection. The proposed algorithm is more robust than linear multi-user detectors for non-Gaussian noise because it uses a multidirectional search to manipulate and maintain a population of potential solutions. Meanwhile, the proposed GA-based algorithm has a comparable complexity because it does not require any complicated computations (e.g., a matrix inverse or derivation). The simulation results show that the GA offers a performance gain over the linear minimum mean square error algorithm for both non-Gaussian and Gaussian noise.
Keywords MIMO Systems, Genetic Algorithm, Multiuser Detection, Non-Gaussian Noise
Using tens to hundreds of antennas for transmitters and receivers, a large-scale multiuser multiple-input multiple-output (MIMO) system offers a much higher spectral efficiency than conventional MIMO systems [^{1}, ^{2}]. It has therefore attracted considerable attention and is regarded as one of the key technologies for 5G wireless communication. However, it also poses a big challenge for detecting signals with large dimensions.
The current existing optimal detectors (e.g., maximum likelihood or maximum a posterior (MAP)) and nonlinear detectors (e.g., sphere decoding) are impractical for implementation because of the prohibitive complexity caused by the extremely large signal dimension. By contrast, although linear detectors (e.g., zero forcing (ZF) and MMSE) are simple to implement, the performance achievable is usually far from optimal. Other detectors, such as sparse-aware detectors [^{3}, ^{4}], have been proposed to achieve a better trade-off between complexity and performance. Most current detectors are largely dominated by the widespread use of additive Gaussian noise assumptions. However, it is well known that in many practical communication channels, such as indoor and urban radio channels, ambient noise is largely impulsive in nature, which can adversely affect the performance of conventional receivers optimized for Gaussian noise [^{5}, ^{6}]. Conventional linear and nonlinear multiuser detectors, which are derived according to the Gaussian noise assumption, may suffer considerable performance losses in the presence of non-Gaussian noise. It is therefore necessary to design a robust multiuser detector that can combat the effects of random impulses introduced through non-Gaussian noise. Therefore, in this study, we propose a genetic algorithm (GA) based multiuser detector. The main contributions of this study are summarized as follows:
The GA is a heuristic search algorithm inspired by the genetic mechanisms of species evolution [^{7}]. The algorithm works well even for nonlinear programming problems and has been successfully applied to signal processing [^{8}]. To the best of our knowledge, few studies have been conducted on the implementation of the GA in large-scale MIMO systems for multiuser detection. This is the first study applying the GA technique to multiuser detection in a large-scale MIMO system in the presence of non-Gaussian noise.
On the one hand, the GA-based detector follows a multiple-directional search approach in which many peaks are searched in parallel, thereby reducing the possibility of local minimum trapping. Consequently, the GA-based detector may perform better than other conventional signal detectors in the presence of non-Gaussian noises. On the other hand, the GA only needs to evaluate the objective function (or fitness function) to guide its search, which means there is no requirement for a matrix inverse or derivation, among other factors. Therefore, the complexity of GA-based multi-user detection is comparable to that of conventional linear detectors.
An imperfect channel is also considered in this study. We observed that the GA-based detector works efficiently under practical scenarios.
The remainder of this paper is organized as follows. The system model is introduced in Section II. In Section III, we present a GA-based multi-user detector for large-scale MIMO systems. The numerical results are presented in Section IV. Finally, we provide some concluding remarks in Section V.
Consider an uplink multiuser MIMO system consisting of one base station equipped with M antennas and
where,
where 0 ≤
Given system model (1), the MAP detector is the optimal detector used for detecting the transmitted symbol vector x, and is expressed as
With Gaussian noise and the equal prior probability of x assumptions, the MAP detector (3) can be equivalently expressed as
The least squares detector, where ||x||^{2} is the
However, for most practical wireless channels, such as urban, indoor radio, and underwater acoustic channels, the ambient noise is known through experimental measurements to be non-Gaussian owing to the impulsive nature of man-made electromagnetic interference and a large amount of natural noise. In single-user wireless systems, it is widely known that non-Gaussian noise can be detrimental to the performance of conventional systems based on the Gaussian noise assumption. It is therefore unsurprising that linear and non-linear multiuser detectors lack robustness to many types of non-Gaussian statistical behaviors. An early study on the bit error rates (BERs) in non-Gaussian direct-sequence code-division multiple-access (CDMA) channels showed that the performance of conventional multiuser detectors depends heavily on the distribution of ambient noise [^{10-12}]. From the results illustrated in Fig. 1, we observe that the performance of the MMSE detector is degraded by non-Gaussian noise. The larger the non-Gaussian noise parameter
In this study, we consider the GA technique, which is a heuristic and stochastic optimization approach, and offers more promising alternatives. Compared with other conventional detectors, the GA may be the most robust in several respects. First, the
GA is a multi-directional search method that seeks many peaks in parallel and can reduce the possibility of local minimum trapping. Second, instead of the optimization function, the GA evaluates the fitness of each signal vector to guide its search. In other words, the GA does not require any advanced computations such as a matrix inverse (which is required by ZF and MMSE detectors). Finally, the GA explores the search space in which the probability of finding the best solution is high. Although the GA requires extremely intensive computations, the development of supercomputing resources makes it a good candidate for most optimization problems. The standard GA allows us to make modifications to suit the design requirements for a given environment. In this paper, considering large-scale MIMO systems, some specific modifications to the chromosome representation, initialization, fitness function, GA parameters, and termination conditions are introduced.
A chromosome encoding scheme may vary according to the nature of the problem, and because it can severely limit the search space observed by the system, it has a major impact on the performance. In the GA-based multiuser detector, the detected symbol
In general, the population of chromosomes
Because it evaluates the fitness of each chromosome, and to achieve a good performance, should guarantee that only the high-quality chromosomes are passed through to the next generation, the fitness function plays a critical role in the GA-based detector. By convention, a fitness function should have a positive value. In this study, in the presence of non-Gaussian noise, detecting the transmitted signal should minimize the difference between the original received signal and the transmitted signal multiplied by the channel coefficients, as given in (5), where
Termination is the criterion by which the GA decides whether to continue or stop a search. With the proposed GA-based detector, the number of iterations required to reach a predefined penalty function is not known in advance, and we adopt the strategy of reaching the maximum generations to avoid an excessively high complexity and detection delay.
The main procedure used for the GA-based detector is shown in Fig. 2. The GA-based detector simulates the evolutionary process by generating an initial population of candidates
where,
In this section, the simulation results are presented to verify the robustness of the GA-based detector for large-scale MIMO systems. BPSK is considered a modulation scheme, such as
Table 1 . Summary of GA parameters.
Parameters | Value |
---|---|
Population size | 60 |
Generation | 50 |
Crossover Probability | 0.88 |
Mutation probability | 0.08 |
Turning parameter | 0.5 |
In Fig. 3, we compare the performances of the conventional MMSE and GA-based detectors in the presence of different non-Gaussian noise distributions for a 64 × 32 MIMO system. We observed that the GA-based detector achieves a better performance than the MMSE for different non-Gaussian noise distributions. More specifically, at BER = 0.01, a performance gain of approximately 1 dB can be achieved using the GA-based detector when
The effects of different MIMO architectures are shown in Fig. 4. From the simulation results, we can observe that the GA-based algorithm always achieves a better performance than the conventional MMSE. Moreover, we observed that the less over-determined the massive MIMO is, the greater the performance gain achievable by the GA. More specifically, at BER = 0.01, the GA increases by approximately 0.3, 0.4, and 0.6 when the massive MIMO size is 64 × 20, 64 × 32, and 64 × 48, respectively. This is reasonable because when the large-scale MIMO system is overdetermined (e.g., 64 × 20), the MMSE approaches the optimal detector, and the performance gain achievable by the GA is limited.
Finally, we verify the behavior of the GA when considering imperfect channel state information (CSI). In this case, we apply the following imperfect channel model [^{14}, ^{15}]:
where, E is the estimation error uncorrelated with H, the entries of E are
In addition to the better performance achievable by the GA-based detector, as another advantage, it does not require any advanced computations, such as a matrix inverse, which is required by the MMSE, and is usually a significant burden for large-scale MIMO systems. Therefore, the GA-based detector may achieve a complexity comparable to that of the MMSE. In Fig. 6, we can see that for both the 64 × 20 and 64 × 32 MIMO systems, the GA-based detector requires a slightly larger average execution time in comparison to the MMSE. However, for the 64 × 48 MIMO system, the average execution time of the GA was less than that of the MMSE, which is due to the main complexity of the MMSE being derived from a matrix inverse. Therefore, the larger the sizes of the MIMO systems, the higher their complexity. Whereas the GA-based detector only needs to calculate the fitness function without any other complicated computations, the complexity of the GA is dominated by the number of iterations rather than the size of the MIMO system. It is therefore reasonable for the complexity of the GA-based detector to be lower than that of the MIMO system when the number of users is close to the number of antennas at the BS.
Non-Gaussian noise can significantly degrade the performance of current linear multiuser detectors applied in many practical wireless channels. In this paper, we presented a GA-based multiuser detector for large-scale MIMO systems in the presence of non-Gaussian noise. The simulation results show that the proposed GA-based detector is efficient in combating non-Gaussian noise. In addition, unlike the MMSE, which requires computations of the matrix inverse, the GA-based detector only needs to calculate the simple fitness function and can therefore achieve a comparable complexity. However, because the GA is a heuristic algorithm, the possibility of convergence depends heavily on the initializations and operator parameters. Therefore, in our future research, we might consider applying deep learning to refine the initializations for achieving a faster convergence and further performance improvement.
This work was supported by the Ajou Research Fund.
received her PhD at Yonsei University in 2009. In 2009, she joined ETRI, Daejeong and worked on IEEE 802. 16 m standardization. She was a research associate at Hongkong University of Science and Technologies in 2010. Since 2014, she has been a faculty member of the Electrical and Computer Engineering Department in Ajou University. She was elevated to IEEE senior member in 2022. Her current research interests include sparse signal processing, massive MIMO, and machine/deep learning.
Journal of information and communication convergence engineering 2022; 20(2): 73-78
Published online June 30, 2022 https://doi.org/10.6109/jicce.2022.20.2.73
Copyright © Korea Institute of Information and Communication Engineering.
Department of Electrical and Computer Engineering, Ajou University, Suwon 16499, Republic of Korea
Correspondence to:Rong Ran (E-mail: sunnyran@ajou.ac.kr, Tel: +82-31-217-2375)
Department of Electrical and Computer Engineering, Ajou University, Suwon 16499, Republic of Korea.
This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0/) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
Based on experimental measurements conducted on many different practical wireless communication systems, ambient noise has been shown to be decidedly non-Gaussian owing to impulsive phenomena. However, most multiuser detection techniques proposed thus far have considered Gaussian noise only. They may therefore suffer from a considerable performance loss in the presence of impulsive ambient noise. In this paper, we consider a large-scale multiuser multiple-input multiple-output system in the presence of non-Gaussian noise and propose a genetic algorithm (GA) based detector for large-dimensional multiuser signal detection. The proposed algorithm is more robust than linear multi-user detectors for non-Gaussian noise because it uses a multidirectional search to manipulate and maintain a population of potential solutions. Meanwhile, the proposed GA-based algorithm has a comparable complexity because it does not require any complicated computations (e.g., a matrix inverse or derivation). The simulation results show that the GA offers a performance gain over the linear minimum mean square error algorithm for both non-Gaussian and Gaussian noise.
Keywords: MIMO Systems, Genetic Algorithm, Multiuser Detection, Non-Gaussian Noise
Using tens to hundreds of antennas for transmitters and receivers, a large-scale multiuser multiple-input multiple-output (MIMO) system offers a much higher spectral efficiency than conventional MIMO systems [^{1}, ^{2}]. It has therefore attracted considerable attention and is regarded as one of the key technologies for 5G wireless communication. However, it also poses a big challenge for detecting signals with large dimensions.
The current existing optimal detectors (e.g., maximum likelihood or maximum a posterior (MAP)) and nonlinear detectors (e.g., sphere decoding) are impractical for implementation because of the prohibitive complexity caused by the extremely large signal dimension. By contrast, although linear detectors (e.g., zero forcing (ZF) and MMSE) are simple to implement, the performance achievable is usually far from optimal. Other detectors, such as sparse-aware detectors [^{3}, ^{4}], have been proposed to achieve a better trade-off between complexity and performance. Most current detectors are largely dominated by the widespread use of additive Gaussian noise assumptions. However, it is well known that in many practical communication channels, such as indoor and urban radio channels, ambient noise is largely impulsive in nature, which can adversely affect the performance of conventional receivers optimized for Gaussian noise [^{5}, ^{6}]. Conventional linear and nonlinear multiuser detectors, which are derived according to the Gaussian noise assumption, may suffer considerable performance losses in the presence of non-Gaussian noise. It is therefore necessary to design a robust multiuser detector that can combat the effects of random impulses introduced through non-Gaussian noise. Therefore, in this study, we propose a genetic algorithm (GA) based multiuser detector. The main contributions of this study are summarized as follows:
The GA is a heuristic search algorithm inspired by the genetic mechanisms of species evolution [^{7}]. The algorithm works well even for nonlinear programming problems and has been successfully applied to signal processing [^{8}]. To the best of our knowledge, few studies have been conducted on the implementation of the GA in large-scale MIMO systems for multiuser detection. This is the first study applying the GA technique to multiuser detection in a large-scale MIMO system in the presence of non-Gaussian noise.
On the one hand, the GA-based detector follows a multiple-directional search approach in which many peaks are searched in parallel, thereby reducing the possibility of local minimum trapping. Consequently, the GA-based detector may perform better than other conventional signal detectors in the presence of non-Gaussian noises. On the other hand, the GA only needs to evaluate the objective function (or fitness function) to guide its search, which means there is no requirement for a matrix inverse or derivation, among other factors. Therefore, the complexity of GA-based multi-user detection is comparable to that of conventional linear detectors.
An imperfect channel is also considered in this study. We observed that the GA-based detector works efficiently under practical scenarios.
The remainder of this paper is organized as follows. The system model is introduced in Section II. In Section III, we present a GA-based multi-user detector for large-scale MIMO systems. The numerical results are presented in Section IV. Finally, we provide some concluding remarks in Section V.
Consider an uplink multiuser MIMO system consisting of one base station equipped with M antennas and
where,
where 0 ≤
Given system model (1), the MAP detector is the optimal detector used for detecting the transmitted symbol vector x, and is expressed as
With Gaussian noise and the equal prior probability of x assumptions, the MAP detector (3) can be equivalently expressed as
The least squares detector, where ||x||^{2} is the
However, for most practical wireless channels, such as urban, indoor radio, and underwater acoustic channels, the ambient noise is known through experimental measurements to be non-Gaussian owing to the impulsive nature of man-made electromagnetic interference and a large amount of natural noise. In single-user wireless systems, it is widely known that non-Gaussian noise can be detrimental to the performance of conventional systems based on the Gaussian noise assumption. It is therefore unsurprising that linear and non-linear multiuser detectors lack robustness to many types of non-Gaussian statistical behaviors. An early study on the bit error rates (BERs) in non-Gaussian direct-sequence code-division multiple-access (CDMA) channels showed that the performance of conventional multiuser detectors depends heavily on the distribution of ambient noise [^{10-12}]. From the results illustrated in Fig. 1, we observe that the performance of the MMSE detector is degraded by non-Gaussian noise. The larger the non-Gaussian noise parameter
In this study, we consider the GA technique, which is a heuristic and stochastic optimization approach, and offers more promising alternatives. Compared with other conventional detectors, the GA may be the most robust in several respects. First, the
GA is a multi-directional search method that seeks many peaks in parallel and can reduce the possibility of local minimum trapping. Second, instead of the optimization function, the GA evaluates the fitness of each signal vector to guide its search. In other words, the GA does not require any advanced computations such as a matrix inverse (which is required by ZF and MMSE detectors). Finally, the GA explores the search space in which the probability of finding the best solution is high. Although the GA requires extremely intensive computations, the development of supercomputing resources makes it a good candidate for most optimization problems. The standard GA allows us to make modifications to suit the design requirements for a given environment. In this paper, considering large-scale MIMO systems, some specific modifications to the chromosome representation, initialization, fitness function, GA parameters, and termination conditions are introduced.
A chromosome encoding scheme may vary according to the nature of the problem, and because it can severely limit the search space observed by the system, it has a major impact on the performance. In the GA-based multiuser detector, the detected symbol
In general, the population of chromosomes
Because it evaluates the fitness of each chromosome, and to achieve a good performance, should guarantee that only the high-quality chromosomes are passed through to the next generation, the fitness function plays a critical role in the GA-based detector. By convention, a fitness function should have a positive value. In this study, in the presence of non-Gaussian noise, detecting the transmitted signal should minimize the difference between the original received signal and the transmitted signal multiplied by the channel coefficients, as given in (5), where
Termination is the criterion by which the GA decides whether to continue or stop a search. With the proposed GA-based detector, the number of iterations required to reach a predefined penalty function is not known in advance, and we adopt the strategy of reaching the maximum generations to avoid an excessively high complexity and detection delay.
The main procedure used for the GA-based detector is shown in Fig. 2. The GA-based detector simulates the evolutionary process by generating an initial population of candidates
where,
In this section, the simulation results are presented to verify the robustness of the GA-based detector for large-scale MIMO systems. BPSK is considered a modulation scheme, such as
Table 1 . Summary of GA parameters..
Parameters | Value |
---|---|
Population size | 60 |
Generation | 50 |
Crossover Probability | 0.88 |
Mutation probability | 0.08 |
Turning parameter | 0.5 |
In Fig. 3, we compare the performances of the conventional MMSE and GA-based detectors in the presence of different non-Gaussian noise distributions for a 64 × 32 MIMO system. We observed that the GA-based detector achieves a better performance than the MMSE for different non-Gaussian noise distributions. More specifically, at BER = 0.01, a performance gain of approximately 1 dB can be achieved using the GA-based detector when
The effects of different MIMO architectures are shown in Fig. 4. From the simulation results, we can observe that the GA-based algorithm always achieves a better performance than the conventional MMSE. Moreover, we observed that the less over-determined the massive MIMO is, the greater the performance gain achievable by the GA. More specifically, at BER = 0.01, the GA increases by approximately 0.3, 0.4, and 0.6 when the massive MIMO size is 64 × 20, 64 × 32, and 64 × 48, respectively. This is reasonable because when the large-scale MIMO system is overdetermined (e.g., 64 × 20), the MMSE approaches the optimal detector, and the performance gain achievable by the GA is limited.
Finally, we verify the behavior of the GA when considering imperfect channel state information (CSI). In this case, we apply the following imperfect channel model [^{14}, ^{15}]:
where, E is the estimation error uncorrelated with H, the entries of E are
In addition to the better performance achievable by the GA-based detector, as another advantage, it does not require any advanced computations, such as a matrix inverse, which is required by the MMSE, and is usually a significant burden for large-scale MIMO systems. Therefore, the GA-based detector may achieve a complexity comparable to that of the MMSE. In Fig. 6, we can see that for both the 64 × 20 and 64 × 32 MIMO systems, the GA-based detector requires a slightly larger average execution time in comparison to the MMSE. However, for the 64 × 48 MIMO system, the average execution time of the GA was less than that of the MMSE, which is due to the main complexity of the MMSE being derived from a matrix inverse. Therefore, the larger the sizes of the MIMO systems, the higher their complexity. Whereas the GA-based detector only needs to calculate the fitness function without any other complicated computations, the complexity of the GA is dominated by the number of iterations rather than the size of the MIMO system. It is therefore reasonable for the complexity of the GA-based detector to be lower than that of the MIMO system when the number of users is close to the number of antennas at the BS.
Non-Gaussian noise can significantly degrade the performance of current linear multiuser detectors applied in many practical wireless channels. In this paper, we presented a GA-based multiuser detector for large-scale MIMO systems in the presence of non-Gaussian noise. The simulation results show that the proposed GA-based detector is efficient in combating non-Gaussian noise. In addition, unlike the MMSE, which requires computations of the matrix inverse, the GA-based detector only needs to calculate the simple fitness function and can therefore achieve a comparable complexity. However, because the GA is a heuristic algorithm, the possibility of convergence depends heavily on the initializations and operator parameters. Therefore, in our future research, we might consider applying deep learning to refine the initializations for achieving a faster convergence and further performance improvement.
This work was supported by the Ajou Research Fund.
Table 1 . Summary of GA parameters..
Parameters | Value |
---|---|
Population size | 60 |
Generation | 50 |
Crossover Probability | 0.88 |
Mutation probability | 0.08 |
Turning parameter | 0.5 |
Hong, Chul-Eui;
The Korea Institute of Information and Commucation Engineering 2010; 8(1): 13-18 https://doi.org/10.6109/jicce.2010.8.1.013Kim, Myoung-Jong;Kim, Hong-Bae;Kang, Dae-Ki;
The Korea Institute of Information and Commucation Engineering 2010; 8(4): 370-376 https://doi.org/10.6109/jicce.2010.8.4.370Lee, Hee-Hyol;
The Korea Institute of Information and Commucation Engineering 2013; 11(1): 30-44 https://doi.org/10.6109/jicce.2013.11.1.030