We present and discuss several novel applications of deep learning for the physical layer. By interpreting a communications system as an autoencoder, we develop a fundamental new way to think about communications system design as an end-to-end reconstruction task that seeks to jointly optimize transmitter and receiver components in a single process. We show how this idea can be extended to networks of multiple transmitters and receivers and present the concept of radio transformer networks as a means to incorporate expert domain knowledge in the machine learning model. Lastly, we demonstrate the application of convolutional neural networks on raw IQ samples for modulation classification which achieves competitive accuracy with respect to traditional schemes relying on expert features. This paper is concluded with a discussion of open challenges and areas for future investigation.

An Introduction to Deep Learning for the Physical Layer

End-to-end learning of communications systems is a fascinating novel concept that has so far only been validated by simulations for block-based transmissions. It allows learning of transmitter and receiver implementations as deep neural networks (NNs) that are optimized for an arbitrary differentiable end-to-end performance metric, e.g., block error rate (BLER). In this paper, we demonstrate that over-the-air transmissions are possible: We build, train, and run a complete communications system solely composed of NNs using unsynchronized off-the-shelf software-defined radios and open-source deep learning software libraries. We extend the existing ideas toward continuous data transmission, which eases their current restriction to short block lengths but also entails the issue of receiver synchronization. We overcome this problem by introducing a frame synchronization module based on another NN. A comparison of the BLER performance of the “learned” system with that of a practical baseline shows competitive performance close to $\text{1}$  dB, even without extensive hyperparameter tuning. We identify several practical challenges of training such a system over actual channels, in particular, the missing channel gradient, and propose a two-step learning procedure based on the idea of transfer learning that circumvents this issue.

Deep Learning Based Communication Over the Air

As a promising machine learning tool to handle the accurate pattern recognition from complex raw data, deep learning (DL) is becoming a powerful method to add intelligence to wireless networks with large-scale topology and complex radio conditions. DL uses many neural network layers to achieve a brain-like acute feature extraction from high-dimensional raw data. It can be used to find the network dynamics (such as hotspots, interference distribution, congestion points, traffic bottlenecks, spectrum availability, etc.) based on the analysis of a large amount of network parameters (such as delay, loss rate, link signal-to-noise ratio, etc.). Therefore, DL can analyze extremely complex wireless networks with many nodes and dynamic link quality. This paper performs a comprehensive survey of the applications of DL algorithms for different network layers, including physical layer modulation/coding, data link layer access control/resource allocation, and routing layer path search, and traffic balancing. The use of DL to enhance other network functions, such as network security, sensing data compression, etc., is also discussed. Moreover, the challenging unsolved research issues in this field are discussed in detail, which represent the future research trends of DL-based wireless networks. This paper can help the readers to deeply understand the state-of-the-art of the DL-based wireless network designs, and select interesting unsolved issues to pursue in their research.

Deep Learning for Intelligent Wireless Networks: A Comprehensive Survey

Massive MIMO is a reality—What is next?: Five promising research directions for antenna arrays

For millimeter wave (mmWave) massive multiple-input multiple-output (MIMO) systems, hybrid processing architecture is usually used to reduce the complexity and cost, which poses a very challenging issue in channel estimation. In this paper, deep convolutional neural network (CNN) is employed to address this problem. We first propose a spatial-frequency CNN (SF-CNN) based channel estimation exploiting both the spatial and frequency correlation, where the corrupted channel matrices at adjacent subcarriers are input into the CNN simultaneously. Then, exploiting the temporal correlation in time-varying channels, a spatial-frequency-temporal CNN (SFT-CNN) based approach is developed to further improve the accuracy. Moreover, we design a spatial pilot-reduced CNN (SPR-CNN) to save spatial pilot overhead for channel estimation, where channels in several successive coherence intervals are grouped and estimated by a channel estimation unit with memory. Numerical results show that the proposed SF-CNN and SFT-CNN based approaches outperform the non-ideal minimum mean-squared error (MMSE) estimator but with reduced complexity, and achieve the performance close to the ideal MMSE estimator that is very difficult to be implemented in practical situations. They are also robust to different propagation scenarios. The SPR-CNN based approach achieves comparable performance to SF-CNN and SFT-CNN based approaches while only requires about one-third of spatial pilot overhead at the cost of complexity. The results in this paper clearly demonstrate that deep CNN can efficiently exploit channel correlation to improve the estimation performance for mmWave massive MIMO systems.

Deep CNN-Based Channel Estimation for mmWave Massive MIMO Systems

This paper presents a low-complexity near-maximum-likelihood-detection (near-MLD) algorithm called one-bit sphere decoding for an uplink massive multiple-input multiple-output system with one-bit analog-to-digital converters. The idea of the proposed algorithm is to estimate the transmitted symbol vector sent by uplink users (a codeword vector) by searching over a sphere, which contains a collection of codeword vectors close to the received signal vector at the base station in terms of a weighted Hamming distance . To reduce the computational complexity for the construction of the sphere, the proposed algorithm divides the received signal vector into multiple subvectors each with a reduced dimension. Then, it generates multiple spheres in parallel, where each sphere is centered at the subvector and contains a list of subcodeword vectors. The detection performance of the proposed algorithm is also analyzed by characterizing the probability that the proposed algorithm performs worse than the MLD. The analysis shows how the dimension of each sphere and the size of the subcodeword list are related to the performance-complexity tradeoff achieved by the proposed algorithm. Simulation results demonstrate that the proposed algorithm achieves near-MLD performance, while reducing the computational complexity compared to the existing MLD method.

One-Bit Sphere Decoding for Uplink Massive MIMO Systems With One-Bit ADCs

In this paper, a new optimization framework is presented for the joint design of user selection, power allocation, and precoding in multi-cell multi-user multiple-input multiple-output (MU-MIMO) systems when imperfect channel state information at transmitter (CSIT) is available. By representing the joint optimization variables in a higher-dimensional space, the weighted sum-spectral efficiency maximization is formulated as the maximization of the product of Rayleigh quotients. Although this is still a non-convex problem, a computationally efficient algorithm, referred to as generalized power iteration precoding (GPIP), is proposed. The algorithm converges to a stationary point (local maximum) of the objective function and therefore it guarantees the first-order optimality of the solution. By adjusting the weights in the weighted sum-spectral efficiency, the GPIP yields a joint solution for user selection, power allocation, and downlink precoding. The GPIP can be extended to the multi-cell scenario where cooperative base stations perform joint user-cell selection and design their precodes by taking into account the inter-cell interference by sharing global imperfect CSIT. System-level simulations show the gains of the proposed approach with respect to conventional user selection and linear downlink precoding.

Joint User Selection, Power Allocation, and Precoding Design With Imperfect CSIT for Multi-Cell MU-MIMO Downlink Systems

This paper considers a multiple-input-multiple-output (MIMO) system with low-resolution analog-to-digital converters (ADCs) In this system, we propose a novel detection framework that performs data symbol detection without explicitly knowing channel state information at a receiver The underlying idea of the proposed framework is to exploit supervised learning Specifically, during channel training, the proposed approach sends a sequence of data symbols as pilots so that the receiver learns a nonlinear function that is determined by both a channel matrix and a quantization function of the ADCs During data transmission, the receiver uses the learned nonlinear function to detect which data symbols were transmitted In this context, we propose two blind detection methods to determine the nonlinear function from the training-data set We also provide an analytical expression for the symbol-vector-error probability of the MIMO systems with one-bit ADCs when employing the proposed framework Simulations demonstrate the performance improvement of the proposed framework compared to existing detection techniques

Blind detection for MIMO systems with low-resolution ADCs using supervised learning

This paper presents a low-complexity near-maximum-likelihood-detection (near-MLD) algorithm called one-bit-sphere-decoding for an uplink massive multiple-input multiple-output (MIMO) system with one-bit analog-to-digital converters (ADCs). The idea of the proposed algorithm is to estimate the transmitted symbol vector sent by uplink users (a codeword vector) by searching over a sphere, which contains a collection of codeword vectors close to the received signal vector at the base station in terms of a weighted Hamming distance. To reduce the computational complexity for the construction of the sphere, the proposed algorithm divides the received signal vector into multiple sub-vectors each with reduced dimension. Then, it generates multiple spheres in parallel, where each sphere is centered at the sub-vector and contains a list of sub-codeword vectors. The detection performance of the proposed algorithm is also analyzed by characterizing the probability that the proposed algorithm performs worse than the MLD. The analysis shows how the dimension of each sphere and the size of the sub-codeword list are related to the performance-complexity tradeoff achieved by the proposed algorithm. Simulation results demonstrate that the proposed algorithm achieves near-MLD performance, while reducing the computational complexity compared to the existing MLD method.

One-Bit Sphere Decoding for Uplink Massive MIMO Systems with One-Bit ADCs

The use of one-bit analog-to-digital converters (ADCs) at a receiver is a power-efficient solution for future wireless systems operating with a large signal bandwidth and/or a massive number of receive radio frequency chains. This solution, however, induces high channel estimation error and therefore makes it difficult to perform the optimal data detection that requires perfect knowledge of likelihood functions at the receiver. In this paper, we propose a likelihood function learning method for multiple-input multiple-output (MIMO) systems with one-bit ADCs using a reinforcement learning approach. The key idea is to exploit input-output samples obtained from data detection, to compensate for the mismatch in the likelihood function. The underlying difficulty of this idea is a label uncertainty in the samples caused by a data detection error. To resolve this problem, we define a Markov decision process (MDP) to maximize the accuracy of the likelihood function learned from the samples. We then develop a reinforcement learning algorithm that efficiently finds the optimal policy by approximating the transition function and the optimal state of the MDP. Simulation results demonstrate that the proposed method provides significant performance gains for data detection methods that suffer from the mismatch in the likelihood function.

Namyoon Lee

Papers

One-Bit Sphere Decoding for Uplink Massive MIMO Systems With One-Bit ADCs

Joint User Selection, Power Allocation, and Precoding Design With Imperfect CSIT for Multi-Cell MU-MIMO Downlink Systems

Blind detection for MIMO systems with low-resolution ADCs using supervised learning

One-Bit Sphere Decoding for Uplink Massive MIMO Systems with One-Bit ADCs

Robust Data Detection for MIMO Systems With One-Bit ADCs: A Reinforcement Learning Approach