Pruning the Pilots: Deep Learning-Based Pilot Design and Channel Estimation for MIMO-OFDM Systems

With the increasing rate of wireless devices and high bandwidth operations, wireless networking and communications are becoming over crowded. To cope with such crowded and messy situation, massive MIMO is designed to work with hundreds of low-cost serving antennas at a time as well as improve the spectral efficiency at the same time. Time Division Duplexing (TDD) has been used for gaining beamforming which is a major part of massive MIMO, to gain its best improvement to transmit and receive pilot sequences. All the benefits are only possible if the channel state information or channel estimation is gained properly. Least Square (LS), Minimum Mean Square Error (MMSE) and Linear Minimum Mean Square Error (LMMSE) are the estimators commonly used for estimating channel matrices. We have optimized these methods using genetic algorithm to minimize the mean squared error and finding the best channel matrix from existing algorithms with less computational complexity. Our simulation result has shown that the use of Genetic Algorithm (GA) worked well on existing algorithms in a Rayleigh slow fading channel and existence of Additive White Gaussian Noise. We found that the GA optimized LS is better than existing algorithms. GA provides optimal result in some few iterations in terms of Mean Square Error (MSE) with respect to SNRand computational complexity.

In orthogonal frequency division multiplexing (OFDM) systems, the least square (LS) in addition to the technique of linear minimum mean square error (LMMSE) channel estimation are compared using frequency as well as time domain in this paper. A constant LMMSE channel estimation has been proposed in time domain where the channel is not intimated before. It is presented by the Simulation outcomes that the channel estimation execution can be improved by the techniques of time domain but not using the techniques of frequency domain. Additionally, using the technique of LMMSE, higher accuracy is achieved by the proposed method which is presented in the outputs of the simulation.

Generalized frequency division multiplexing (GFDM) is a promising candidate waveform for next-generation wireless communication systems. However, GFDM channel estimation is still challenging due to the inherent interference. In this paper, we formulate a pilot design framework with linear minimum mean square error (LMMSE) channel estimation for GFDM, and propose a novel pilot design to achieve interference precancellation during pilot generation with the fixed transmit sample values at selected frequency bins. Numerical results demonstrate that the proposed method reduces the channel estimation mean square error and the symbol error rate (SER) in high signal-to-noise ratio (SNR) regions, compared with the conventional methods.

Massive multiple input multiple output (MIMO) transmission and coordinated multipoint transmission are candidate technologies for increasing data throughput in evolving 5G standards. Frequency division duplex (FDD) is likely to remain predominant in large parts of the spectrum below 6 GHz for future 5G systems. Therefore, it is important to estimate the downlink FDD channels from a very large number of antennas, while avoiding an excessive downlink reference signal overhead. We here propose and investigate a three part solution. First, massive MIMO downlinks use a fixed grid of beams. For each user, only a subset of beams will then be relevant, and require estimation. Second, sets of coded reference signal sequences, with cyclic patterns over time, are used. Third, each terminal estimates its most relevant channels. We here propose and compare a linear mean square estimation and a Kalman estimation. Both utilize frequency and antenna correlation, and the later also utilizes temporal correlation. In extensive simulations, this scheme provides channel estimates that lead to an insignificant beamforming performance degradation as compared to full channel knowledge. The cyclic pattern of coded reference signals is found to be important for reliable channel estimation, without having to adjust the reference signals to specific users.

SummaryThis paper introduces the concept of spatial and media‐based modulated (SMBM) orthogonal frequency division multiplexing (OFDM) as a potential candidate for highly mobile next generation beyond 5G (B5G) wireless communications. The proposed SMBM‐OFDM technique utilizes not only the transmit antenna and channel state indices but also OFDM subcarriers to improve the system performance under high mobility. In addition, this study sheds light on challenging fast time‐varying channel estimation problem of MBM‐based systems by using the linear minimum mean square error (LMMSE) approach due to its optimality to investigate the achievable system performance with the aid of basis expansion modeling. The minimum lower bound on the channel estimation error (Bayesian Cramer–Rao bound) is derived theoretically and shown to be attainable by the considered LMMSE estimator. Moreover, symbol detection performance is provided for different modulation types and higher mobile velocities. Simulation results demonstrate that SMBM‐OFDM system under high mobility is able to provide around 12‐dB performance gains in terms of both channel estimation and symbol detection error compared to conventional spatial modulation (SM)‐OFDM systems without MBM. The presented framework is important due to addressing the high mobility support of SMBM‐OFDM systems for B5G wireless communications in terms of achievable channel estimation and data detection performance.

Channel estimation (CE) is a challenging problem and one of the key technologies in Orthogonal Frequency Division Multiplexing (OFDM) systems. The Linear Minimum Mean Square Error (LMMSE) proposed for OFDM systems has excellent Mean Square Error (MSE) performance. However, the conventional method requires the statistical knowledge of the channel information in advance and the complicated inverse operation of large dimension matrices. In this case, an enhanced fast LMMSE channel estimation using Fast Fourier Transform (FFT) operation and the most significant taps (MST) algorithm for OFDM systems is proposed. This method has the advantage of low computational complexity and no requirement on the detailed channel information. In addition, simulation results demonstrate that the proposed algorithm outperforms other LMMSE methods in terms of bit error rate (BER) without the loss of MSE performance.

Pair-wise error probability (PEP) is analyzed in the presence of channel estimation error (CEE) for orthogonal frequency division multiplexing (OFDM) in a quasi-static Rayleigh fading channel. Subcarriers in OFDM are grouped in an equi-spaced manner with the number of subcarriers in a group equal to the number of channel taps. One group is dedicated for training and the rest are for data transmission. A linear minimum mean square error (LMMSE) based channel estimation for coherent detection is considered in this paper. This enables the signal dependent CEE to be uncorrelated to the data. Since ML decoding employed with perfect CSI becomes suboptimal in the presence of CEE, an optimal ML decoding is derived. It is observed from our training-based PEP expression that the CEE does not reduce the diversity order but contributes to a loss of coding gain. Moreover, a code design criterion is established. To reduce the loss of coding gain, an optimal training scheme is developed, based on the PEP expression. Loss of performance due to an imperfect channel estimate is quantified in terms of bounds on bit error probability (BEP) for high SNR. Our analytical findings are corroborated by simulation examples.

Reconfigurable intelligent surfaces (RISs) play an important role in extending the connectivity and improving the data rate of future wireless communication systems. However, the conventional (passive) RISs have their limitations and, thus, a hybrid-relay RIS (HR-RIS) architecture is proposed to reap the benefits of relaying systems with high power consumption but higher throughput, and passive RIS systems with cascaded fading effects but low complexity. In this paper, we investigate the performance of HR-RISs in a massive multiple-input multiple-output (M-MIMO) system with zero-forcing (ZF) processing, where channel state information (CSI) is unavailable. We first model the uplink/downlink channels and derive the linear minimum mean square error (LMMSE) estimate of the effective channels. We, then, derive a closed-form expression for the signal to interference and noise ratio (SINR) and spectral efficiency (SE). Finally, we provide some useful engineering insights with our asymptotic analysis and numerical results.

In this paper, we develop the channel estimation algorithm for a massive multiple input multiple output (MIMO) system using one-bit analog-to-digital converters (ADCs). Although, one-bit quantization significantly reduces the deployment cost and power consumption of the massive MIMO, the great distortion induced by one-bit quantization makes channel estimation more difficult. Therefore, a channel estimation method by executing a deep neural network (DNN) over multiple signal segments is proposed for the uplink of one-bit massive MIMO. The average of the DNN’s outputs throughout all the segments is the final channel estimate for a transmission block. In order to improve the estimation accuracy without increasing the length of pilot, the data symbols got based on the initial channel estimates are used as the other part of pilots to refine the estimation result. Moreover, a sliding window based pilot segment method is adopted to increase the number of signal segments with a same pilot length. The simulation results show that the proposed scheme outperforms least squares (LS) and Bussgang linear minimum mean squared error (BLMMSE) channel estimators in the whole signal-to-noise-ratio (SNR) region.

Channel estimation is a critical component in orthogonal frequency division multiplexing (OFDM) systems for ensuring reliable wireless communication. In this study, we propose a fast super-resolution convolutional neural network (FSRCNN) model for channel estimation, designed to reduce computational complexity while maintaining high estimation accuracy. The proposed FSRCNN model incorporates modifications such as replacing linear interpolation with zero padding and leveraging a new fast CNN architecture to estimate channel coefficients. Our numerical experiments and simulations demonstrate that the FSRCNN model significantly outperforms traditional methods, such as least square (LS) and linear minimum mean square error (LMMSE), in terms of mean square error (MSE) across various signal-to-noise ratios (SNRs). Specifically, the FSRCNN model achieves MSE values comparable to MMSE estimation, particularly at higher SNRs, while maintaining lower computational complexity. At an SNR of 20 dB, the FSRCNN model shows a notable improvement in MSE performance compared to the ChannelNet and LS methods. The proposed model also demonstrates robust performance across different SNR levels, with optimal results observed when the training SNR is close to the operating SNR. These findings validate the effectiveness of the FSRCNN model in providing a low-complexity, high-accuracy alternative for channel estimation, making it suitable for real-time applications and devices with limited computational resources. This advancement holds significant promise for enhancing the reliability and efficiency of current and future wireless communication networks.

Massive multiple input multiple output (MIMO) technology is one of the promising technologies for fifth generation (5G) cellular communications. In this technology, each cell has a base station (BS) with a large number of antennas, allowing the simultaneous use of the same resources (e.g., frequency and/or time slots) by multiple users of a cell. Therefore, massive MIMO systems can bring very high spectral and power efficiencies. However, this technology faces some important issues that need to be addressed. One of these issues is the performance degradation due to hardware impairments, since low-cost RF chains need to be employed. Another issue is the channel estimation and channel aging effects, especially in fast mobility environments. In this paper we will perform a comprehensive study on these two issues considering two of the most promising candidate waveforms for massive MIMO systems: Orthogonal frequency division multiplexing (OFDM) and single-carrier frequency domain processing (SC-FDP). The studies and the results show that hardware impairments and inaccurate channel knowledge can degrade the performance of massive MIMO systems extensively. However, using suitable low complex estimation and compensation techniques and also selecting a suitable waveform can reduce these effects.

A decision-directed (DD) channel estimation based on iterative linear minimum mean square error (LMMSE) is proposed for orthogonal frequency division multiplexing systems. Existing DD channel estimation is well known to have the problem of error propagation because of symbol-by-symbol detection. The proposed algorithm can estimate the correction term of current channel state information (CSI) according to the error vector of previous CSI by applying the orthogonality principle, and corrects the current CSI with this correction term. Analysis and simulation results have shown that this method has no error propagation problem. The performance of the proposed algorithm is much better than the conventional DD channel estimation, and close to the optimal LMMSE estimator, but with much less computational complexity compared with the optimal LMMSE estimator.

Orthogonal frequency division multiplexing (OFDM) is multi carrier modulation scheme. The channel estimation is a process of characterizing the effect of the transmission channel on the input signal. In this paper we compare the performance of Least Square (LS) and Linear Minimum Mean Square Error (LMMSE) channel estimation technique for Wavelet based OFDM system. The channel estimation based on block type pilot arrangement is performed by sending pilots at every sub-channel and using this estimation for a specific number of following symbols. In this paper we used wavelet transform instead of fast Fourier transform (FFT), which have more bandwidth efficiency, less prone to Doppler shift and also complexity of order O(N) as opposed to the FFTs O(N log <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> N).

In this thesis, we cope with the fundamental mathematical and physical problems of the space-time-Doppler UWB system design for fading channels: multi-input multi-output (MIMO) wireless communication with adaptive filtering. The estimation algorithm from equalizer providing an accurate parameters estimate is investigated. UWB radio is a fast emerging technology with uniquely attractively features inviting major advances in wireless communications, networking, radar, imaging, and positioning systems. By its rule-making proposal in 2002, the Federal Communications Commission (FCC) in the United States essentially unleashed huge new bandwidth (3.6-10.6 GHz) at the noise floor, where UWB radios overlaying coexistence RF systems cerate using low-power ultra-short information bearing pulses. Right now, there are three basic types of UWB: multiband OFDM UWB (MB-OFDM UWB), impulse-UWB (I-UWB), and direct sequence UWB (DS-UWB). We focus on I-UWB and MB-OFDM-UWB, and compare their performance. A simple means for spreading the spectrum of low duty cycle pulse trains is time hopping (TH), with pulse position modulation (PPM) for data modulation at the rate of many pulses per data bit. The main contribution of this thesis for I-UWB is the design of leading edge detectors, coherent correlation detector (CCD), and pilot performance enhancement compared with different Rayleigh and Ricean fading conditions. For MB-OFDM UWB, we have considered the performance analysis and design criteria of MIMO OFDM UWB systems for high data-rate wireless transmission. The signal processing of frame detection, time synchronization, frequency synchronization, channel estimation, synchronization tracking using pilot subcarriers and 2-D MIMO detection algorithms is discussed. The main contributions of this thesis are 1) Compared with receiver employing the Maximum Likelihood (ML) detector, the receiver employing a low-complexity linear Minimum Mean Square Error (MMSE) demodulator can perform a limited performance loss in spatially uncorrelated channels. 2) Due to the operations of spreading and dispreading combined with MMSE-based frequency domain equalization, the adverse effects of the low-SNR subcarriers on the average BER performance are potentially improved. This is a direct consequence of spreading, because even if the signal corresponding to a specific chip is obliterated by a deep frequency domain channel fade, after dispreading these effects are spread over the Walsh-Hadamard Transform (WHT) length. Hence there is a high chance of still recovering all the partially affected subcarrier symbols without errors. 3) As a test case, the OFDM-based 200 Mb/s MB-UWB network (IEEE 802.15.3a) are considered, but the simulation results are shown above section. 4) The simulation channel can be easily applied to NOS and NLOS situation with WHT transformation from Simulink model. The fading channels of UWB with low/high signal to noise ratio (SNR), multipath effects, and multiuser interference may introduce large errors in location. The location engine performs the following tasks: █ Data fusion techniques: Different data fusion techniques are implemented using Time Of Arrival (TOA), Angle Of Arrival (AOA), or a combination of both. █ Channel modeling: A multipath, multiuser channel environment is created that models path loss, shadowing, Rayleigh fading, and Doppler frequency effects. █ Parameter estimation: TOA and AOA estimation algorithms are implemented as part of the location finding engine. Different variations of algorithms are implemented for performance and comparison purposes. █ Configuring the physical layer for different wireless networks. Among the programmable parameters are spreading factor, packet size, training length, constellation type, modulation technique, carrier frequency, level of transmitted signal power, and the number of antennas at the transmitter for both sides. █ Configuring the mobile user conditions. The wireless channel models depend on the Doppler frequencies present in the environment. The Doppler frequency depends on the mobile speed and carrier frequencies as input and generates a Rayleigh fading channel with the U-shape Doppler spectrum. █ Configuring the environmental parameters and network geographical structure. One of the factors affecting the performance of the wireless location system is the environment type (e.g., bad urban, urban, suburban, or rural area). For example, in a bad urban area with many blocking objects and buildings, non-line of sight (NLOS) effects plays an important role in the estimation accuracy.

In this paper, a staggered frame structure is proposed for single-cell massive multiple-input multiple-output (MIMO) systems, and the key idea is that different users transmit training pilots at nonoverlapped time. As a result, users do not have to be synchronized strictly to send pilots and orthogonal pilots are not required. Moreover, we also propose two interference suppressed channel estimation methods, i.e., the linear minimum mean square error (LMMSE)-based and orthogonal projection based least squares (OPLS) methods for the staggered frame structure. Specifically, the LMMSE-based method minimizes the mean square error of the estimation, whereas the OPLS method only estimates the part of the user's channel response that is orthogonal to the other users. All conducted simulation results demonstrate that the massive MIMO system with the both proposed methods can achieve high average achievable rate. Furthermore, when the conjugate beamforming is employed, the massive MIMO system could obtain even higher average achievable data rate with the proposed OPLS method than that of the system with perfect channel state information. Moreover, the computational complexity of the proposed OPLS method is very low.