Implicit Pilots for an Efficient Channel Estimation in Simplified Massive MIMO Schemes with Precoding

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.

In massive multiple-input multiple-output (MIMO) system with time-shifted pilots, the interference from other cell groups, where the pilots are staggered with the ones in the target cell group, can be eliminated when the number of antennas at base station (BS) is infinite. However, with only hundreds of antennas at the BS in practice, both intra-group interference and inter-group interference can not be ignored. Aiming at this problem, a Signal to Leakage and Noise Ratio (SLNR) based downlink precoding and power control scheme is proposed in this paper. In the design of precoder, not only the interference leaked to the users within the same cell is considered, but also the interference leaked to the BSs which are receiving the uplink pilots is included by introducing a conversion factor. Furthermore, the channel estimation error (CEE) is modelled and considered to enhance the robustness of the precoder. To obtain the tradeoff between uplink channel estimation and downlink data transmission, the preferable transmission power and conversion factor are found by maximizing the asymptotic sum-rate, which is dependent on the large-scale fading coefficients and some constants. In the calculation of asymptotic sum-rate, the truncated polynomial expansion (TPE) method is used to simplify the precoder and further to decouple the sum-rate computation from the small-scale fading coefficients. Simulation results show that the proposed downlink transmission scheme outperforms the maximum ratio transmission (MRT) based downlink scheme remarkably. Moreover, the performance obtained by asymptotic sum-rate optimization is very close to the complicated instantaneous sum-rate optimization.

Massive Multiple Input Multiple Output (MIMO) has great potential to improve spectrum efficiency in the fifth generation (5G) wireless communication systems. However, the efficiency was disastrously reduced by the heavy burden of overhead for device detection and channel estimation of the large amount of small data packets in the uplink channel. In the paper, we proposed a novel transmission scheme by superposing the training symbols for active device detection and channel estimation on the data symbols in the uplink transmission to improve the efficiency. More specifically, in order to mitigate the cross interference among the superposed signals, we proposed to split the transmission into the training phase and the traffic phase. Then we superposed the training phase in the next transmission with the traffic phase in the current transmission. Furthermore, we give the optimization of power allocation ratio between training phase and traffic phase to obtain the optimal overall performance. The analytic and simulation results show that, with the help of spatial isolation among devices, our proposed transmission scheme can significantly improve the transmission efficiency compared with the existing schemes.

It is well-known that massive multiple-input multiple-output (MIMO) systems have high potential for future wireless broadband systems. Requirements such as high spectral and power efficiency are also crucial in 5G. Based on a multi-amplifier structure it is possible to define a double layered structure where each amplification branch is connected to an antenna array to achieve both constellation and power directivies, assuring at same time similar performances to systems using transmitters with 2-dimensional antenna arrays. Thus, a different path can be followed to improve energy efficiency of power amplification where the usage of parallel amplification branches is combined with big arrays of antennas and multi-stream communication systems. These systems can be combined with single-carrier with frequency domain equalization (SC-FDE) schemes to improve the power efficiency in uplink due to the low envelope fluctuations.

Outage capacity analysis of the massive MIMO diversity channel

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.

Channel estimation is very challenging for millimeter wave (mmWave) massive multiple input multiple output (MIMO) systems with low-resolution analog-to-digital converters (ADCs) owing to the severe nonlinear distortion introduced by quantization. In this paper, we develop an advanced channel estimation method based on generalized expectation consistent signal recovery (GEC-SR) algorithm, which can obtain accurate channel state information from quantized signal. Specifically, we consider Laplacian prior to model angular domain mmWave channel coefficients and embed the expectation-maximization (EM) principle into GEC-SR algorithm to learn the unknown prior parameters. Numerical results show that our method outperforms state-of-the-art generalized-approximate-message-passing-based channel estimator, and can reduce the required pilot overhead significantly by using orthogonal pilot. © 2019 IEEE.

In this paper, we present a new performance bound for uplink channel estimation (CE) accuracy in the Massive Multiple Input Multiple Output (MIMO) system. The proposed approach is based on noise power calculation after the CE unit in a multi-antenna receiver. We decompose a non-line of sight (NLOS) channel into separate taps and calculate the cross-covariance matrix between them. Then a linear minimum mean squared error (MMSE) method is applied with these taps to estimate residual CE error value for each unique scenario, assuming Gaussian distribution of tap amplitudes and antenna noise. An artificial CE is calculated as a sum of the ideal noiseless channel (pre-defined Quadriga model) and the leftover noise after the optimal estimate. The artificial CE is then utilized in the MIMO detector and decoder units to calculate performance bound. Our method outperforms the accuracy of a well-known Cramer-Rao lower bound (CRLB) due to considering more statistics (number of taps and correlation between them) since performance strongly depends on several channel taps and their power ratio. Additionally, we show that our bound can be obtained from the generalized Bayesian CRLB. Simulation results are presented for the 5G QuaDRiGa 2.0 NLOS channel.

With the large number of antennas and subcarriers the overhead due to pilot transmission for channel estimation can be prohibitive in wideband massive multiple-input multiple-output (MIMO) systems. This can degrade the overall spectral efficiency significantly, and as a result, curtail the potential benefits of massive MIMO. In this paper, we propose a neural network (NN)-based joint pilot design and downlink channel estimation scheme for frequency division duplex (FDD) MIMO orthogonal frequency division multiplex (OFDM) systems. The proposed NN architecture uses fully connected layers for frequency-aware pilot design, and outperforms linear minimum mean square error (LMMSE) estimation by exploiting inherent correlations in MIMO channel matrices utilizing convolutional NN layers. Our proposed NN architecture uses a non-local attention module to learn longer range correlations in the channel matrix to further improve the channel estimation performance.We also propose an effective pilot reduction technique by gradually pruning less significant neurons from the dense NN layers during training. This constitutes a novel application of NN pruning to reduce the pilot transmission overhead. Our pruning-based pilot reduction technique reduces the overhead by allocating pilots across subcarriers non-uniformly and exploiting the inter-frequency and inter-antenna correlations in the channel matrix efficiently through convolutional layers and attention module.

Chapter 6 - Channel estimation for mmWave massive MIMO systems

We propose a blind channel estimation method for space-time block-coded single-carrier with frequency-domain equalization (SC-FDE) systems based on a simple, nonredundant precoding. This method of precoding allows us to better structure the relation between the covariance matrices of the received data and the products of channel coefficients. Using this structure, we can easily obtain the products of channel coefficients by using only subtraction and division. Then each of the two channel impulse response vectors is obtained by computing the eigenvector that is associated with the maximal eigenvalue of a Hermitian matrix formed from the corresponding products of channel coefficients. The proposed framework gaurantees the unique recovery of all the products of channel coefficients for colored or white noise cases. The impact of the precoding on channel estimation and equalization is also discussed. Simulations are used to demonstrate the performance of the proposed method.

Large-scale channel matrices in massive multiple-input multiple-output (MIMO) systems increase the difficulty of channel estimation. Conventional best linear unbiased estimator (BLUE) algorithms include multiple inverse operations for large-scale matrices; however this typically reduces algorithm efficiency. Efficiency can be improved by converting inverse operations into a system of linear equations, which are more easily solved for large matrices. This approach is used in the conjugate gradient (CG) method, which exhibits higher efficiency and precision when solving for approximate optimal solutions. As such, we propose a hybrid conjugate gradient (CG BLUE) algorithm, an improved version of the conventional BLUE technique. This algorithm reduces the dimensions of the channel model through a vectorization transform and uses the CG method to improve algorithm process efficiency during channel estimation for massive MIMO systems. Simulated results of NMSE and algorithm processing time show the proposed CG-BLUE algorithm resulted in nearly one order of magnitude higher calculation efficiency while maintaining the same level of accuracy as conventional BLUE.

This paper considers pilot-based channel estimation in large-scale multiple-input multiple-output (MIMO) communication systems, also known as “massive MIMO”. Unlike previous works on this topic, which mainly considered the impact of inter-cell disturbance due to pilot reuse (so-called pilot contamination), we are concerned with the computational complexity. The conventional minimum mean square error (MMSE) and minimum variance unbiased (MVU) channel estimators rely on inverting covariance matrices, which has cubic complexity in the multiplication of number of antennas at each side. Since this is extremely expensive when there are hundreds of antennas, we propose to approximate the inversion by an L-order matrix polynomial. A set of low-complexity Bayesian channel estimators, coined Polynomial ExpAnsion CHannel (PEACH) estimators, are introduced. The coefficients of the polynomials are optimized to yield small mean square error (MSE). We show numerically that near-optimal performance is achieved with low polynomial orders. In practice, the order L can be selected to balance between complexity and MSE. Interestingly, pilot contamination is beneficial to the PEACH estimators in the sense that smaller L can be used to achieve near-optimal MSEs.

In frequency-division duplexing (FDD) massive multiple-input-multiple-output (MIMO) systems, channel estimation about reducing the training and feedback overhead has always been a hot research area. The previous studies have shown that the method of utilizing channel sparsity in discrete Fourier transform (DFT) domain and angle reciprocity works well in particular channel environment. In this paper, we propose an improved method based on pilot reuse for general channel environment. The proposed method is applied to uplink/downlink channel estimation in FDD massive MIMO systems. Based on practical characteristics of the channel in massive MIMO systems, we modify the original method and propose an improved algorithm in assigning the pilot resources dynamically. The numerical results corroborate that compared to the original method, the improved method is more suitable and performs better in general channel environment. Meanwhile, the proposed algorithm can save the pilot resources and reduce the feedback overhead efficiently.

The limited fronthaul capacity imposes a challenge on the uplink of a centralized radio access network (C-RAN). We propose to boost the fronthaul capacity of a massive multiple-input multiple-output (MIMO)-aided C-RAN by globally optimizing the power sharing between channel estimation and data transmission both for the user devices (UDs) and the remote radio units (RRUs). Intuitively, allocating more power to the channel estimation will result in more accurate channel estimates, which increases the achievable throughput. However, increasing the power allocated to the pilot training will reduce the power assigned to data transmission, which reduces the achievable throughput. In order to optimize the powers allocated to the pilot training and to the data transmission of both the UDs and the RRUs, we assign an individual power sharing factor to each of them and derive an asymptotic closed-form expression of the signal-to-interference-plus-noise ratio for the massive MIMO-aided C-RAN consisting of both the UD-to-RRU links and the RRU-to-baseband unit (BBU) links. We then exploit the C-RAN architecture's central computing and control capability for jointly optimizing the UDs' power sharing factors and the RRUs' power sharing factors aiming at maximizing the fronthaul capacity. Our simulation results show that the fronthaul capacity is significantly boosted by the proposed global optimization of the power allocation between channel estimation and data transmission both for the UDs and for their host RRUs. As a specific example of 32 receive antennas (RAs) deployed by the RRU and 128 RAs deployed by the BBU, the sum rate of 10 UDs achieved with the optimal power sharing factors improves by 33% compared with the one attained without optimizing power sharing factors.