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Register a new userQuantization Design and Channel Estimation for Massive MIMO Systems with One-Bit ADCs
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Added by
Feiyu Wang
Publication date
2017
fields
Informatics Engineering
and research's language is
English
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We consider the problem of channel estimation for uplink multiuser massive MIMO systems, where, in order to significantly reduce the hardware cost and power consumption, one-bit analog-to-digital converters (ADCs) are used at the base station (BS) to quantize the received signal. Channel estimation for one-bit massive MIMO systems is challenging due to the severe distortion caused by the coarse quantization. It was shown in previous studies that an extremely long training sequence is required to attain an acceptable performance. In this paper, we study the problem of optimal one-bit quantization design for channel estimation in one-bit massive MIMO systems. Our analysis reveals that, if the quantization thresholds are optimally devised, using one-bit ADCs can achieve an estimation error close to (with an increase by a factor of $pi/2$) that of an ideal estimator which has access to the unquantized data. The optimal quantization thresholds, however, are dependent on the unknown channel parameters. To cope with this difficulty, we propose an adaptive quantization (AQ) approach in which the thresholds are adaptively adjusted in a way such that the thresholds converge to the optimal thresholds, and a random quantization (RQ) scheme which randomly generate a set of nonidentical thresholds based on some statistical prior knowledge of the channel. Simulation results show that, our proposed AQ and RQ schemes, owing to their wisely devised thresholds, present a significant performance improvement over the conventional fixed quantization scheme that uses a fixed (typically zero) threshold, and meanwhile achieve a substantial training overhead reduction for channel estimation. In particular, even with a moderate number of pilot symbols (about 5 times the number of users), the AQ scheme can provide an achievable rate close to that of the perfect channel state information (CSI) case.
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This paper considers a multipair amplify-and-forward massive MIMO relaying system with one-bit ADCs and one-bit DACs at the relay. The channel state information is estimated via pilot training, and then utilized by the relay to perform simple maximum-ratio combining/maximum-ratio transmission processing. Leveraging on the Bussgang decomposition, an exact achievable rate is derived for the system with correlated quantization noise. Based on this, a closed-form asymptotic approximation for the achievable rate is presented, thereby enabling efficient evaluation of the impact of key parameters on the system performance. Furthermore, power scaling laws are characterized to study the potential energy efficiency associated with deploying massive one-bit antenna arrays at the relay. In addition, a power allocation strategy is designed to compensate for the rate degradation caused by the coarse quantization. Our results suggest that the quality of the channel estimates depends on the specific orthogonal pilot sequences that are used, contrary to unquantized systems where any set of orthogonal pilot sequences gives the same result. Moreover, the sum rate gap between the double-quantized relay system and an ideal non-quantized system is a moderate factor of $4/pi^2$ in the low power regime.
In massive multiple-input multiple-output (MIMO) systems, it may not be power efficient to have a high-resolution analog-to-digital converter (ADC) for each antenna element. In this paper, a near maximum likelihood (nML) detector for uplink multiuser massive MIMO systems is proposed where each antenna is connected to a pair of one-bit ADCs, i.e., one for each real and imaginary component of the baseband signal. The exhaustive search over all the possible transmitted vectors required in the original maximum likelihood (ML) detection problem is relaxed to formulate an ML estimation problem. Then, the ML estimation problem is converted into a convex optimization problem which can be efficiently solved. Using the solution, the base station can perform simple symbol-by-symbol detection for the transmitted signals from multiple users. To further improve detection performance, we also develop a two-stage nML detector that exploits the structures of both the original ML and the proposed (one-stage) nML detectors. Numerical results show that the proposed nML detectors are efficient enough to simultaneously support multiple uplink users adopting higher-order constellations, e.g., 16 quadrature amplitude modulation. Since our detectors exploit the channel state information as part of the detection, an ML channel estimation technique with one-bit ADCs that shares the same structure with our proposed nML detector is also developed. The proposed detectors and channel estimator provide a complete low power solution for the uplink of a massive MIMO system.
We propose a fast and near-optimal approach to joint channel-estimation, equalization, and decoding of coded single-carrier (SC) transmissions over frequency-selective channels with few-bit analog-to-digital converters (ADCs). Our approach leverages parametric bilinear generalized approximate message passing (PBiGAMP) to reduce the implementation complexity of joint channel estimation and (soft) symbol decoding to that of a few fast Fourier transforms (FFTs). Furthermore, it learns and exploits sparsity in the channel impulse response. Our work is motivated by millimeter-wave systems with bandwidths on the order of Gsamples/sec, where few-bit ADCs, SC transmissions, and fast processing all lead to significant reductions in power consumption and implementation cost. We numerically demonstrate our approach using signals and channels generated according to the IEEE 802.11ad wireless local area network (LAN) standard, in the case that the receiver uses analog beamforming and a single ADC.
In order to reduce hardware complexity and power consumption, massive multiple-input multiple-output (MIMO) systems employ low-resolution analog-to-digital converters (ADCs) to acquire quantized measurements $boldsymbol y$. This poses new challenges to the channel estimation problem, and the sparse prior on the channel coefficient vector $boldsymbol x$ in the angle domain is often used to compensate for the information lost during quantization. By interpreting the sparse prior from a probabilistic perspective, we can assume $boldsymbol x$ follows certain sparse prior distribution and recover it using approximate message passing (AMP). However, the distribution parameters are unknown in practice and need to be estimated. Due to the increased computational complexity in the quantization noise model, previous works either use an approximated noise model or manually tune the noise distribution parameters. In this paper, we treat both signals and parameters as random variables and recover them jointly within the AMP framework. The proposed approach leads to a much simpler parameter estimation method, allowing us to work with the quantization noise model directly. Experimental results show that the proposed approach achieves state-of-the-art performance under various noise levels and does not require parameter tuning, making it a practical and maintenance-free approach for channel estimation.
This paper considers a multipair amplify-and-forward massive MIMO relaying system with low-resolution ADCs at both the relay and destinations. The channel state information (CSI) at the relay is obtained via pilot training, which is then utilized to perform simple maximum-ratio combining/maximum-ratio transmission processing by the relay. Also, it is assumed that the destinations use statistical CSI to decode the transmitted signals. Exact and approximated closed-form expressions for the achievable sum rate are presented, which enable the efficient evaluation of the impact of key system parameters on the system performance. In addition, optimal relay power allocation scheme is studied, and power scaling law is characterized. It is found that, with only low-resolution ADCs at the relay, increasing the number of relay antennas is an effective method to compensate for the rate loss caused by coarse quantization. However, it becomes ineffective to handle the detrimental effect of low-resolution ADCs at the destination. Moreover, it is shown that deploying massive relay antenna arrays can still bring significant power savings, i.e., the transmit power of each source can be cut down proportional to $1/M$ to maintain a constant rate, where $M$ is the number of relay antennas.
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