How Much Training Is Needed in One-Bit Massive MIMO Systems at Low SNR?
01 Dec 2016-pp 1-6
TL;DR: In this paper, the authors considered training-based transmissions in massive MIMO systems with one-bit ADCs and derived an approximate closed-form expression for the uplink achievable rate in the low SNR region.
Abstract: This paper considers training-based transmissions in massive multi-input multi-output (MIMO) systems with one-bit analog-to-digital converters (ADCs). We assume that each coherent transmission block consists of a pilot training stage and a data transmission stage. The base station (BS) first employs the linear minimum mean-square-error (LMMSE) method to estimate the channel and then uses the maximum-ratio combining (MRC) receiver to detect the data symbols. We first obtain an approximate closed-form expression for the uplink achievable rate in the low SNR region. Then based on the result, we investigate the optimal training length that maximizes the sum spectral efficiency for two cases: i) The training power and the data transmission power are both optimized; ii) The training power and the data transmission power are equal. Numerical results show that, in contrast to conventional massive MIMO systems, the optimal training length in one-bit massive MIMO systems is greater than the number of users and depends on various parameters such as the coherence interval and the average transmit power. Also, unlike conventional systems, it is observed that in terms of sum spectral efficiency, there is relatively little benefit to separately optimizing the training and data power.
Citations
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TL;DR: It is shown that, compared with conventional massive MIMO systems, the performance loss in one-bit massive M IMO systems can be compensated for by deploying approximately 2.5 times more antennas at the BS.
Abstract: In this letter, we investigate the downlink performance of massive multiple-input multiple-output (MIMO) systems where the base station is equipped with one-bit analog-to-digital/digital-to-analog converters (ADC/DACs) We assume that the base station employs the linear minimum mean-squared-error channel estimator and treats the channel estimate as the true channel to precode the data symbols We derive an expression for the downlink achievable rate for matched-filter precoding A detailed analysis of the resulting power efficiency is pursued using our expression of the achievable rate Numerical results are presented to verify our analysis In particular, it is shown that, compared with conventional massive MIMO systems, the performance loss in one-bit massive MIMO systems can be compensated for by deploying approximately 25 times more antennas at the BS
108 citations
TL;DR: 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, and 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 a constant rate.
Abstract: This paper considers a multipair amplify-and-forward massive MIMO relaying system with low-resolution analog-to-digital converters (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.
64 citations
TL;DR: Two techniques to compensate inphase/quadrature-phase imbalance (IQI) are investigated in the uplink-quantized massive multiple-input and multiple-output (MIMO) systems for different models of randomized IQI parameters to obtain better performance based on the Monte Carlo simulation results.
Abstract: In this paper, two techniques to compensate inphase/quadrature-phase imbalance (IQI) are investigated in the uplink-quantized massive multiple-input and multiple-output (MIMO) systems for different models of randomized IQI parameters. One is referred to as combined-signal-based channel estimation and compensation (CCEC) and the other is denoted by effective channel estimation and compensation (ECEC). First, an independent automatic gain control (AGC) scheme is proposed to calibrate the dynamic range of both the I branch and the Q branch. By doing that, different quantization steps are used for analog-to-digital converters following the AGCs in these two branches at each receive antenna. Second, considering the impacts of both quantization and IQI, we give the details of channel estimation and IQI compensation for both the CCEC and the ECEC using bilinear generalized approximate message passing (Bi-GAMP). Moreover, to exploit the Bi-GAMP for ECEC reasonably, we theoretically derive the probability density function PDF of the elements in the effective channel for the case where only RX IQI is considered. Furthermore, we extend the ECEC to the case where both RX IQI and TX IQI are incorporated into the systems and derive the similar pdf as well. Finally, we use the numerical results to testify the validity of our theoretical analysis and the fact that the analytic PDF can be approximated by a Gaussian distribution when the IQI parameters are relatively small. Compared with other classical methods, the proposed methods can obtain better performance based on the Monte Carlo simulation results.
29 citations
TL;DR: This research considers the channel estimation problem to fill this gap and proposes a two-step channel estimator by utilizing the different features of mixed outputs, which yields significantly lower mean square errors than the conventional maximum likelihood estimator.
Abstract: A receiver architecture with low-resolution analog-to-digital converters (ADCs) coupled with large antenna arrays has drawn considerable interest in the millimeter wave (mm-wave) system. Although architecture with pure one-bit ADCs has low power cost, such a system presents many challenges for synchronization, channel estimation, and power level estimation. Research has been conducted recently on the so-called mixed one-bit system, in which most antennas are equipped with one-bit ADCs, and a few have high-resolution ADCs. Despite the advantages of this system, studies on how to efficiently use high-resolution outputs to aid the one-bit system are lacking. This research considers the channel estimation problem to fill this gap and proposes a two-step channel estimator by utilizing the different features of mixed outputs. The channel gain can be extracted from high-resolution ADCs, and the channel angle can be extracted by the combination of additional one-bit ADCs. The proposed estimator leverages the sparsity feature of the channel in mm-wave. In contrast to previous works that used compressive sensing techniques, which confine the estimate to the set of grid angle points and induce estimation bias, the proposed estimator is gridless and treats the angle as a continuous parameter. The simulation results demonstrate that the proposed method yields significantly lower mean square errors than the conventional maximum likelihood estimator. In addition, this paper investigates ways to further improve the channel estimate by arranging the locations of high-resolution ADCs. Several useful observations on system design are obtained through our analysis.
26 citations
01 Feb 2017
TL;DR: An analogy is drawn between the one-bit wireless transceiver cell proposed herein and a “computational cell” commonly used in neural networks that allows us to apply neural-network type algorithms to aid in difficult tasks such as channel estimation for a large number of transceivers.
Abstract: We analyze a one-bit wireless transceiver whose architecture is simple enough that its power versus performance profile can be modeled analytically. We then utilize multiple such transceivers in a communication system operating at millimeter-wave carrier frequencies. Various aspects of the system are analyzed, including the optimum achievable throughput for a given amount of total consumed power. An analogy is drawn between the “transceiver cell” proposed herein and a “computational cell” commonly used in neural networks that allows us to apply neural-network type algorithms to aid in difficult tasks such as channel estimation for a large number of transceivers.
25 citations
References
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TL;DR: The Fundamentals of Statistical Signal Processing: Estimation Theory as mentioned in this paper is a seminal work in the field of statistical signal processing, and it has been used extensively in many applications.
Abstract: (1995). Fundamentals of Statistical Signal Processing: Estimation Theory. Technometrics: Vol. 37, No. 4, pp. 465-466.
14,342 citations
TL;DR: A cellular base station serves a multiplicity of single-antenna terminals over the same time-frequency interval and a complete multi-cellular analysis yields a number of mathematically exact conclusions and points to a desirable direction towards which cellular wireless could evolve.
Abstract: A cellular base station serves a multiplicity of single-antenna terminals over the same time-frequency interval. Time-division duplex operation combined with reverse-link pilots enables the base station to estimate the reciprocal forward- and reverse-link channels. The conjugate-transpose of the channel estimates are used as a linear precoder and combiner respectively on the forward and reverse links. Propagation, unknown to both terminals and base station, comprises fast fading, log-normal shadow fading, and geometric attenuation. In the limit of an infinite number of antennas a complete multi-cellular analysis, which accounts for inter-cellular interference and the overhead and errors associated with channel-state information, yields a number of mathematically exact conclusions and points to a desirable direction towards which cellular wireless could evolve. In particular the effects of uncorrelated noise and fast fading vanish, throughput and the number of terminals are independent of the size of the cells, spectral efficiency is independent of bandwidth, and the required transmitted energy per bit vanishes. The only remaining impairment is inter-cellular interference caused by re-use of the pilot sequences in other cells (pilot contamination) which does not vanish with unlimited number of antennas.
6,248 citations
TL;DR: In this paper, the tradeoff between the energy efficiency and spectral efficiency of a single-antenna system is quantified for a channel model that includes small-scale fading but not large scale fading, and it is shown that the use of moderately large antenna arrays can improve the spectral and energy efficiency with orders of magnitude compared to a single antenna system.
Abstract: A multiplicity of autonomous terminals simultaneously transmits data streams to a compact array of antennas. The array uses imperfect channel-state information derived from transmitted pilots to extract the individual data streams. The power radiated by the terminals can be made inversely proportional to the square-root of the number of base station antennas with no reduction in performance. In contrast if perfect channel-state information were available the power could be made inversely proportional to the number of antennas. Lower capacity bounds for maximum-ratio combining (MRC), zero-forcing (ZF) and minimum mean-square error (MMSE) detection are derived. An MRC receiver normally performs worse than ZF and MMSE. However as power levels are reduced, the cross-talk introduced by the inferior maximum-ratio receiver eventually falls below the noise level and this simple receiver becomes a viable option. The tradeoff between the energy efficiency (as measured in bits/J) and spectral efficiency (as measured in bits/channel use/terminal) is quantified for a channel model that includes small-scale fading but not large-scale fading. It is shown that the use of moderately large antenna arrays can improve the spectral and energy efficiency with orders of magnitude compared to a single-antenna system.
2,770 citations
TL;DR: This work compute a lower bound on the capacity of a channel that is learned by training, and maximize the bound as a function of the received signal-to-noise ratio (SNR), fading coherence time, and number of transmitter antennas.
Abstract: Multiple-antenna wireless communication links promise very high data rates with low error probabilities, especially when the wireless channel response is known at the receiver. In practice, knowledge of the channel is often obtained by sending known training symbols to the receiver. We show how training affects the capacity of a fading channel-too little training and the channel is improperly learned, too much training and there is no time left for data transmission before the channel changes. We compute a lower bound on the capacity of a channel that is learned by training, and maximize the bound as a function of the received signal-to-noise ratio (SNR), fading coherence time, and number of transmitter antennas. When the training and data powers are allowed to vary, we show that the optimal number of training symbols is equal to the number of transmit antennas-this number is also the smallest training interval length that guarantees meaningful estimates of the channel matrix. When the training and data powers are instead required to be equal, the optimal number of symbols may be larger than the number of antennas. We show that training-based schemes can be optimal at high SNR, but suboptimal at low SNR.
2,466 citations