AoD and AoA tracking with directional sounding beam design for millimeter wave MIMO systems
03 Dec 2015-pp 2271-2276
TL;DR: Simulation results demonstrate that the proposed AoD and AoA tracking outperforms other benchmark schemes when compared in a low SNR setting.
Abstract: Millimeter wave multiple-input multiple-output (MIMO) systems equipped with large-sized array antennas have a great potential to boost the achievable data rates by leveraging large bandwidth available at the spectrum. In this paper, we focus on the angle of departure (AoD) and angle of arrival (AoA) tracking problem for temporally correlated sparse millimeter wave MIMO channels. With the beam space MIMO channel modeling, a low complexity two-sided channel sounding scheme for the AoD and AoA tracking is investigated. The adoption of the sparse beam space MIMO channel representation eventually converts the AoD and AoA estimation problem to the support recovery problem. For the support recovery, we employ an iterative soft thresholding algorithm which is broadly referred to as the approximate message passing (AMP) algorithm. The support recovery performance of the AMP, however, suffers from serious deterioration especially at the low SNR regime. To remedy, several directional sounding beam design schemes are proposed to ameliorate the performance of the channel tracking at the low SNR. Simulation results demonstrate that the proposed AoD and AoA tracking outperforms other benchmark schemes when compared in a low SNR setting.
Citations
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01 Dec 2016
TL;DR: A beam tracking method requiring to train only one beam pair to track a path in the analog beamforming architecture is developed, considering its low complexity which is suitable for mobile settings, the extended Kalman filter is chosen as the tracking filter.
Abstract: Millimeter wave (mmWave) is an attractive option for high data rate applications. Enabling mmWave communications requires appropriate beamforming, which is conventionally realized by a lengthy beam training process. Such beam training will be a challenge for applying mmWave to mobile environments. As a solution, a beam tracking method requiring to train only one beam pair to track a path in the analog beamforming architecture is developed. Considering its low complexity which is suitable for mobile settings, the extended Kalman filter is chosen as the tracking filter. Several effects impacting the performance of the proposed tracking algorithm, such as the signal-to-noise ratio (SNR) and array size, are investigated. It is found that at the same SNR, narrower beams, which are more sensitive to angular changes, can provide more accurate estimate. Too narrow beams, however, degrade tracking performance because beam misalignment could happen during the measurement. Finally, a comparison to prior work is given where it is shown that our approach is more suitable for fast-changing environments thanks to the low measurement overhead.
243 citations
Cites background from "AoD and AoA tracking with direction..."
...Prior work on beam tracking for mmWave systems includes [6], [8]–[10]....
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Posted Content•
TL;DR: This paper proposes to use the vehicle's position to query a multipath fingerprint database, which provides prior knowledge of potential pointing directions for reliable beam alignment, the inverse of fingerprinting localization.
Abstract: Efficient beam alignment is a crucial component in millimeter wave systems with analog beamforming, especially in fast-changing vehicular settings. This paper proposes a position-aided approach where the vehicle's position (e.g., available via GPS) is used to query the multipath fingerprint database, which provides prior knowledge of potential pointing directions for reliable beam alignment. The approach is the inverse of fingerprinting localization, where the measured multipath signature is compared to the fingerprint database to retrieve the most likely position. The power loss probability is introduced as a metric to quantify misalignment accuracy and is used for optimizing candidate beam selection. Two candidate beam selection methods are developed, where one is a heuristic while the other minimizes the misalignment probability. The proposed beam alignment is evaluated using realistic channels generated from a commercial ray-tracing simulator. Using the generated channels, an extensive investigation is provided, which includes the required measurement sample size to build an effective fingerprint, the impact of measurement noise, the sensitivity to changes in traffic density, and beam alignment overhead comparison with IEEE 802.11ad as the baseline. Using the concept of beam coherence time, which is the duration between two consecutive beam alignments, and parameters of IEEE 802.11ad, the overhead is compared in the mobility context. The results show that while the proposed approach provides increasing rates with larger antenna arrays, IEEE 802.11ad has decreasing rates due to the larger beam training overhead that eats up a large portion of the beam coherence time, which becomes shorter with increasing mobility.
112 citations
Cites methods from "AoD and AoA tracking with direction..."
...For example, compressive sensing is used in [16], [17] while an approximate maximum likelihood estimator is derived using the channel structure directly in [18]....
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01 Jan 2013
TL;DR: In this paper, an efficient beam alignment technique using adaptive subspace sampling and hierarchical beam codebooks was proposed to solve the problem of spectrum reusability and flexible prototyping radio platform using software-defined radio (SDR).
Abstract: Mobile data traffic will continue its tremendous growth in some markets, and has already resulted in an apparent radio spectrum scarcity. There is a strong need for more efficient methods to use spectrum resources, leading to extensive research on increasing spectrum reusability on flexible radio platforms. This study solves this problem in two sub topics, millimeter wave communication on wireless backhaul for spectrum reusability, and flexible prototyping radio platform using software-defined radio (SDR).
Wireless backhaul has received significant attention as a key technology affecting the development of future wireless cellular networks because it helps to easily deploy many small size cells, an essential part of a high capacity system. Millimeter wave is considered a possible candidate for cost-effective wireless backhaul. In the outdoor deployment using a millimeter wave, beamforming methods are key techniques to establish wireless links in the 60 GHz to 80 GHz to overcome pathloss constraints (i.e., rainfall effect and oxygen absorption). The millimeter wave communication system cannot directly access the channel knowledge. To overcome this, a beamforming method based on codebook search is considered. The millimeter wave communication cannot access channel knowledge, therefore alternatively a beamforming method based on a codebook search is considered. In the first part, we propose an efficient beam alignment technique using adaptive subspace sampling and hierarchical beam codebooks. A wind sway analysis is presented to establish a notion of beam coherence time. This highlights a previously unexplored tradeoff between array size and wind-induced movement. Generally, it is not possible to use larger arrays without risking a performance loss from wind-induced beam misalignment. The performance of the proposed alignment technique is analyzed and compared with other search and alignment methods. Results show significant performance improvement with reduced search time.
In the second part of this study, SDR is discussed as an approach toward flexible wireless communication systems. Most layers of SDR are implemented by software. Therefore, only a software change is needed to transform the type of radio system. The translation of the signal processing into software performed by a regular computer opens up a huge number of possibilities at a reasonable price and effort. SDR systems are widely used to build prototypes, saving time and money. In this project, a robust wireless communication system in high interference environment was developed. For the physical layer (PHY) of the system, we implemented a channel sub-bandding method that utilizes frequency division multiplexing to avoid interference. Then, to overcome a further interfered channel, Direct Spread Spectrum System (DSSS) was considered and implemented. These prototyped testbeds were evaluated for system performance in the interference environment.
103 citations
TL;DR: This paper uses a multi-armed bandit framework to develop the online learning algorithms for beam pair selection and refinement, which uses the upper confidence bound with a newly proposed risk-aware feature, while the beam refinement uses a modified optimistic optimization algorithm.
Abstract: Accurate beam alignment is essential for the beam-based millimeter wave communications. The conventional beam sweeping solutions often have large overhead, which is unacceptable for mobile applications, such as a vehicle to everything. The learning-based solutions that leverage the sensor data (e.g., position) to identify the good beam directions are one approach to reduce the overhead. Most existing solutions, though, are supervised learning, where the training data are collected beforehand. In this paper, we use a multi-armed bandit framework to develop the online learning algorithms for beam pair selection and refinement. The beam pair selection algorithm learns coarse beam directions in some predefined beam codebook, e.g., in discrete angles, separated by the 3 dB beamwidths. The beam refinement fine-tunes the identified directions to match the peak of the power angular spectrum at that position. The beam pair selection uses the upper confidence bound with a newly proposed risk-aware feature, while the beam refinement uses a modified optimistic optimization algorithm. The proposed algorithms learn to recommend the good beam pairs quickly. When using $16\times 16$ arrays at both transmitter and receiver, it can achieve, on average, 1-dB gain over the exhaustive search (over $271\times 271$ beam pairs) on the unrefined codebook within 100 time steps with a training budget of only 30 beam pairs.
90 citations
Cites background from "AoD and AoA tracking with direction..."
...ment has been investigated intensively in the literature. Several directions have been pursued such as approaches based on beam sweeping [9], [10], angle of arrival and departure (AoA/AoD) estimation [11], [12], blackbox function optimization [13], [14], and the use of sideinformation [1]–[3], [15]. We refer to [1] for a summary of the differences of these approaches for beam alignment. The last categ...
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TL;DR: In this paper, a codebook-based beam tracking strategy for mobile millimeter-wave (mmWave) systems, where the temporal variation of the angle of departure (AoD) is considered, is derived and further optimized.
Abstract: In this paper, we propose a codebook-based beam tracking strategy for mobile millimeter-wave (mmWave) systems, where the temporal variation of the angle of departure (AoD) is considered. A closed-form upper bound of the average tracking error probability (ATEP) is derived and further optimized. We first consider a slow-varying scenario where narrow training beams implemented by single radio-frequency (RF) chain are employed. We show that the ATEP can be reduced by optimizing the power allocation strategy over these training beams, which is formulated and transformed into a second-order cone programming. The fast-varying scenario is further considered where the use of narrow training beams becomes inefficient due to the rapid variations of AoD. In order to reduce the training time, multiple RF chains generating wide beams are employed to track the AoD’s variations, and the associated beam pattern design problem is shown to be a 0 – 1 nonlinear optimization problem (NLP). A sequential quadratic programming method is used to solve this binary NLP. To reduce the complexity, a progressive edge-growth algorithm is further introduced by associating the binary NLP with a bipartite graph. Numerical results demonstrate significant gains of the proposed beam tracking strategy over existing benchmarks for both scenarios.
58 citations
References
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TL;DR: In this paper, the authors considered the problem of recovering a vector x ∈ R^m from incomplete and contaminated observations y = Ax ∈ e + e, where e is an error term.
Abstract: Suppose we wish to recover a vector x_0 Є R^m (e.g., a digital signal or image) from incomplete and contaminated observations y = Ax_0 + e; A is an n by m matrix with far fewer rows than columns (n « m) and e is an error term. Is it possible to recover x_0 accurately based on the data y?
To recover x_0, we consider the solution x^# to the l_(1-)regularization problem min ‖x‖l_1 subject to ‖Ax - y‖l(2) ≤ Є, where Є is the size of the error term e. We show that if A obeys a uniform uncertainty principle (with unit-normed columns) and if the vector x_0 is sufficiently sparse, then the solution is within the noise level ‖x^# - x_0‖l_2 ≤ C Є. As a first example, suppose that A is a Gaussian random matrix; then stable recovery occurs for almost all such A's provided that the number of nonzeros of x_0 is of about the same order as the number of observations. As a second instance, suppose one observes few Fourier samples of x_0; then stable recovery occurs for almost any set of n coefficients provided that the number of nonzeros is of the order of n/[log m]^6. In the case where the error term vanishes, the recovery is of course exact, and this work actually provides novel insights into the exact recovery phenomenon discussed in earlier papers. The methodology also explains why one can also very nearly recover approximately sparse signals.
6,727 citations
TL;DR: The motivation for new mm-wave cellular systems, methodology, and hardware for measurements are presented and a variety of measurement results are offered that show 28 and 38 GHz frequencies can be used when employing steerable directional antennas at base stations and mobile devices.
Abstract: The global bandwidth shortage facing wireless carriers has motivated the exploration of the underutilized millimeter wave (mm-wave) frequency spectrum for future broadband cellular communication networks. There is, however, little knowledge about cellular mm-wave propagation in densely populated indoor and outdoor environments. Obtaining this information is vital for the design and operation of future fifth generation cellular networks that use the mm-wave spectrum. In this paper, we present the motivation for new mm-wave cellular systems, methodology, and hardware for measurements and offer a variety of measurement results that show 28 and 38 GHz frequencies can be used when employing steerable directional antennas at base stations and mobile devices.
6,708 citations
"AoD and AoA tracking with direction..." refers background in this paper
...In the millimeter wave, the large number of array antennas can be packed in a small form factor making largescale multiple-input multiple-output (MIMO) feasible [1], [2]....
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...Recent studies have demonstrated that practical millimeter wave MIMO channel exhibits substantial sparsity [1], [2]....
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Posted Content•
TL;DR: It is shown that it is possible to recover x0 accurately based on the data y from incomplete and contaminated observations.
Abstract: Suppose we wish to recover an n-dimensional real-valued vector x_0 (e.g. a digital signal or image) from incomplete and contaminated observations y = A x_0 + e; A is a n by m matrix with far fewer rows than columns (n << m) and e is an error term. Is it possible to recover x_0 accurately based on the data y?
To recover x_0, we consider the solution x* to the l1-regularization problem min \|x\|_1 subject to \|Ax-y\|_2 <= epsilon, where epsilon is the size of the error term e. We show that if A obeys a uniform uncertainty principle (with unit-normed columns) and if the vector x_0 is sufficiently sparse, then the solution is within the noise level \|x* - x_0\|_2 \le C epsilon.
As a first example, suppose that A is a Gaussian random matrix, then stable recovery occurs for almost all such A's provided that the number of nonzeros of x_0 is of about the same order as the number of observations. Second, suppose one observes few Fourier samples of x_0, then stable recovery occurs for almost any set of p coefficients provided that the number of nonzeros is of the order of n/[\log m]^6. In the case where the error term vanishes, the recovery is of course exact, and this work actually provides novel insights on the exact recovery phenomenon discussed in earlier papers. The methodology also explains why one can also very nearly recover approximately sparse signals.
6,226 citations
"AoD and AoA tracking with direction..." refers background or methods in this paper
...The tracking technique employing the omni-directional sounding beam presented in the previous section could show a reliable estimation performance at high SNR, because the isometry property of the sensing matrix [14], [15] is derived assuming a high SNR setting....
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...In the compressed sensing literature, a property of a good sensing matrix is referred to as the isometry property [14], [15], in which A∗A is required to be close to the identity matrix....
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...A preferred sounding beam property that guarantees high support recovery rate is defined by the isometry property [14], [15]....
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TL;DR: This paper considers transmit precoding and receiver combining in mmWave systems with large antenna arrays and develops algorithms that accurately approximate optimal unconstrained precoders and combiners such that they can be implemented in low-cost RF hardware.
Abstract: Millimeter wave (mmWave) signals experience orders-of-magnitude more pathloss than the microwave signals currently used in most wireless applications and all cellular systems. MmWave systems must therefore leverage large antenna arrays, made possible by the decrease in wavelength, to combat pathloss with beamforming gain. Beamforming with multiple data streams, known as precoding, can be used to further improve mmWave spectral efficiency. Both beamforming and precoding are done digitally at baseband in traditional multi-antenna systems. The high cost and power consumption of mixed-signal devices in mmWave systems, however, make analog processing in the RF domain more attractive. This hardware limitation restricts the feasible set of precoders and combiners that can be applied by practical mmWave transceivers. In this paper, we consider transmit precoding and receiver combining in mmWave systems with large antenna arrays. We exploit the spatial structure of mmWave channels to formulate the precoding/combining problem as a sparse reconstruction problem. Using the principle of basis pursuit, we develop algorithms that accurately approximate optimal unconstrained precoders and combiners such that they can be implemented in low-cost RF hardware. We present numerical results on the performance of the proposed algorithms and show that they allow mmWave systems to approach their unconstrained performance limits, even when transceiver hardware constraints are considered.
3,146 citations
"AoD and AoA tracking with direction..." refers methods in this paper
...The hybrid analog-digital MIMO precoding and combing techniques have also been proposed in [6], [7], which further enhance the spectral efficiency by customizing both the analog and digital precoder/combiner....
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TL;DR: An adaptive algorithm to estimate the mmWave channel parameters that exploits the poor scattering nature of the channel is developed and a new hybrid analog/digital precoding algorithm is proposed that overcomes the hardware constraints on the analog-only beamforming, and approaches the performance of digital solutions.
Abstract: Millimeter wave (mmWave) cellular systems will enable gigabit-per-second data rates thanks to the large bandwidth available at mmWave frequencies. To realize sufficient link margin, mmWave systems will employ directional beamforming with large antenna arrays at both the transmitter and receiver. Due to the high cost and power consumption of gigasample mixed-signal devices, mmWave precoding will likely be divided among the analog and digital domains. The large number of antennas and the presence of analog beamforming requires the development of mmWave-specific channel estimation and precoding algorithms. This paper develops an adaptive algorithm to estimate the mmWave channel parameters that exploits the poor scattering nature of the channel. To enable the efficient operation of this algorithm, a novel hierarchical multi-resolution codebook is designed to construct training beamforming vectors with different beamwidths. For single-path channels, an upper bound on the estimation error probability using the proposed algorithm is derived, and some insights into the efficient allocation of the training power among the adaptive stages of the algorithm are obtained. The adaptive channel estimation algorithm is then extended to the multi-path case relying on the sparse nature of the channel. Using the estimated channel, this paper proposes a new hybrid analog/digital precoding algorithm that overcomes the hardware constraints on the analog-only beamforming, and approaches the performance of digital solutions. Simulation results show that the proposed low-complexity channel estimation algorithm achieves comparable precoding gains compared to exhaustive channel training algorithms. The results illustrate that the proposed channel estimation and precoding algorithms can approach the coverage probability achieved by perfect channel knowledge even in the presence of interference.
2,424 citations
"AoD and AoA tracking with direction..." refers methods in this paper
...The hybrid analog-digital MIMO precoding and combing techniques have also been proposed in [6], [7], which further enhance the spectral efficiency by customizing both the analog and digital precoder/combiner....
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