Joint Spatial Division and Multiplexing—The Large-Scale Array Regime

By Ansuman Adhikary, Junyoung Nam, J. Ahn, Giuseppe Caire. IEEE Transactions on Information Theory, 2012

1,293 citations recorded by the source corpus.

We propose joint spatial division and multiplexing (JSDM), an approach to multiuser MIMO downlink that exploits the structure of the correlation of the channel vectors in order to allow for a large number of antennas at the base station while requiring reduced-dimensional channel state information at the transmitter (CSIT). JSDM achieves significant savings both in the downlink training and in the CSIT uplink feedback, thus making the use of large antenna arrays at the base station potentially suitable also for frequency division duplexing (FDD) systems, for which uplink/downlink channel reciprocity cannot be exploited. In the proposed scheme, the multiuser MIMO downlink precoder is obtained by concatenating a prebeamforming matrix, which depends only on the channel second-order statistics, with a classical multiuser precoder, based on the instantaneous knowledge of the resulting reduced dimensional “effective” channel matrix. We prove a simple condition under which JSDM incurs no loss of optimality with respect to the full CSIT case. For linear uniformly spaced arrays, we show that such condition is approached in the large number of antennas limit. For this case, we use Szego's asymptotic theory of Toeplitz matrices to show that a DFT-based prebeamforming matrix is near-optimal, requiring only coarse information about the users angles of arrival and angular spread. Finally, we extend these ideas to the case of a 2-D base station antenna array, with 3-D beamforming, including multiple beams in the elevation angle direction. We provide guidelines for the prebeamforming optimization and calculate the system spectral efficiency under proportional fairness and max-min fairness criteria, showing extremely attractive performance. Our numerical results are obtained via asymptotic random matrix theory, avoiding lengthy Monte Carlo simulations and providing accurate results for realistic (finite) number of antennas and users.

Subfields: Computer Networks and Communications, Electrical and Electronic Engineering, Signal Processing

View Paper: https://www.semanticscholar.org/paper/c51ecd5b10312f62799a7a5f379dd80ce43cb46d

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Citations in the corpus

Hybrid Beamforming for Massive MIMO - A Survey (2016, methodology): “Reference [10] proposed a scheme called “Joint Spatial Division Multiplexing” (JSDM), which considered the hybrid structures at the BS and single-antenna UEs; to further alleviate the downlink training and uplink feedback burden, UEs with similar transmit channel covariance are grouped together and ”
Millimeter Wave MIMO With Lens Antenna Array: A New Path Division Multiplexing Paradigm (2015, background): “Similarly in [42], [43], an AoA-based user grouping technique is proposed, which leads to the so-called joint spatial division and multiplexing scheme that makes massive MIMO also possible for frequency division duplexing (FDD) systems due to the signiﬁcantly reduced channel estimation overhead…”
Massive MIMO Systems With Non-Ideal Hardware: Energy Efficiency, Estimation, and Capacity Limits (2013, background): “An important property of this model is that R might not have full rank as N grows large [43], [44], due to insufficient scattering.”
Massive MIMO Transmission for LEO Satellite Communications (2020, background): “As different UTs are usually spatially separated by a few wavelengths, it is reasonable to assume that the channel realizations between the satellite and different UTs are uncorrelated [17].”
Dynamic Subarrays for Hybrid Precoding in Wideband mmWave MIMO Systems (2016, background): “Due to the design of the optimal unconstrained RF precoder in (22), which depends on the channel singular vectors, and because these singular vectors take a DFT structure for uniform arrays as N →∞ [18], [27], [28], this simple solution is a reasonable substitute for the unknown optimal solution, wh”
A Unified Transmission Strategy for TDD/FDD Massive MIMO Systems With Spatial Basis Expansion Model (2017, methodology): “By contrast, FDD reciprocity has not been reported either from covariance-based methods [18], [20] or CS-based methods [17], [21].”
5G: A Tutorial Overview of Standards, Trials, Challenges, Deployment, and Practice (2017, neutral): “tion [88], [89], [121], [19], [122], [20].”
Pilot Reuse for Massive MIMO Transmission over Spatially Correlated Rayleigh Fading Channels (2015, background): “Similar channel covariance matrix decomposition for the ULA case was derived in [11] and [21], however, the result in Lemma 1 applies to the more general BS array conﬁgurations.”
Joint Spatial Division and Multiplexing for mm-Wave Channels (2013, methodology): “…power is less for both groups after the removal of the common scatterer, more users can be served simultaneously, thereby giving a higher spatial multiplexing, which is a factor of 2 compared to Orthogonalization (this is reflected by the slope of the spectral efficiency curves at high SNR).”
Limited Feedback Hybrid Precoding for Multi-User Millimeter Wave Systems (2014, methodology): “In [19], twolayer beamforming algorithms were proposed to group the users and reduce the channel feedback overhead in massive MIMO systems.”
Deep Learning for Super-Resolution Channel Estimation and DOA Estimation Based Massive MIMO System (2018, methodology): “In the next comparison, we investigate the BER performance against the SNR of the proposed DL based scheme, the JSDM scheme[12], and the SBEM scheme[17], where L = 12 bits and the batch size is 50.”
Joint Spatial Division and Multiplexing: Opportunistic Beamforming, User Grouping and Simplified Downlink Scheduling (2014, methodology): “The multiuser MIMO precoding matrix is allowed to depend on instantaneous realization (on each channel coherence block) of the “effective” channel .”
Millimeter Wave Cellular Networks: A MAC Layer Perspective (2015, background): “Digital beamforming provides further spatial gain by multiplexing within a group, which is affordable due to a substantial reduction in the dimension of the effective channel, that is, the channel from a digital beamformer perspective [36].”
Beam Division Multiple Access Transmission for Massive MIMO Communications (2015, background): “After the prebeamforming stage, the training dimensions are significantly reduced [13].”
A Comprehensive Survey of Pilot Contamination in Massive MIMO—5G System (2016, methodology): “However, [18]–[21] proposed the use of FDD.”
6G Wireless Systems: Vision, Requirements, Challenges, Insights, and Opportunities (2020, background): “Promising research efforts in this area include the adaptation of the pilot signal spacing in time and frequency domains, exploitation of limited angular spread of the channel [77], and advanced signal processing methods for reduction of pilot contamination [78].”