Abstract
In this paper, we propose an efficient feedback scheme for an angle of departure (AoD) based channel estimation in frequency division duplex (FDD) massive multiple-input multiple-output (MIMO) systems with multiple antennas at the users. The channel feedback scheme is based on zero-forcing block diagonalization (BD) and it is proposed for two distinct design cases; in case I, the number of streams intended for a user equals the number of antennas at that user; in case II, the number of streams is less than the number of receive antennas. Case I is applicable in scenarios where high data rate requirements are needed as it transmits data symbols over all of the available degrees of freedom of the system. Diversely, case II is applicable when reliability is a priority in the system as it uses the additional <i>receive</i> antennas at the user to achieve spatial diversity to enhance the link performance. The proposed scheme is analyzed for the two cases by quantifying the downlink rate gap from the case of perfect channel state information (CSI). Moreover, we design structured feedback codebooks based on optimal subspace packing in the Grassmannian manifold and show that these codes achieve close performance to the perfect CSI case. Additionally, a vector quantization scheme is proposed to quantize the user’s channel matrix when optimal power allocation across multiple streams is adopted in the low signal-to-noise ratio (SNR) region. The feedback codebooks are based on optimal line packing in the Grassmannian manifold, where every vector of the user’s channel matrix is quantized and sent to the BaseStation. The results demonstrate a fundamental trade-off between vector quantization, with power optimization across the data streams, and subspace quantization. Specifically, vector quantization codebooks outperform subspace-based codebooks in the low SNR region, while the situation is reversed in the high SNR region.
Highlights
Massive multiple-input multiple-output (MIMO) wireless communication systems have been shown to introduce dramatic improvements, in both spectral and energy efficiency, by simultaneously serving multiple users with simple linear precoders [1]–[3]
The contributions of this paper can be summarized as follows: 1) We propose an efficient and structured feedback block diagonalization (BD)-based angle of departure (AoD)-adaptive codebooks using optimal subspace packing on the Grassmannian manifold for massive MIMO systems with multiple antenna users
4) A vector quantization codebook, based on optimal line packing on the Grassmannian manifold, is proposed to enhance the per-user rate in the low signal-to-noise ratio (SNR) region when power allocation across multiple data streams is used, where it is shown that vector quantization codebooks outperform subspace-based codebooks in the low SNR region, while the situation is reversed in the high SNR region
Summary
Massive multiple-input multiple-output (MIMO) wireless communication systems have been shown to introduce dramatic improvements, in both spectral and energy efficiency, by simultaneously serving multiple users with simple linear precoders [1]–[3]. In [9], the authors were able to estimate the users’ downlink channel covariance matrix from the uplink pilots using the fact that the angular scattering function of the user channels is invariant over frequency bands They proposed a novel sparsifying precoder, based on the covariance information, to maximize the effective sparsified channel matrix’s rank when the sparsity of each effective user channel is not larger than some desired downlink pilot dimension, resulting in reducing the downlink training and the CSI feedback overhead. The contributions of this paper can be summarized as follows: 1) We propose an efficient and structured feedback BD-based AoD-adaptive codebooks using optimal subspace packing on the Grassmannian manifold for massive MIMO systems with multiple antenna users. IP denotes the identity matrix of size P × P
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