Mode Switching for MIMO Broadcast Channel Based on Delay and Channel Quantization
📝 Abstract
Imperfect channel state information degrades the performance of multiple-input multiple-output (MIMO) communications; its effect on single-user (SU) and multi-user (MU) MIMO transmissions are quite different. In particular, MU-MIMO suffers from residual inter-user interference due to imperfect channel state information while SU-MIMO only suffers from a power loss. This paper compares the throughput loss of both SU and MU MIMO on the downlink due to delay and channel quantization. Accurate closed-form approximations are derived for the achievable rates for both SU and MU MIMO. It is shown that SU-MIMO is relatively robust to delayed and quantized channel information, while MU MIMO with zero-forcing precoding loses spatial multiplexing gain with a fixed delay or fixed codebook size. Based on derived achievable rates, a mode switching algorithm is proposed that switches between SU and MU MIMO modes to improve the spectral efficiency, based on the average signal-to-noise ratio (SNR), the normalized Doppler frequency, and the channel quantization codebook size. The operating regions for SU and MU modes with different delays and codebook sizes are determined, which can be used to select the preferred mode. It is shown that the MU mode is active only when the normalized Doppler frequency is very small and the codebook size is large.
💡 Analysis
Imperfect channel state information degrades the performance of multiple-input multiple-output (MIMO) communications; its effect on single-user (SU) and multi-user (MU) MIMO transmissions are quite different. In particular, MU-MIMO suffers from residual inter-user interference due to imperfect channel state information while SU-MIMO only suffers from a power loss. This paper compares the throughput loss of both SU and MU MIMO on the downlink due to delay and channel quantization. Accurate closed-form approximations are derived for the achievable rates for both SU and MU MIMO. It is shown that SU-MIMO is relatively robust to delayed and quantized channel information, while MU MIMO with zero-forcing precoding loses spatial multiplexing gain with a fixed delay or fixed codebook size. Based on derived achievable rates, a mode switching algorithm is proposed that switches between SU and MU MIMO modes to improve the spectral efficiency, based on the average signal-to-noise ratio (SNR), the normalized Doppler frequency, and the channel quantization codebook size. The operating regions for SU and MU modes with different delays and codebook sizes are determined, which can be used to select the preferred mode. It is shown that the MU mode is active only when the normalized Doppler frequency is very small and the codebook size is large.
📄 Content
Over the last decade, the point-to-point multiple-input multiple-output (MIMO) link (SU-MIMO) has been extensively researched and has transited from a theoretical concept to a practical technique [1], [2]. Due to space and complexity constraints, however, current mobile terminals only have one or two antennas, which limits the performance of the SU-MIMO link. Multi-user MIMO (MU-MIMO) provides the opportunity to overcome such a limitation by communicating with multiple mobiles simultaneously. It effectively increases the number of equivalent spatial channels and provides spatial multiplexing gain proportional to the number of transmit antennas at the base station even with single-antenna mobiles. In addition, MU-MIMO has higher immunity to propagation limitations faced by SU-MIMO, such as channel rank loss and antenna correlation [3].
There are many technical challenges that must be overcome to exploit the full benefits of MU-MIMO. A major one is the requirement of channel state information at the transmitter (CSIT), which is difficult to get especially for the downlink/broadcast channel. For the MIMO downlink with N t transmit antennas and N r receive antennas, with full CSIT the sum throughput can grow linearly with N t even when N r = 1, but without CSIT the spatial multiplexing gain is the same as for SU-MIMO, i.e. the throughput grows linearly with min(N t , N r ) at high SNR [4].
Limited feedback is an efficient way to provide partial CSIT, which feeds back the quantized channel information to the transmitter via a low-rate feedback channel [5], [6]. However, such imperfect CSIT will greatly degrade the throughput gain provided by MU-MIMO [7], [8]. Besides quantization, there are other imperfections in the available CSIT, such as estimation error and feedback delay. With imperfect CSIT, it is not clear whether-or more to the point, when-MU-MIMO can outperform SU-MIMO. In this paper, we compare SU and MU-MIMO transmissions in the MIMO downlink with CSI delay and channel quantization, and propose to switch between SU and MU MIMO modes based on the achievable rate of each technique with practical receiver assumptions.
For the MIMO downlink, CSIT is required to separate the spatial channels for different users.
To obtain the full spatial multiplexing gain for the MU-MIMO system employing zero-forcing (ZF) or block-diagonalization (BD) precoding, it was shown in [7], [9] that the quantization codebook size for limited feedback needs to increase linearly with SNR (in dB) and the number of transmit antennas. Zero-forcing dirty-paper coding and channel inversion systems with limited feedback were investigated in [8], where a sum rate ceiling due to a fixed codebook size was derived for both schemes. In [10], it was shown that to exploit multiuser diversity for ZF, both channel direction and information about signal-to-interference-plus-noise ratio (SINR) must be fed back. More recently, a comprehensive study of the MIMO downlink with ZF precoding was done in [11], which considered downlink training and explicit channel feedback and concluded that significant downlink throughput is achievable with efficient CSI feedback. For a compound MIMO broadcast channel, the information theoretic analysis in [12] showed that scaling the CSIT quality such that the CSIT error is dominated by the inverse of the SNR is both necessary and sufficient to achieve the full spatial multiplexing gain.
Although previous studies show that the spatial multiplexing gain of MU-MIMO can be achieved with limited feedback, it requires the codebook size to increase with SNR and the number of transmit antennas. Even if such a requirement is satisfied, there is an inevitable rate loss due to quantization error, plus other CSIT imperfections such as estimation error and delay.
In addition, most of prior work focused on the achievable spatial multiplexing gain, mainly based on the analysis of the rate loss due to imperfect CSIT, which is usually a loose bound [7], [9], [12]. Such analysis cannot accurately characterize the throughput loss, and no comparison with SU-MIMO has been made. In this paper, we derive good approximations for the achievable throughput for both SU and MU MIMO systems with fixed channel information accuracy, i.e. with a fixed delay and a fixed quantization codebook size. We are interested in the following question: With imperfect CSIT, including delay and channel quantization, when can MU-MIMO actually deliver a throughput gain over SU-MIMO? Based on this, we can select the one with the higher throughput as the transmission technique.
In this paper, we investigate SU and MU-MIMO in the broadcast channel with CSI delay and limited feedback. The main contributions of this paper are as follows.
• SU vs. MU Analysis. We investigate the impact of imperfect CSIT due to delay and channel quantization. We show that the SU mode is more robust to imperfect CSIT as it only suffers a constant rate loss, while MU-MIMO suffers mo
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