Peilu Ding

Multiple Antenna Broadcast Channels With Shape Feedback and Limited Feedback

In this paper, we consider two different models of partial channel state information at the base station transmitter (CSIT) for multiple antenna broadcast channels: 1) the shape feedback model where the normalized channel vector of each user is available at the base station and 2) the limited feedback model where each user quantizes its channel vector according to a rotated codebook that is optimal in the sense of mean squared error and feeds back the codeword index. This paper is focused on characterizing the sum rate performance of both zero-forcing dirty paper coding (ZFDPC) systems and channel inversion (CI) systems under the given two partial CSIT models. Intuitively speaking, a system with shape feedback loses the sum rate gain of adaptive power allocation. However, shape feedback still provides enough channel knowledge for ZFDPC and CI to approach their own optimal throughput in the high signal-to-noise ratio (SNR) regime. As for limited feedback, we derive sum rate bounds for both signaling schemes and link their throughput performance to some basic properties of the quantization codebook. Interestingly, we find that limited feedback employing a fixed codebook leads to a sum rate ceiling for both schemes for asymptotically high SNR.

On the sum rate of channel subspace feedback for multi-antenna broadcast channels

When a base-station with multiple antennas is transmitting to a single user with one antenna, feeding back the normalized channel vector (channel subsapce feedback) to the transmitter can achieve the same capacity as if the exact channel state information is available at the transmitter. For the multiuser scenario, however, perfect channel knowledge is usually required at the transmitter to obtain the sum rate advantage provided by the multiple transmit antennas. In this paper, we consider the sum rate of a multi-antenna broadcast channel when each user only feeds back the normalized channel vector. We show that in such situation the zero-forcing dirty paper (ZFDP) encoding scheme designed using channel subspace feedback achieves the throughput of full channel knowledge ZFDP encoding without optimal power allocation. It is shown to be asymptotically optimal for high signal-to-noise ratios. The closed-form expression of the ergodic sum rate for an independent Rayleigh fading channel is derived. The throughput performance of the regularized channel inversion technique under channel subspace feedback is also analyzed. We show that channel subspace feedback in the multi-antenna broadcast channel enables the system to achieve most of the sum rate advantage provided by the multiple antennas

Multiple Antenna Broadcast Channels With Limited Feedback

In this paper, we study the limited feedback model for partial CSI at the basestation (BS) for multiple antenna broadcast channels: the BS has the knowledge of quantized CSI of each user. We first give a practical limited feedback scheme designed for multiple antenna broadcast channels. Then, we study the sum rate performance of zero-forcing dirty paper coding under the proposed limited feedback scheme. An upper bound is also derived to get some insight about the impact of the use of limited feedback. Interestingly, we find that the systems experience a ceiling effect on the sum rate for a fixed feedback rate

Space-time coding and beamforming with partial channel state information

In this paper, a STBC/BF hybrid technique is proposed for outdoor multipath multi-input multi-output (MIMO) channel. Depending on the amount of partial channel state information (CSI), this system evolves from pure diversity waveform signalling to pure beamforming. The performance of this technique, in terms of signal vs noise ratio (SNR), is investigated in various multi-input single-output (MISO) scenarios. Though the method is evaluated in MISO, we give a simple way to extend it to MIMO case. In addition, a beamforming scheme based on sub-space approximation is also discussed which can reduce the amount of feedback from the receiver to transmitter. Simulation results are given at the end of this paper

On the Sum Rate of Multi-Antenna Broadcast Channels with Channel Estimation Error

For multiple antenna broadcast channels, perfect channel state information (CSI) at the basestation plays a critical role in achieving the sum rate advantage provided by the multiple antennas. For practical system implementation, the CSI is usually estimated from training sequences. In this paper, we study the effect of channel estimation error on the sum rate capacity of multiple antenna broadcast channels. A lower bound is derived based on the sum rate performance of the zero forcing dirty paper coding scheme under CSI estimation error. A cooperative upper bound is established from the capacity upper bound of a single user multiple-input multiple-output (MIMO) channel given the same channel imperfectness. We further analyze the asymptotic sum rate loss caused by channel estimation error. If we assume that the variance of the channel estimation error is fixed, imperfect CSI results in a sum rate ceiling for high SNR. For systems with orthogonal training sequences and minimum mean square error (MMSE) channel estimator, the asymptotic sum rate loss is about N bit per channel use where N is the number of transmit antennas. I. INTRODUCTION Techniques employing multiple antennas are important for wireless communication systems because they provide the possibility of a significant increase in system spectrum effi- ciency. In the last decade, lots of works have been done on point-to-point, i.e., single user, multiple-input multiple-output (MIMO) systems. Larger rate gains, however, are available when MIMO multi-user systems are considered. Recently, the sum rate capacity of the multiple antenna broadcast channel, which models the downlink in a MIMO cellular network, was solved (1), (2), (3), (4). These works show that perfect channel state information (CSI) at the basestation is critical for the system to achieve the sum rate advantage. With perfect CSI,

Hybrid transmit waveform design based on beam-forming and orthogonal space-time block coding

We derive a hybrid of beam-forming (BF) and space-time block coding (STBC), where the space-time code is transmitted over the beams generated by the steering vectors corresponding to the channel path directions. This is for the practical case where the transmit array may have adequate information on the departure angles of the dominant paths between transmitter and receiver, but unreliable information on the associated complex path gains. We compute analytically the signal-to-noise ratio (SNR) of the proposed hybrid for the specific case of a two-path channel model and using the orthogonal Alamouti code, and compare the result to the SNR of optimal linear precoding (LP) and the theoretically possible SNR of orthogonal STBC (OSTBC). Simulation results show that the performance of the BF/STBC hybrid can be very close to LP /sup n/der certain conditions - or even better in the practical case where there are phase estimation errors in the path gain estimates employed at the transmitter.

Low Complexity Adaptive Design for Full-Diversity Full-Rate Space-Time Codes

Full-diversity full-rate (FDFR) space-time codes for open-loop multiple antenna systems achieve both high data rate and good performance but come with very high decoding complexity. In this paper, we propose a low-complexity adaptive FDFR design for closed-loop multiple-input multiple-output systems. With only partial channel subspace knowledge at the transmitter, we adapt the open-loop FDFR code to the channel to maintain the special layer structure of the code at the receiver. That special layer structure enables us to decouple the joint detection over dimension CNt2 into Nt individual decoders of dimension CNt, where Nt is the number of transmit antennas. This can also be seen as combining the channel diagonalization with signal diversity rotation. The performance of the proposed scheme is analyzed, and it is shown that the full diversity property is maintained in the adaptive design. Adaptive power loading is also incorporated to further exploit channel state information in term of the knowledge of the singular values of the channel. The optimal loading schemes are derived for systems with linear receivers

Combining circulant space-time coding with IFFT/FFT and spreading

Space-time transmit structures for multi-antenna systems have received considerable interest. Circulant structures were among the first space-time coding techniques ever used for multiple-input multiple-output (MIMO) systems due to their simplicity and full rate. The fact that a circulant matrix is diagonalized by the discrete Fourier transformation matrix suggests that the circulant structure can be combined with an inverse fast Fourier transform (IFFT) at the transmitter and a fast Fourier transform (FFT) at the receiver. Using this method, the spatial mixing effect of the MIMO channel is decoupled but the diversity gain is lost. To recover the diversity advantage, we propose to spread the transmitted symbols over the diagonalized channel using the constellation rotation matrix for signal diversity designs. After spreading, every symbol experiences all the components of the frequency counterpart of the channel vector which makes our scheme provide full diversity. The proposed scheme is full rate and can be easily applied to any number of transmit antennas. Our simulation results show that the performance of our scheme is close to the performance of the ideal orthogonal space-time code and much better than the conventional circulant space-time code.

WLC26-2: Limited Feedback in Multiple Antenna Broadcast Channels

In this paper, we consider limited feedback for multiple antenna broadcast channels: each user quantizes its channel vector according to a rotated codebook which is optimal in the sense of mean square error and feeds back the codeword index. The paper is focused on characterizing the sum rate performance of zero-forcing dirty paper coding (ZFDPC) systems under limited feedback. We derive sum rate upper bound for systems employing Gaussian random codebooks and minimum distance decoding and link the throughput performance to some basic properties of the quantization codebook. Interestingly, we find that limited feedback employing a fixed codebook leads to a sum rate ceiling for asymptotically high SNR.

Adaptive full diversity full rate codes with channel state information

Full-diversity full-rate (FDFR) space-time codes achieve both high spectral efficiency and good performance. However, the associated high decoding complexity limits their practical application. In this paper, we use channel state information (CSI) at the transmitter to effectively reduce the decoding complexity at the receiver side. We propose to diagonalize the multiple-input multiple-output (MIMO) channel based on the singular value decomposition which only involves linear processing at the transmitter and receiver. Thus the special layer structure in the FDFR code matrix is still maintained after transmission through the channel. That special layer structure enables us to decouple the joint detection over dimension C N 2 t into N t individual decoders of dimension C N t . The full diversity performance is maintained in the proposed low complexity adaptive scheme. Adaptive power loading is also incorporated to further exploit the CSI at the transmitter and improve the performance.