Incremental Grassmannian Feedback Schemes for Multi-User MIMO Systems

Abstract

The communication of side information forms a key component of several effective strategies for transmitter adaptation to slowly fading channels. When the relevant side information is a subspace, the feedback scheme can be viewed as a lossy source compression scheme on the Grassmannian manifold. Memoryless vector quantization on each fading block is a viable compression scheme, but it neglects any temporal correlation between the blocks. In this paper, we propose an incremental approach to Grassmannian quantization that takes advantage of temporal correlation. The approach leverages existing codebooks for memoryless quantization schemes and employs a quantized form of geodesic interpolation. Two schemes that implement the principles of the proposed approach are presented. In the first scheme, the choice of the step size in the incremental update is adapted to a first-order GaussMarkov model for the channel, which enables the use of higher resolution codebooks. In the second scheme, a single bit is allocated to the step size, which enables adaptation of the step size to the channel realization rather than the channel statistics. This provides substantial robustness against mismatches in the model for the temporal correlation. A distinguishing feature of the proposed approach is that the direction of the geodesic interpolation is specified implicitly using a point in a conventional codebook. As a result, the approach has an inherent ability to recover autonomously from errors in the feedback path. Simulation results demonstrate that these features result in improved performance over some existing schemes in a variety of channel environments.

Differential Feedback of Geometrical Mean Decomposition Precoder for Time-Correlated MIMO Systems

“…The 'PMI' curve refers to the case when the PMI codebook [36][37] is used to quantized the precoder. We have also shown the model-based incremental Grassmannian scheme in [19] ('iGSM') and the rotation matrix based differential precoder system in [16] ('dRotate'). We use method 2 in [16] for finite codebook evolution with 10, i.e., when channel index is larger than 10, the rotation codebook does not change.…”

“…Exploitation of the channel correlation leads to more efficient feedback of channel information [11]- [19]. When the precoders in the consecutive blocks are along a geodesic curve, the differential feedback of precoder is proposed in [11].…”

“…Feedback of bit loading using predictive quantization for a MIMO system with a decision feedback equalizer is presented in [18]. Using a geodesic interpolation approach, a robust differential feedback scheme for precoder is proposed in [19]. In [20], differential feedback of channel impulse response that exploits channel correlation in time, frequency, and space is considered for massive MISO-OFDM systems.…”

“…Simulations are given to demonstrate that with a small feedback rate the performance of the proposed feedback scheme is close to that of GMD with perfect CSI. Differential feedback of precoder has also been addressed earlier [11][16] [19], where the design criterion is capacity. For the capacity criterion, the optimal precoder remains optimal when it is multiplied a unitary matrix on the right.…”

“…In this case, only the subspace formed by the column vectors of precoder matters. Therefore, the tracking of subspace is considered in [11][16] [19] rather than the tracking of the optimal precoder itself. For other criteria like bit error rate, the tracking of subspace may be not suitable.…”