1. 2. System Setup MIMO systems: Limited feedback systems: Perfect Channel State Information (CSI) at the receiver. Partial CSI at the transmitter characterized by a finite feedback link with rate B from the receiver. Linear Dispersion (LD) space-time codes: (subsumes all linear space-time codes) Spatially correlated MIMO Channels: Channel remains constant within the coherence time block and varies ergodically from block to block. Frequency flat channel. two dimensional spatial Fourier transform Coding Across Time in Quantized Feedback Systems Che Lin, Vasanthan Raghavan, and Venugopal V. Veeravalli Illinois Center for Wireless Systems [1] C. Lin, V. Raghavan, and V. Veeravalli, Optimal Power Allocation for Linear Dispersion Codes over Correlated MIMO Channels with Channel State Feedback, to appear in Globcom 07. [2] C. Lin and V. Veeravalli, A Limited Feedback Scheme for Linear Dispersion Codes over Correlated MIMO Channels, to appear in ICASSP 07, Honolulu, Hawaii, Apr. 2007. [3] C. Lin and V. Veeravalli, Optimal Linear Dispersion Codes for Correlated MIMO Channels, to appear in IEEE Trans. Wireless Communication. 9. Conclusions Uniform code covariance matrices is optimal with any amount of CSIT. With any amount of CSIT, rank-one codebooks are optimal. Rank-one space-time codes do not code across time and greatly reduce complexity for implementation. Therefore, the optimal codes do not code across time even with 1 bit of feedback. 0. Motivations Advantage of MIMO systems can be fully exploited only when there is perfect channel state information (CSI) at the transmitter. Next generation wireless systems often utilize the reverse link feedback to convey CSI to the transmitter to enhance overall performance. Codebook-based feedback systems have been adopted in latest standards, e.g. 802.11n, 802.16e, and 3GPP-LTE etc.. If the channel varies slowly enough, how can one design a good codebook that accounts for the redundancy in time? 1. Limited Feedback System Goal: maximize mutual information of the effective MIMO channel limited feedback link of rate B 4. Properties of Optimal LD Codes Uniform code covariance matrices is optimal for any amount of channel knowledge at the transmitter. When the transmitter has access of only statistical information, optimal spatial power allocation excites multiple modes in general. Optimal spatial power allocation is of rank-one when there is perfect CSIT. Initial research suggests that optimal spatial power allocation is also of rank-one when there is any amount of CSI feedback. 5. Evolution of Space-time Codes Code, at time t, depends on t and channel realization H in general. x1(H)x2(H)x3(H)x4(H)x5(H) coherence time block 6. Coding Across Time With partial CSIT, space-time code can have two components: one that evolves with the channel, and the other that does not. Either component can evolve with time in the most general case. In this context, we say that the space-time code does not code across time if and only if the component that evolves with channel is independent of time. 7. Rank-one Codebooks Structure of optimal rank-one codebooks Code at time t, Rank-one space-time codes do not code across time. 8. Simulations (i.i.d. channel) 3. Quantized Feedback Schemes Channel Stat Codebook constructed before hand Channel Estimation Feedback as its LD codeTx picks Spatial power allocation Code covariance matrix