Grassmannian Frames with Applications to Coding and Communication

For a given class ${\cal F}$ of uniform frames of fixed redundancy we define a Grassmannian frame as one that minimizes the maximal correlation $|< f_k,f_l >|$ among all frames $\{f_k\}_{k \in {\cal I}} \in {\cal F}$. We first analyze finite-dimensional Grassmannian frames. Using links to packings in Grassmannian spaces and antipodal spherical codes we derive bounds on the minimal achievable correlation for Grassmannian frames. These bounds yield a simple condition under which Grassmannian frames coincide with uniform tight frames. We exploit connections to graph theory, equiangular line sets, and coding theory in order to derive explicit constructions of Grassmannian frames. Our findings extend recent results on uniform tight frames. We then introduce infinite-dimensional Grassmannian frames and analyze their connection to uniform tight frames for frames which are generated by group-like unitary systems. We derive an example of a Grassmannian Gabor frame by using connections to sphere packing theory. Finally we discuss the application of Grassmannian frames to wireless communication and to multiple description coding.Comment: Submitted in June 2002 to Appl. Comp. Harm. Ana

Adaptive Bit Partitioning for Multicell Intercell Interference Nulling with Delayed Limited Feedback

Base station cooperation can exploit knowledge of the users' channel state information (CSI) at the transmitters to manage co-channel interference. Users have to feedback CSI of the desired and interfering channels using finite-bandwidth backhaul links. Existing codebook designs for single-cell limited feedback can be used for multicell cooperation by partitioning the available feedback resources between the multiple channels. In this paper, a new feedback-bit allocation strategy is proposed, as a function of the delays in the communication links and received signal strengths in the downlink. Channel temporal correlation is modeled as a function of delay using the Gauss-Markov model. Closed-form expressions for bit partitions are derived to allocate more bits to quantize the stronger channels with smaller delays and fewer bits to weaker channels with larger delays, assuming random vector quantization. Cellular network simulations are used to show that the proposed algorithm yields higher sum-rates than an equal-bit allocation technique.Comment: Submitted to IEEE Transactions on Signal Processing, July 201