Spherical Linear Interpolation for Transmit Beamforming in MIMO-OFDM Systems with Limited Feedback

Transmit beamforming with receive combining is a simple approach to exploiting the significant diversity provided by multiple-input multiple-output (MIMO) systems, and this technique can be easily extended to frequency selective MIMO channels by employing orthogonal frequency division multiplexing (OFDM). Optimal beamforming requires channel state information in the form of the beamforming vectors corresponding to all the OFDM subcarriers. When the uplink and downlink channels are not reciprocal, this information must be conveyed back to the transmitter. To reduce the amount of feedback information, a new approach to transmit beamforming is proposed that combines limited feedback and beamformer interpolation. Because the length of the OFDM cyclic prefix is designed to be much less than the number of subcarriers to increase spectral efficiency, the neighboring subchannels of a MIMO-OFDM system are substantially correlated. Thus, the beamforming vectors determined by the subchannels are also significantly correlated. To reduce the feedback information using the correlation between beamforming vectors, the receiver of the proposed scheme sends back only a fraction of information about the optimal beamforming vectors to the transmitter. Then the transmitter evaluates the beamforming vectors for all subcarriers through interpolation of the conveyed beamforming vectors. Since a beamforming vector is phase invariant and has unit norm, a new spherical linear interpolator is proposed that exploits additional parameters for phase rotation. These parameters are determined at the receiver in the sense of maximizing the minimum channel gain or capacity, and they are sent back to the transmitter along with the beamforming vectors through the feedback channel. For practical implementation, the proposed interpolator with quantized phase rotations is combined with existing approaches for beamforming vector quantization. The performance of the proposed beamforming scheme is found to outperform comparable beamforming techniques in terms of bit error rate (BER) and capacity and yet requires less channel state information. Report Documentation Page Form Approved OMB No. 0704-0188 Public reporting burden for the collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden, to Washington Headquarters Services, Directorate for Information Operations and Reports, 1215 Jefferson Davis Highway, Suite 1204, Arlington VA 22202-4302. Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to a penalty for failing to comply with a collection of information if it does not display a currently valid OMB control number. 1. REPORT DATE 20 DEC 2004 2. REPORT TYPE N/A 3. DATES COVERED 4. TITLE AND SUBTITLE Spherical Linear Interpolation for Transmit Beamforming in MIMO-OFDM Systems with Limited Feedback 5a. CONTRACT NUMBER