Opportunistic scheduling and beamforming schemes are proposed for multiuser MIMO-SDMA downlink systems with linear combining in this work. Signals received from all antennas of each mobile terminal (MT) are linearly combined to improve the effective signal-to-noise-interference ratios (SINRs). By exploiting limited feedback on the effective SINRs, the base station (BS) schedules simultaneous data transmission on multiple beams to the MTs with the largest effective SINRs. Utilizing the extreme value theory, we derive the asymptotic system throughputs and scaling laws for the proposed scheduling and beamforming schemes with different linear combining techniques. Computer simulations confirm that the proposed schemes can substantially improve the system throughput. Multiple-input multiple-output (MIMO) technology employing multiple transmit and receive antennas has emerged as one of the most promising techniques for broadband data transmissions in wireless communication systems [1] . In particular, recent studies have shown that MIMO can substantially increase the sum-rate capacity of a downlink system where a base station (BS) communicates simultaneously with multiple mobile terminals (MTs) [2] . However, the capacity achieving strategy using dirty paper coding not only incurs high computational complexity but also requires perfect channel state information available to the BS [2] . To circumvent these obstacles, opportunistic beamforming with proportional fair scheduling (OB-PFS) has been proposed in [3] as an effective means of achieving the asymptotic sum-rate capacity by exploiting multiuser diversity with limited channel feedback. In OB-PFS, the downlink transmission time is divided in slots comprised of mini-slots. Users' channels are assumed to be approximately invariant during one slot but may vary from one slot to another. In the beginning of each slot, the BS broadcasts one pilot symbol weighted by a randomly generated complex vector (also referred to as the random beam). Then, each MT evaluates the signal-to-noise ratio (SNR) by exploiting the pilot signal and feeds back the SNR information to the BS. Taking into account fairness, the BS schedules data transmission to the MT with the best normalized instantaneous channel condition throughout the rest of the slot. Recently, some extensions of [3] employing multiple beams have been developed [4, 5] . Regardless of the number of beams employed in [3] [4] [5] , these opportunistic schemes schedule only one MT in each slot, and so can generally be considered to be the time-sharing scheduling schemes (TS-SS). In contrast, [6] has proposed an opportunistic spacedivision multiple access-based scheduling scheme (OSDMA-SS) employing multiple orthonormal beams to serve multiple MTs simultaneously in each slot. Denote by M and N the number of transmit and receive antennas, respectively. It has been shown recently that the sum-rate of OSDMA-SS grows linearly with M whereas that of TS-SS increases only linearly with min(M, N ) [7] . In addition to the more rapidly growing scaling law, OSDMA-SS is particularly attractive for practical systems with stringent latency requirements since multiple users can be served during each time slot. In OSDMA-SS, the BS broadcasts pilot signals weighted by multiple orthonormal beams in the beginning of each time slot [6] . For each single-antenna MT, it evaluates the signal-tointerference-noise ratio (SINR) on each beam and feeds back information on its desired beam with the highest SINR. Assuming that each beam is requested by at least one MT, the BS awards each beam to the MT with the highest corresponding SINR among all MTs. For MTs with multiple receive antennas, [6] proposes to let each antenna compete for its desired beam as if it were an individual MT. As a result, each beam is assigned to a specific receive antenna of a chosen MT. Since signals received from the undesignated antennas of a chosen MT are discarded, [6] entails inefficient utilization of multiple receive antennas. In this work, we propose opportunistic beamforming and scheduling schemes with different linear combining techniques for MIMO-SDMA downlink systems. In contrast with [6], signals received from all antennas of a chosen MT are jointly exploited to improve the effective SINR through the use of low-complexity linear combining techniques. Then, the M effective SINRs are returned to the BS and employed as the scheduling metric. Using the extreme value theory, we prove that the cumulative distribution functions (CDFs) of the effective signal-to-interference ratios (SIRs) obtained with different linear combining techniques converge asymptotically to the Frechet-type limiting distributions. Based on the limiting distributions, we derive the asymptotic throughput and closedform scaling laws for the proposed opportunistic beamforming and scheduling schemes. Notation: Vectors and matrices are denoted by boldface letters. · represents the Euclidean norm of the enclosed vector. I N is the N × N identity matrix. [a] i indicates the ith entry of vector a. We use E {·}, (·) T and (·) H for expectation, transposition and Hermitian transposition. Finally, log and ln are the logarithms to the base 2 and e, respectively, and |·| denotes the amplitude of the enclosed complex-valued quantity.
In REF , the authors used Extreme Value Theory (EVT) to derive the scaling laws for scheduling systems using beamforming and linear combining.
Opportunistic Scheduling and Beamforming for MIMO-SDMA Downlink Systems with Linear Combining
2007 IEEE 18th International Symposium on Personal, Indoor and Mobile Radio Communications
2007 IEEE 18th International Symposium on Personal, Indoor and Mobile Radio Communications
Computer Science Mathematics