Iterative Optimization Algorithms to Determine Transmit and Receive Weights for MIMO Systems

As a technology to realize high data rates and high capacity in wireless communication systems, Multiple-Input Multiple-Output (MIMO) system has received increasing attention. In MIMO systems, high spectral efficiency is achieved by spatially multiplexing multiple data streams at the same time and frequency [1]. The MIMO system with space division multiplexing (SDM) technique is categorized into two cases, i.e., no channel state information (CSI) is needed at the transmitter or CSI is exploited in both transmitter and receiver. As a method used in the former systems, spatial filtering and maximum likelihood detection (MLD) are known [1], where the received SDM signal is de-multiplexed with signal processing at the receiver. One of the latter MIMO systems is called the Eigenbeam SDM (E-SDM) [1][2], where data streams are transmitted through multiple orthogonal eigenpath channels between the transmitter and the receiver. Thus, the E-SDM system with power control based on the water-filling theorem [3] improves the MIMO channel capacity, provided that accurate CSI is known to the transmitter and the receiver. Therefore, it is expected that the E-SDM system achieves significant increase of spectral efficiency. In the E-SDM system, it is important to find optimum transmit and receive weights for maximizing its capacity. Such the optimum weights are determined based on eigenvector of HHH, where H denotes channel matrix and suffix H denotes complex conjugate transpose. As a method to find these eigenvectors, eigenvalue decomposition (EVD) of HHH or singular value decomposition (SVD) of H is well-known. Generally, SVD or EVD requires matrix decomposition operation based on QR decomposition. MIMO techniques can be used for multiple access systems where multiple signals are sent from multiple terminals at the same time and same frequency, i.e., Space Division Multiple Access (SDMA) or multi-user MIMO (MU-MIMO) [6]-[9]. When such a multi-antenna system is used at a transmitter, the transmit weights are optimized under the constraint of total transmit power [5]-[9]. However, the maximum transmit power for each antenna element in SDMA systems is not restricted in general assumptions. Therefore, in the worst case, an amplifier whose maximum output power is the same as total transmit power is needed for each antenna element; these amplifiers cause an increase in cost. From this point of view, it is desirable to use a reasonable (i.e., low cost) power amplifier for each antenna element, where per-antenna transmit power is limited within a permissible output power.