RBD Regularized block diagonalization

RBD, which stands for Regularized Block Diagonalization, is a technique used in wireless communication systems to mitigate interference and improve the performance of multiple-input multiple-output (MIMO) systems. It is particularly effective in scenarios where the number of transmit antennas is larger than the number of receive antennas, commonly referred to as the "overloaded" case.

To understand RBD, let's first discuss the basic concept of MIMO systems. In MIMO, multiple antennas are used at both the transmitter and receiver to transmit and receive multiple data streams simultaneously. This allows for increased data rates, improved reliability, and enhanced spatial multiplexing gains.

However, in MIMO systems, interference between the transmit antennas can degrade the performance of the system. This interference arises due to the correlation between the antennas and the limited spatial separation between them. Traditional MIMO transmission techniques, such as maximum ratio transmission (MRT) or zero-forcing beamforming (ZFBF), do not fully address this interference issue, especially in overloaded scenarios.

RBD comes into play to mitigate this interference by exploiting the underlying structure of the channel matrix. The key idea behind RBD is to create a block diagonal channel matrix by carefully designing the precoding matrix at the transmitter. The block diagonal structure allows for independent transmission on each diagonal block, reducing interference between the antennas.

The RBD precoding matrix is designed by solving an optimization problem that incorporates a regularization term. The regularization term encourages the precoding matrix to have a block diagonal structure and penalizes the off-diagonal elements, thus promoting interference suppression.

The specific formulation of the RBD optimization problem varies depending on the system model and performance objectives. Typically, the optimization problem aims to minimize the interference caused by off-diagonal elements while satisfying power constraints and other system-specific requirements. The regularization term acts as a constraint or penalty term in the optimization problem, driving the solution towards the desired block diagonal structure.

The solution to the RBD optimization problem yields the precoding matrix that achieves the block diagonal structure of the channel matrix. Once the precoding matrix is obtained, it can be applied to the transmitted signals at the transmitter to shape the transmitted signal in a way that reduces interference.

At the receiver, the block diagonal structure of the received signal is exploited to separate the desired signals from interference. Various techniques can be used at the receiver, such as linear receivers, successive interference cancellation, or advanced signal processing algorithms, to recover the original transmitted signals.

Overall, RBD is an effective technique to combat interference in overloaded MIMO systems. It leverages the inherent structure of the channel matrix and utilizes regularization to design a precoding matrix that facilitates independent transmission on each diagonal block, thereby improving system performance.