SFBC (Space-Frequency Block Coding)
Space-Frequency Block Coding (SFBC) is a technique used in wireless communication systems to enhance the performance of multiple-input multiple-output (MIMO) systems. MIMO systems utilize multiple antennas at both the transmitter and receiver to improve the data rate, reliability, and spectral efficiency of wireless communication.
SFBC is specifically designed for MIMO-OFDM (Orthogonal Frequency Division Multiplexing) systems, where the transmission of data is divided into multiple subcarriers that are orthogonal to each other. Each subcarrier carries a portion of the data, and the combination of these subcarriers forms the complete transmitted signal.
SFBC takes advantage of the spatial and frequency diversities provided by MIMO-OFDM systems. It achieves this by mapping the data symbols onto multiple subcarriers in such a way that the transmitted signal experiences both spatial and frequency diversity gains.
To understand how SFBC works, let's consider a MIMO-OFDM system with two transmit antennas and two receive antennas. SFBC requires a total of four subcarriers, two for each transmit antenna.
The data symbols intended for transmission are first divided into pairs. Let's say the data symbols are denoted as (x₁, x₂, x₃, x₄). SFBC then combines these symbols with a predetermined code matrix to form four new symbols as follows:
s₁ = x₁ + jx₂ s₂ = x₃ + jx₄ s₃ = -jx₁ + x₂ s₄ = -jx₃ + x₄
In the above equations, j represents the imaginary unit.
The four symbols (s₁, s₂, s₃, s₄) are then mapped to the four subcarriers. The first transmit antenna transmits (s₁, s₂) on the first subcarrier, and the second transmit antenna transmits (s₃, s₄) on the second subcarrier.
At the receiver, the signals received by the two antennas are separated, and the four received symbols are obtained. These received symbols are then used to decode the original transmitted symbols.
The key advantage of SFBC is that it provides both spatial and frequency diversity gains. Spatial diversity is achieved by using multiple transmit antennas, which helps combat fading and improve the reliability of the wireless link. Frequency diversity is achieved through the use of multiple subcarriers, which helps mitigate the effects of frequency-selective fading and improves the overall system performance.
SFBC is particularly useful in environments where both spatial and frequency diversities are present, such as in wireless channels with multipath propagation. It is commonly used in modern wireless communication standards, including LTE (Long-Term Evolution) and WiMAX (Worldwide Interoperability for Microwave Access), to improve the performance and efficiency of MIMO-OFDM systems.