OSTBC orthogonal space–time block code

Orthogonal Space-Time Block Codes (OSTBCs) are a type of coding scheme used in wireless communication systems to improve the reliability and performance of data transmission over multiple antennas. They are specifically designed for multiple-input multiple-output (MIMO) systems, where multiple antennas are used at both the transmitter and receiver ends.

The primary objective of OSTBCs is to combat the effects of fading and improve the overall spectral efficiency of the system. Fading refers to the variation in the received signal strength caused by changes in the propagation environment, such as multipath interference and signal attenuation. By utilizing multiple antennas, MIMO systems can exploit the spatial diversity and multiplexing gains to mitigate the impact of fading and enhance the system capacity.

The basic idea behind OSTBCs is to encode the transmitted data across multiple antennas in such a way that the received signals can be decoded effectively at the receiver. OSTBCs achieve this by constructing a set of orthogonal space-time codes that satisfy certain properties, including full diversity and high coding gain.

Full diversity implies that the code can achieve the maximum possible diversity gain, which is the ability to combat fading and improve the reliability of the system. High coding gain refers to the ability of the code to provide additional redundancy and improve the system's error performance.

One of the most widely used OSTBCs is the Alamouti code, proposed by S. M. Alamouti in 1998. The Alamouti code is a two-transmit-antenna, one-receive-antenna code that achieves full diversity with a simple encoding and decoding structure. The code is designed to transmit two complex symbols over two consecutive time slots, where each symbol is transmitted from a different antenna.

The encoding process of the Alamouti code involves taking two data symbols and mapping them onto the two transmit antennas. In the first time slot, the first symbol is transmitted from the first antenna, while the complex conjugate of the second symbol is transmitted from the second antenna. In the second time slot, the roles are reversed, and the complex conjugate of the first symbol is transmitted from the first antenna, while the second symbol is transmitted from the second antenna.

At the receiver, the received signals from both antennas are combined and processed to extract the transmitted symbols. The decoding process of the Alamouti code takes advantage of the orthogonality between the transmitted signals in the two time slots. By applying a suitable decoding algorithm, such as maximum likelihood (ML) decoding, the receiver can effectively separate the transmitted symbols and recover the original data.

The Alamouti code is particularly attractive due to its simplicity and effectiveness in combating fading. It achieves full diversity with only two antennas, making it suitable for practical implementations. Furthermore, the orthogonal structure of the code allows for simple decoding algorithms, which reduces the computational complexity at the receiver.

In addition to the Alamouti code, there are several other OSTBCs that have been proposed in the literature. These codes are designed for different numbers of antennas and provide various trade-offs between complexity, diversity gain, and data rate.

For instance, the Space-Time Block Trellis Code (STBC) is an extension of OSTBCs that achieves full diversity and high coding gain while supporting a larger number of antennas. STBCs are constructed based on trellis structures, which allow for efficient decoding using techniques such as the Viterbi algorithm.

Another example is the Golden code, which is a four-transmit-antenna code that achieves full diversity with low decoding complexity. The Golden code is derived from the properties of a special number known as the Golden ratio, and it provides an attractive trade-off between performance and complexity.

Overall, OSTBCs, including codes like the Alamouti code, STBCs, and the Golden code, play a crucial role in improving the performance of MIMO systems. They enable reliable data transmission over multiple antennas, combat the effects of fading, and enhance the overall spectral efficiency of wireless communication systems. These codes continue to be an active area of research, with ongoing efforts to develop more advanced and efficient OSTBCs for future wireless communication technologies.