CB (Coherence Bandwidth)

Coherence Bandwidth (CB) is a fundamental concept in wireless communication systems, especially in radio frequency (RF) and microwave systems. It is a critical parameter that characterizes the ability of a communication channel to transmit data with minimum distortion. In this article, we will explore the definition, significance, and mathematical formulation of coherence bandwidth.

Coherence Time and Bandwidth

Before we dive into coherence bandwidth, let us first understand coherence time and coherence bandwidth. Coherence time is the duration over which a wireless channel remains constant. It is the time period within which the signal's phase remains unchanged. Coherence time is inversely proportional to the Doppler spread of the channel. It is given by the following formula:

Coherence Time (Tc) = 1 / Doppler Spread

The Doppler spread is the rate at which the channel changes due to the movement of the transmitter or receiver. When the coherence time is long, the channel changes slowly, and the communication link is more stable. Conversely, when the coherence time is short, the channel changes rapidly, leading to a less stable link.

Coherence bandwidth is the frequency range over which a wireless channel remains constant. It is the bandwidth over which the signal's phase remains unchanged. Coherence bandwidth is directly proportional to the Doppler spread of the channel. It is given by the following formula:

Coherence Bandwidth (CB) = Doppler Spread / 2π

The coherence bandwidth and coherence time are related by the following formula:

CB x Tc = 1 / 2π

Significance of Coherence Bandwidth

Coherence bandwidth plays a vital role in wireless communication systems. It determines the maximum data rate that can be transmitted without significant distortion due to multipath fading. Multipath fading is a phenomenon that occurs when a wireless signal takes multiple paths to reach the receiver. These signals interfere with each other and cause distortion.

The coherence bandwidth is inversely proportional to the multipath delay spread. Multipath delay spread is the time difference between the arrival of the first and the last signal from multiple paths. When the coherence bandwidth is smaller than the multipath delay spread, the wireless channel is said to be frequency-selective. In such a case, the channel attenuates different frequency components of the transmitted signal differently, leading to inter-symbol interference (ISI) and inter-carrier interference (ICI). This, in turn, limits the maximum data rate that can be transmitted without errors.

On the other hand, when the coherence bandwidth is larger than the multipath delay spread, the wireless channel is said to be frequency-flat. In such a case, the channel attenuates all frequency components of the transmitted signal equally, resulting in a flat fading channel. This means that the channel distortion is the same for all frequency components, allowing for high-speed data transmission.

Coherence Bandwidth in Wireless Systems

Coherence bandwidth is a crucial factor in the design and implementation of wireless communication systems. It determines the bandwidth allocation, modulation scheme, and error correction coding to be used for data transmission.

For example, in a wireless system with a frequency-selective channel, the bandwidth allocation must be carefully chosen to avoid overlap between adjacent subcarriers. If the coherence bandwidth is too small, then the bandwidth allocated to each subcarrier must be reduced, resulting in a lower data rate. Similarly, if the coherence bandwidth is too large, the bandwidth allocated to each subcarrier can be increased, resulting in a higher data rate.

In addition, the modulation scheme and error correction coding must be chosen based on the coherence bandwidth. If the coherence bandwidth is small, then the modulation scheme must be chosen such that it is robust to frequency-selective fading. For example, Orthogonal Frequency Division Multiplexing (OFDM) is a modulation scheme that is widely used in wireless systems with small coherence bandwidths as it can efficiently mitigate the effects of ISI and ICI. Moreover, error correction coding must be used to correct errors due to the frequency-selective fading.

On the other hand, if the coherence bandwidth is large, then the modulation scheme can be chosen based on the power efficiency and data rate requirements. For example, Quadrature Amplitude Modulation (QAM) is a high-data rate modulation scheme that can be used in frequency-flat channels.

In wireless communication systems, coherence bandwidth is also used to design and optimize antenna systems. Antennas that are too large or too small can lead to significant distortion due to multipath fading. Therefore, the antenna dimensions are chosen based on the coherence bandwidth of the wireless channel to achieve maximum efficiency and performance.

Coherence Bandwidth in 5G Networks

In 5G networks, coherence bandwidth plays a vital role in achieving high data rates and low latency. 5G networks operate at higher frequencies, which leads to a larger Doppler spread and a smaller coherence bandwidth. Therefore, the 5G system design must take into account the coherence bandwidth to ensure reliable and efficient communication.

One of the key features of 5G networks is beamforming, which uses directional antennas to improve the signal-to-noise ratio (SNR) and reduce interference. Beamforming requires accurate channel estimation, which is challenging in frequency-selective fading channels. Therefore, 5G networks use hybrid beamforming, which combines the benefits of analog and digital beamforming to improve channel estimation accuracy.

Coherence bandwidth is also used to optimize the frequency allocation in 5G networks. The 5G frequency bands are divided into sub-bands, and the bandwidth allocation is chosen based on the coherence bandwidth of the wireless channel. This ensures that the sub-bands are chosen such that they are frequency-flat, leading to efficient and reliable communication.

Conclusion

Coherence bandwidth is a fundamental concept in wireless communication systems. It characterizes the frequency range over which a wireless channel remains constant and determines the maximum data rate that can be transmitted without significant distortion. Coherence bandwidth plays a vital role in the design and optimization of wireless communication systems, including antenna design, modulation scheme, error correction coding, and frequency allocation. In 5G networks, coherence bandwidth is critical in achieving high data rates and low latency, and it is used to optimize the frequency allocation and improve channel estimation accuracy.