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Control Engineering

SISO and MIMO Systems

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Interference Management

Interference Management is more complex in MIMO systems as they have to handle and mitigate interference between multiple transmitted and received signals. In contrast, SISO systems only have one signal path to manage.

Diversity Gain

Diversity Gain is achieved through MIMO systems by using multiple antennas to receive the same signal, thereby reducing the fading effect. SISO systems do not have this advantage due to the single antenna use.

Open-Loop MIMO

Open-Loop MIMO operates without the use of feedback and relies on predefined algorithms and channel state information. While both SISO and MIMO systems can operate in open-loop, the complexity is higher for MIMO due to multiple channels.

Channel Capacity

Channel Capacity is higher in MIMO systems compared to SISO systems due to the use of multiple transmission and receiving antennas, which can exploit the spatial domain to increase throughput.

Spatial Multiplexing

Spatial Multiplexing is a transmission technique in MIMO systems that allows the transmission of separate data streams simultaneously over the same frequency band, which is not possible with SISO systems.

Beamforming

Beamforming is a signal processing technique used in MIMO systems to direct the transmission or reception of signal in specific directions. It increases signal strength and reduces interference, which is not applicable in SISO systems.

Closed-Loop MIMO

Closed-Loop MIMO refers to MIMO systems that utilize feedback to optimize performance, improving the system's adaptability to channel conditions. SISO systems can also use feedback but in a simpler single-channel context.

Capacity Formula for SISO

The channel capacity for a SISO system is given by the Shannon-Hartley theorem:

C = B \log_2 \left(1 + \frac{S}{N}\right)

where

C

is capacity,

B

is bandwidth, and

S/N

is the signal-to-noise ratio.

Capacity Formula for MIMO

The channel capacity for a MIMO system with perfect channel state information at the transmitter and receiver is given by:

C = B \log_2 \det\left(I + \frac{1}{N_0B}HH^*\sigma_x^2\right)

where

B

is the bandwidth,

H

is the channel matrix,

H^*

is the conjugate transpose of

H

N_0

is the noise power spectral density, and

\sigma_x^2

is the signal power.

SISO

Single-Input Single-Output (SISO) refers to a control system with one input and one output. In SISO systems, there is a direct and single path from the input to the output.

Antenna Correlation

Antenna Correlation, which affects the performance of MIMO systems, is the measure of how antennas influence each other's signal. SISO systems do not face this issue as they have a single antenna.

MIMO

Multiple-Input Multiple-Output (MIMO) refers to a control system that has multiple inputs and multiple outputs. These systems leverage the use of multiple sensors and actuators to perform more complex control tasks.

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