Ergodic Capacity Analysis: MATLAB Simulation & Results, MIMO Channel

This report presents an analysis of ergodic capacity in Multiple-Input Multiple-Output (MIMO) systems using MATLAB simulations. The study explores the performance of MIMO systems under various conditions, including different numbers of transmit and receive antennas. The report examines the impact of signal-to-noise ratio (SNR) on ergodic capacity and analyzes the cumulative distribution function (CDF) of capacity. The results, obtained through MATLAB coding, provide insights into the behavior of MIMO channels, particularly in Rayleigh fading environments. The analysis includes the examination of channel reciprocity and antenna selection techniques. The report references relevant research papers that contribute to the understanding of MIMO channel modeling and capacity analysis. The aim is to investigate how these factors affect the capacity and performance of MIMO systems.

Ergodic capacity:
Suppose that H is the Gaussian random matric whose understanding is introduced at recipient
side, or uniformly, that the medium output comprises of the (y,H) pair. (Joshi, T s, & H m,
2010)The input power is dispersed as evenly in entire communicating antenna. Assume block
fading replica, it is introduced that the ergodic capacity for the random MIMO channel s
elaborated as:
C = EH {log det ( I N + σ / N.H H H )}
Where,
E H = Assumption is used wrt. the whole figures of H.
Which is Gaussian distributed in the particular system for instance
H ≈ N(0, I N X I N ),
So the envelops are Rayleigh distributed in the system. The conclude structure is elaborated
as for the uneven number of transmit and receive antennas.
C = N (log 2 (σ + 1))
Result:
The proposed system structure and the capacity performance observation have done by using
the MATLAB coding. (Uthansakul,, Nattaphat, & Uthansakul, 2011)
The exact expressions for the mean channel capacity and the instantaneous channel capacity
are acquired in this inference as the outcome affirms that the MIMO system usage will
broadly enhances the obtainable figure on the Rayleigh fading channels with determined
degree of correlation.
Coding Result:
Part(a)
Erdoic capacity vs. SNR:
For the value,

M =2,4,6
0 ≤ γ≤ 30
Part(b)
Erdoic capacity vs. SNR for MIMO system with CSI:
For the value,
M =2,4,6
0 ≤ γ≤ 30

Part(c)
Cdf of capacity:
γ= 20
M = 2,4,6,8

References
Joshi, S. , T s, R. & H m, M. (2010). MODELING AND CAPACITY ANALYSIS OF
CORRELATED MIMO CHANNELS. International Journal of Engineering Science
and Technology, 2(10), 5419-5423.
Uthansakul, P. , Nattaphat, P. & Uthansakul, M. (2011). Performance of Antenna Selection in
MIMO System Using Channel Reciprocity with Measured Data. International
Journal of Antennas and Propagation, 2011(854350), 1-10.