SMMSE (Successive MMSE)

SMMSE, or Successive Minimum Mean Square Error, is an iterative algorithm used for multiuser detection in wireless communication systems. It is commonly employed in scenarios where multiple users transmit their signals simultaneously over a shared channel, leading to interference and reduced performance. The goal of SMMSE is to recover the original transmitted signals by mitigating the interference caused by other users.

To understand SMMSE, let's break down the algorithm into its key components and steps:

System Model:

• We consider a wireless communication system with multiple users transmitting simultaneously over a common channel.
• Each user's transmitted signal is corrupted by additive noise and interference from other users.
• The received signal at the receiver is a superposition of the transmitted signals from all users, distorted by the channel and noise.

Minimum Mean Square Error (MMSE) Receiver:

• The MMSE receiver is an optimal receiver that minimizes the mean square error between the original transmitted signal and the estimated signal.
• In a multiuser scenario, the MMSE receiver considers the interference from other users as noise and estimates the desired signal.

Successive MMSE Algorithm:

• SMMSE builds upon the MMSE receiver and aims to iteratively improve the estimation of user signals.
• The algorithm works in iterations, with each iteration refining the estimates based on the previous iteration's estimates.

Initialization:

• The algorithm begins by initializing the estimates of the transmitted signals for all users.
• These initial estimates can be obtained using methods like zero forcing or matched filtering.

Iterative Estimation:

• In each iteration, SMMSE computes the MMSE estimate of each user's transmitted signal, treating the interference from other users as noise.
• The estimates from the previous iteration are used as inputs to the current iteration.

Interference Cancellation:

• After obtaining the MMSE estimate for each user, SMMSE subtracts the estimated interference from the received signal to obtain an interference-cancelled signal.
• The interference cancellation step reduces the effect of interference from other users on the desired signal.

Signal Decoding:

• The interference-cancelled signal is processed further to decode the transmitted information.
• This can involve techniques such as symbol detection, demodulation, and error correction coding.

Convergence:

• The iterative process continues for a fixed number of iterations or until a convergence criterion is met.
• Convergence is typically determined by monitoring the change in estimates between iterations or the reduction in the interference level.

Performance Evaluation:

• The performance of SMMSE is assessed in terms of metrics like bit error rate (BER) or symbol error rate (SER).
• Simulation or analytical methods can be used to evaluate the algorithm's performance under various channel conditions and interference scenarios.

SMMSE is an effective technique for mitigating multiuser interference in wireless communication systems. By iteratively estimating and canceling interference, it improves the quality of the received signals and enhances the overall system performance.