What is MMSE IRC Minimum Mean Squared Error – Interference Rejection Combining

Technical details of MMSE-IRC (Minimum Mean Squared Error – Interference Rejection Combining).

1. Background:
   • Massive MIMO (Multiple-Input Multiple-Output) is a key technology for fifth-generation (5G) mobile networks due to its high spectral capacity and energy efficiency.
   • In uplink massive MIMO systems, the MMSE-IRC algorithm plays a crucial role in mitigating interference and improving system performance.
2. Objective:
   • The primary goal of MMSE-IRC is to minimize the mean squared error between the received signal and the desired signal while effectively rejecting interference.
3. Algorithm Overview:
   • The combining process in MMSE-IRC is based on a mathematical algorithm.
   • It takes into account the following components:
     • Interference Estimate: An estimate of the interference from other users or cells.
     • Received Signal Characteristics: Power and phase information of the received signals.
     • Noise in the System: Background noise affecting the received signal.
4. Mathematical Formulation:
   • Given the received signal vector y (containing contributions from both the desired user and interfering users), the MMSE-IRC algorithm computes an estimate x̂ of the desired user’s transmitted signal x.
   • The estimate x̂ is obtained by minimizing the mean squared error (MSE) between the received signal y and the estimated signal Hx̂, where H represents the channel matrix.
   • Mathematically, the MMSE-IRC estimate x̂ is given by: [ x̂ = (H^H R_y^{-1} H + I)^{-1} H^H R_y^{-1} y ]
     • (R_y) is the covariance matrix of the received signal y (including both desired and interfering components).
     • (I) is the identity matrix.
5. Complexity Considerations:
   • The conventional MMSE-IRC algorithm involves computing the inverse of the interference and noise covariance matrix.
   • For large antenna arrays, this matrix inversion can be computationally expensive.
   • To address this, a low-complexity variant of MMSE-IRC based on eigenvalue decomposition (EVD) is proposed.
   • The EVD method reduces the matrix inversion complexity while maintaining performance.
6. Performance and Equivalence:
   • The proposed low-complexity MMSE-IRC algorithm achieves similar performance to the conventional MMSE-IRC.
   • Under the assumption of uncorrelated interference and noise, the proposed algorithm is equivalent to the conventional one.