Rank Indicator (RI)

A UE feedback index that recommends a specific precoding matrix from a predefined codebook. While RI specifies how many spatial layers to use, PMI specifies how to weight each antenna to form those beams. The PMI is selected to maximize post-processing Signal-to-Interference-plus-Noise Ratio (SINR) given the current channel estimate.

• Reported alongside RI and CQI in closed-loop spatial multiplexing
• Codebook-based PMI is standardized in 3GPP TS 38.214 for 5G NR
• Wideband PMI applies a single matrix across all sub-bands; sub-band PMI provides frequency-selective precision

A metric reported by the UE to the gNB indicating the highest Modulation and Coding Scheme (MCS) that can be decoded with a target Block Error Rate (BLER) — typically 10%. CQI is conditioned on the reported RI and PMI; a higher rank may increase throughput but reduce the sustainable CQI per layer.

• CQI values range from 1 to 15 in LTE and 5G NR
• A CQI of 15 corresponds to 64QAM with a coding rate of 948/1024
• The gNB may override the reported CQI based on its own scheduler logic

The known channel properties — including scattering, fading, and power decay — that characterize the wireless propagation environment. CSI is the raw input from which RI, PMI, and CQI are derived. Accurate CSI acquisition via Sounding Reference Signals (SRS) or Demodulation Reference Signals (DMRS) is critical for reliable rank estimation.

• CSI is decomposed via Singular Value Decomposition (SVD) to identify eigenmodes
• The number of dominant singular values directly informs the optimal RI
• Channel aging — the mismatch between estimated and actual CSI — degrades RI accuracy in high-mobility scenarios

The increase in data rate capacity achieved by transmitting independent data streams over multiple spatial paths. This gain scales linearly with min(N_TX, N_RX) under ideal, richly scattered conditions. The RI directly quantifies the achievable spatial multiplexing gain at any instant.

• A 4×4 MIMO system with RI=4 achieves up to 4× the capacity of a SISO link
• Spatial correlation reduces the effective rank, lowering the achievable multiplexing gain
• Adaptive RI selection balances multiplexing gain against diversity gain based on channel condition

A metric describing the sensitivity of a MIMO channel matrix to inversion, defined as the ratio of the largest to smallest singular value. A high condition number indicates a poorly conditioned channel where spatial layers are highly correlated, limiting the effective rank and degrading the reliability of spatial multiplexing.

• Condition number near 1 (0 dB): well-conditioned channel, full rank usable
• Condition number > 20 dB: ill-conditioned, RI should be reduced
• Used as a heuristic for rank adaptation in practical schedulers

A matrix factorization method that decomposes the MIMO channel matrix H into H = U Σ V^H, where Σ contains the singular values. These singular values represent the gains of independent eigenmodes. The number of significant singular values directly determines the optimal RI for capacity-achieving transmission.

• Eigen-beamforming uses the right singular vectors (V) as precoding weights
• Water-filling power allocation distributes power across eigenmodes based on singular values
• SVD-based RI estimation is optimal but computationally intensive for real-time feedback