What is PMI, RI, and CQI in LTE

In LTE, the radio channel between the eNodeB and the UE is constantly changing due to mobility, multipath fading, interference, and varying load conditions.
If the eNodeB always used the same modulation, coding rate, and antenna configuration, network performance would be far from optimal, some users would get unnecessarily low throughput in good conditions, while others would suffer from excessive errors in poor conditions.

To solve this, LTE uses link adaptation,a dynamic process where the eNodeB adjusts:

• Modulation (e.g., QPSK, 16QAM, 64QAM)
• Coding rate (how much redundancy is added for error protection)
• MIMO spatial configuration (how many layers, and how they’re transmitted)

This ensures two main goals:

1. Efficiency – Deliver the highest possible throughput without wasting spectrum.
2. Reliability – Keep block error rates (BLER) within acceptable limits (typically ≤ 10%).

For the eNodeB to make these smart adjustments, it needs accurate, real-time knowledge of the downlink channel as experienced by the UE. This is where three critical feedback parameters come in:

Parameter	Purpose in Link Adaptation
PMI (Precoding Matrix Indicator)	Suggests the optimal antenna precoding configuration (beamforming direction and phase weights) to maximize signal quality at the UE.
RI (Rank Indicator)	Indicates the number of independent spatial layers that can be transmitted in parallel without excessive interference between them.
CQI (Channel Quality Indicator)	Recommends the highest MCS that will achieve a BLER of ≤ 10% under current channel conditions.

How they work together

• RI answers: “How many separate data streams can you send me right now?”
• PMI answers: “Given that number of streams, here’s the best way to map them onto your antennas.”
• CQI answers: “Given that setup, here’s the fastest safe modulation and coding you can use.”

Together, PMI, RI, and CQI form the UE’s Channel State Information (CSI), enabling the eNodeB to optimize both spatial and spectral efficiency on a per-subframe basis.

Channel State Information (CSI) in LTE

Before diving into each parameter, it’s important to understand that PMI, RI, and CQI are all part of CSI (Channel State Information) feedback in LTE.
CSI gives the eNodeB insight into the instantaneous channel conditions at the UE’s side.

Types of CSI in LTE:

• CQI → Channel quality (affects MCS selection)
• PMI → Best precoding vector/matrix (affects beamforming direction)
• RI → Spatial multiplexing capability (affects number of streams)

The UE measures the downlink reference signals (CRS or CSI-RS) from the eNodeB, processes them, and sends back CSI reports over the uplink (PUCCH or PUSCH).

What is PMI (Precoding Matrix Indicator)?

The Precoding Matrix Indicator (PMI) is the UE’s recommendation to the eNodeB on which precoding matrix should be used in the downlink transmission.
It tells the eNodeB how to weight and phase-adjust signals across multiple transmit antennas so that they arrive at the UE constructively — maximizing the received Signal-to-Noise Ratio (SNR) and minimizing inter-layer interference.

In LTE, PMI is not the precoding matrix itself; it’s an index pointing to an entry in a predefined codebook (as specified in 3GPP TS 36.211, Annex B).

In MIMO systems, the eNodeB uses multiple antennas to transmit parallel streams of data. However, without proper phase and amplitude adjustment, these streams could interfere destructively when they arrive at the UE.

Precoding solves this by applying a carefully chosen transformation matrix W to the transmit signals so they align optimally with the UE’s channel conditions.

The PMI:

• Selects the spatial beamforming pattern that best matches the instantaneous channel.
• Ensures constructive combining at the UE’s antenna ports.
• Minimizes interference between multiple MIMO layers.
• Adapts dynamically as the radio channel changes.

How PMI Works

Reference Signal Transmission
The eNodeB periodically sends Cell-specific Reference Signals (CRS) or CSI-RS.
These reference signals are known patterns that the UE uses to estimate the channel.

Channel Estimation at the UE :The UE estimates the downlink channel matrix H, where each element hij​ represents the complex gain from the j-th transmit antenna to the i-th receive antenna.

Precoding Matrix Computation

• The UE determines the optimal precoding matrix W that would:
• Maximize received SNR.
• Minimize layer interference.
• Support the desired MIMO rank (based on RI).
• This is typically done by maximizing a metric like capacity or SNR per stream.

Codebook Matching

• LTE defines a finite set of allowed precoding matrices — the codebook.
• The UE compares its computed optimal W with every matrix in the codebook.
• The index of the closest match is selected as the PMI.

PMI Feedback

• The UE sends the PMI to the eNodeB over PUCCH or PUSCH.
• The eNodeB uses this PMI for upcoming downlink transmissions.

PMI in Practice

• Rank 1 MIMO → PMI essentially chooses the best beamforming vector for single-stream transmission.
• Rank 2 MIMO → PMI chooses the best 2-column matrix that minimizes inter-layer interference.
• PMI is often reported together with RI and CQI as part of the UE’s CSI report.

Rank Indicator (RI)

The Rank Indicator (RI) is a UE feedback parameter that tells the eNodeB how many independent data layers (spatial streams) the downlink channel can reliably support without significant inter-layer interference.

• Rank 1: Single-layer transmission — typically chosen in poor channel conditions (low SNR) or when there is high correlation between transmit antenna paths.
• Rank 2 or higher: Multi-layer MIMO — feasible in good channel conditions with low antenna correlation and rich scattering.

Key point: The “rank” does not always equal the number of antennas; it is limited by channel conditions and spatial diversity.

How RI Works

The eNodeB and UE operate in MIMO modes where the number of spatial layers (rank) determines:

• The degree of spatial multiplexing.
• How transmit power is divided among layers.
• The link adaptation strategy.

RI Determination Process (at UE):

1. Channel Estimation: The UE estimates the downlink channel using reference signals (CRS or CSI-RS).
2. Spatial Correlation Analysis:
   • Low correlation between antenna paths → more independent layers possible → higher RI.
   • High correlation → spatial diversity is reduced → only lower RI feasible.
3. Singular Value Decomposition (SVD):
   • If H is the channel matrix, the rank is the number of significant singular values from SVD:

H=UΣV^H

The count of significant singular values (above a noise threshold) = RI.

4. BLER Target Consideration: The UE determines the RI that can achieve the target BLER (usually 10%) when paired with an appropriate MCS.

Channel Quality Indicator (CQI)

The Channel Quality Indicator (CQI) is a UE-reported metric that tells the eNodeB the highest MCS the UE can reliably decode while maintaining a target BLER , typically 10% in LTE.

• CQI = 15 → 64-QAM with highest code rate → Best channel conditions.
• CQI = 1 → QPSK with lowest code rate → Poor channel conditions.

Key point: CQI does not directly measure SNR/SINR; instead, it’s an interpretation of SINR mapped to MCS capability based on 3GPP tables.

How CQI Works

Measurement:

• UE measures the Signal-to-Interference-plus-Noise Ratio (SINR) for reference signals (CRS or CSI-RS).
• Measurements can be wideband (one CQI for the whole band) or subband (different CQIs for frequency segments).

Mapping to CQI: UE uses predefined lookup tables in 3GPP TS 36.213 (Table 7.2.3-1) to convert SINR into a CQI value that ensures the target BLER.

Reporting:

• CQI is reported periodically or aperiodically (PUCCH or PUSCH).
• May be accompanied by PMI and RI to form the full Channel State Information (CSI).

Usage by eNodeB:

• eNodeB selects the MCS using Adaptive Modulation and Coding (AMC) based on CQI.
• The goal is to maximize throughput while keeping BLER within limits.

How PMI, RI, and CQI Are Related

These three parameters form the CSI (Channel State Information) feedback in LTE and are interdependent:

RI affects PMI and CQI:

• Higher RI → More layers → PMI needs to choose a precoder for multi-layer transmission.
• Higher RI may require a lower CQI for each layer since power is divided.

PMI affects CQI:

• A good PMI choice increases SINR → higher CQI possible.
• Wrong PMI choice → degraded SINR → lower CQI.

CQI feedback is based on RI and PMI:

• UE estimates CQI assuming the recommended PMI and RI are used by the eNodeB.
• This is why they are reported together in PUCCH/ PUSCH as per 36.213.

RI, PMI, and CQI in LTE are interdependent CSI feedback parameters: RI defines the number of transmission layers, influencing PMI choice and per-layer CQI; PMI determines the precoder, directly affecting SINR and thus CQI; CQI is estimated assuming the reported RI and PMI are used, as specified in 3GPP TS 36.213, 36.211, and 36.212.

References:

• 3GPP TS 36.213 – CSI reporting rules for RI, PMI, and CQI
• 3GPP TS 36.211 – Precoding methods and PMI usage
• 3GPP TS 36.212 – CSI feedback coding structure
• Dahlman et al. – 4G: LTE/LTE-Advanced for Mobile Broadband, RI–PMI–CQI interaction
• Holma & Toskala – LTE for UMTS, practical CSI feedback and link adaptation