OFDM Profile Performance Analysis - Part: 1

This guide outlines the theory and workflow for measuring DOCSIS 3.1 OFDM channel performance, quantifying capacity margins, and correlating them with error‑correction events.

Mathematical Foundations

1. Shannon Capacity Limit

For each subcarrier, the theoretical maximum bits/sec/Hz is:

\[ C = \log_{2}\bigl(1 + \mathrm{SNR}_{\mathrm{lin}}\bigr), \]

\[ \mathrm{SNR}_{\mathrm{lin}} = 10^{\mathrm{SNR}_{\mathrm{dB}} / 10} \]

2. MER‑Derived Capacity

From the average Modulation Error Ratio (MER) in dB per subcarrier:

1. Convert to linear SNR: $10^{\mathrm{MER}_i/10}$.
2. Apply Shannon’s formula.
3. Round down:

\[ C_{\mathrm{MER},i} = \left\lfloor \log_{2}\bigl(1 + 10^{\mathrm{MER}_i/10}\bigr) \right\rfloor. \]

3. Profile‑Derived Capacity

Using configured per‑subcarrier SNR limits from the modulation profile:

\[ C_{\mathrm{profile},i} = \left\lfloor \log_{2}\bigl(1 + 10^{\mathrm{SNR}_{\mathrm{profile},i}/10}\bigr) \right\rfloor. \]

4. Capacity Delta

The margin for each subcarrier:

\[ \Delta C_i = C_{\mathrm{profile},i} - C_{\mathrm{MER},i}. \]

Positive $\Delta C$ indicates margin; negative signals under‑margin.

5. FEC Counter Aggregation

Over the capture interval $[t_0, t_N]$, sum forward‑error‑correction events:

\[ \mathrm{FEC}_{\mathrm{total}} = \sum_{t=t_0}^{t_N}\sum_j \mathrm{FEC}_j(t), \]

where $j$ indexes FEC counters (corrected, uncorrectable, etc.).

High-Level Workflow

1. Compute MER Capacity

2. Retrieve average MER per subcarrier.

3. Calculate $C_{\mathrm{MER},i}$.

4. Identify Capture Window

5. Gather all timestamps.

6. Determine start $t_0$ and end $t_N$.

7. Aggregate FEC Counters

8. Sum FEC metrics for each codeword counter between $t_0$ and $t_N$.

9. Profile Performance Comparison For each capture timestamp and profile:

10. Compute $C_{\mathrm{profile},i}$.

11. Calculate $\Delta C_i$ per subcarrier.

12. Assemble Performance Ledger Compile per-channel results including:

13. Average MER and $C_{\mathrm{MER}}$

14. Total FEC counts
15. Time‑series of $\Delta C$ for each profile

Outcome

This process yields a structured performance ledger to:

• Assess Capacity Margins: Identify subcarriers with insufficient margin.
• Correlate Reliability: Link error‑correction events to capacity deficits.
• Monitor Trends: Track performance over time and detect transients.

Workflow Flowchart

flowchart TD
    A[Start] --> B[Compute MER Capacity]
    B --> C[Identify Capture Window]
    C --> D[Aggregate FEC Counters]
    D --> E[Profile Performance Comparison]
    E --> F[Assemble Performance Ledger]
    F --> G[End]