Confusion Matrix

The most intuitive metric, representing the ratio of correct predictions to the total number of predictions. It is calculated as (TP + TN) / (TP + TN + FP + FN). While useful for balanced datasets, accuracy can be highly misleading in scenarios with class imbalance, such as when one modulation scheme dominates the spectrum. A high accuracy score might simply reflect the classifier's ability to guess the majority class.

Precision answers: Of all signals classified as a specific modulation, how many actually were that modulation? It is the ratio of True Positives (TP) to the sum of True Positives and False Positives (TP + FP). High precision is critical in electronic warfare or spectrum enforcement, where a false positive (misidentifying a friendly signal as a threat, or a legal signal as illegal) triggers costly, incorrect actions.

Recall answers: Of all actual signals of a given modulation, how many did the classifier correctly identify? It is the ratio of True Positives (TP) to the sum of True Positives and False Negatives (TP + FN). High recall is vital in signal intelligence (SIGINT), where missing an instance of a target signal (a false negative) means a complete failure to detect a potentially critical transmission.

The harmonic mean of Precision and Recall, providing a single balanced metric that penalizes extreme trade-offs. Calculated as 2 * (Precision * Recall) / (Precision + Recall). The F1 score is the preferred metric when you seek a balance between avoiding false alarms (Precision) and missing real signals (Recall), and it is especially robust on datasets with uneven class distributions.

Specificity answers: Of all signals that are NOT a target modulation, how many were correctly rejected? It is the ratio of True Negatives (TN) to the sum of True Negatives and False Positives (TN + FP). In spectrum monitoring, high specificity ensures that the classifier does not constantly raise false alarms by incorrectly labeling benign background noise or other known signals as the target modulation of interest.

For multi-class problems like modulation recognition, per-class metrics must be aggregated. Macro-averaging computes the metric independently for each class and takes the unweighted mean, treating all modulation schemes equally. Weighted averaging computes the mean weighted by each class's true support (number of instances), giving more influence to frequently occurring modulations. The choice depends on whether rare signal types are as important as common ones.

A graphical plot illustrating the diagnostic ability of a binary classifier by mapping the True Positive Rate (TPR) against the False Positive Rate (FPR) as the decision threshold varies. For modulation classification, ROC curves are often generated per class using a one-vs-all approach. The Area Under the Curve (AUC) provides a single scalar value summarizing performance: an AUC of 1.0 indicates perfect separation, while 0.5 represents random guessing. This tool is essential for selecting operating points that balance sensitivity and specificity in signal identification systems.

Two fundamental per-class metrics derived directly from confusion matrix cell counts. Precision answers: 'Of all signals predicted as Class X, what fraction truly belong to Class X?' It is calculated as TP / (TP + FP). Recall answers: 'Of all true Class X signals, what fraction did the classifier correctly identify?' It is calculated as TP / (TP + FN). In spectrum monitoring, high precision minimizes false alarms, while high recall ensures few threat signals are missed. The F1-Score provides the harmonic mean of the two for a balanced single metric.

A statistical measure of inter-rater agreement that accounts for the possibility of agreement occurring by chance. Unlike simple accuracy, Cohen's Kappa provides a more robust picture by subtracting the expected accuracy of a random classifier. The formula is κ = (p_o - p_e) / (1 - p_e), where p_o is observed agreement and p_e is expected agreement. Values range from -1 to 1:

• κ = 1: Perfect agreement
• κ = 0: Agreement equivalent to chance
• κ < 0: Agreement worse than random This is critical when evaluating classifiers on imbalanced modulation datasets.

The probability that a detected symbol differs from the transmitted symbol. In the context of a confusion matrix for modulation classification, SER is the sum of all off-diagonal elements divided by the total number of test samples. For a given modulation scheme M, the SER is 1 - (TP_M / Total_M). This metric is fundamental for evaluating the raw physical-layer performance of a classifier and is often plotted against Signal-to-Noise Ratio (SNR) to generate performance curves that reveal the SNR threshold required for reliable operation.

A transformation of the raw confusion matrix where each cell is divided by the total number of true samples for its corresponding class. This produces row-wise proportions that sum to 1.0, revealing the conditional probability P(Predicted Class | True Class). Normalization is essential when classes are imbalanced—for example, when QPSK signals appear 100x more often than 256-QAM in a dataset. It prevents the visual representation from being dominated by high-prevalence classes and exposes systematic confusion patterns, such as a classifier frequently mistaking 16-QAM for 64-QAM.

Two strategies for aggregating per-class metrics into a single global score. Macro-averaging computes the metric independently for each class and then takes the unweighted mean, treating all modulation schemes equally regardless of their frequency. Micro-averaging aggregates the contributions of all classes by summing the individual true positives, false positives, and false negatives globally before computing the metric. Micro-averaging is dominated by frequent classes, while macro-averaging reveals how well the classifier handles rare modulation types. The choice depends on whether all signal types are equally important.