Direction of Arrival (DOA)

Overview

The ESP-SR DOA (Direction of Arrival) module estimates the direction of a sound source relative to the microphone array. It is based on the Capon/MVDR (Minimum Variance Distortionless Response) algorithm with an embedded-optimized implementation, and is widely used in scenarios such as speaker localization, camera steering, and as the front end of beamforming (see GSC Beamforming).

Note

The embedded DOA module described in this document is currently only supported on ESP32-P4.

The embedded DOA module has the following features:

Arbitrary microphone array geometry: any array shape with 2 to 8 microphones, microphone coordinates are configured at runtime
Frame size: 128 samples per channel at 16 kHz (8 ms per frame)
FFT size: 256 points
Processing bandwidth: 1500–4500 Hz (optimized for speech)
Angle resolution: 10 degrees (36 candidate angles: 0°, 10°, …, 350°)
Single precision floating point only
Zero dynamic memory allocation during processing (all buffers are pre-allocated at creation)

Usage

The header file is include/esp32p4/esp_doa_capon_embedded.h.

Basic Flow:

Define the microphone array geometry

Microphone coordinates are given in meters, in a right-hand coordinate system, one entry per microphone. The entries may be in any order, but audio channel i passed to esp_doa_capon_embedded_process() must always come from the microphone at mic_coord[i].

#include "esp_doa_capon_embedded.h"

/* 4-mic uniform circular array, radius 5 cm; mic i sits at i*90 degrees */
PlaneCoord mic_coords[4] = {
    { 0.05f, 0.0f, 0.0f},
    { 0.0f,  0.05f, 0.0f},
    {-0.05f, 0.0f, 0.0f},
    { 0.0f, -0.05f, 0.0f},
};

Create a DOA instance

All memory (handle and internal memory pool) is allocated by the module itself and released by esp_doa_capon_embedded_destroy(). Buffers are allocated from PSRAM by default; see Memory Configuration below.
```
esp_doa_capon_embedded_handle_t *doa =
    esp_doa_capon_embedded_create(mic_coords, 4);
```
Process audio frames

The input is mic_num-channel 16-bit PCM audio in planar layout ([ch0_0..ch0_127, ch1_0..ch1_127, ...]), 128 samples per channel per frame.
```
int16_t audio_frame[128 * 4];  // 4 channels, planar: [ch0_0..ch0_127, ch1_0..ch1_127, ...]
int vad = 1;                   // 1 = speech, 0 = noise/silence
float angle = esp_doa_capon_embedded_process(doa, audio_frame, vad);
```
The returned angle is in degrees, range 0–360, defined in the absolute array coordinate system (0° = positive x-axis, counter-clockwise), independent of the microphone ordering in mic_coord. -1.0f is returned on error.
Note
- When vad_result is 0, all adaptive state (covariance recursion, matrix inversion, spectrum) is frozen and the last estimated angle is returned unchanged. Feeding a VAD result from the AFE module is recommended, so that noise-only frames do not corrupt the estimation.
- The covariance recursion needs several frames to converge. Estimates from the first few frames after creation (or reset) should be discarded.
(Optional) Reset the processor state

Resets the covariance matrix and smoothing filters, e.g., after a long pause:
```
esp_doa_capon_embedded_reset(doa);
```
Release resources

esp_doa_capon_embedded_destroy() releases all resources allocated by esp_doa_capon_embedded_create() (passing NULL is safely ignored):
```
esp_doa_capon_embedded_destroy(doa);
```

Warning

When chaining DOA with GSC beamforming, pass the same microphone coordinate array to both modules, otherwise the estimated angle refers to the wrong channels.

Tip

esp_doa_capon_embedded_print_info(doa) prints the processor configuration (frame size, FFT size, frequency range, etc.) for debugging.

Memory Configuration

On ESP32-P4, the DOA internal buffers (memory pool, about 200 KB for 4 microphones) are allocated in PSRAM by default.
To place them in internal RAM instead, define ESP_DOA_DISABLE_PSRAM before including esp_doa_capon_embedded.h (or as a compile definition).

Accuracy Evaluation

The test application test_apps/esp-sr-gsc-doa evaluates the DOA estimation accuracy on chip. The test dataset is a simulated 4-mic uniform circular array (radius 5 cm) with clean speech; the sound source is placed on a 2 m circle at angles 0° to 330° in 30° steps (counter-clockwise from the +x axis).

Test method:

For each of the 12 angles, 64 frames are fed to esp_doa_capon_embedded_process() (VAD forced to speech).
The first 10 frames are skipped to let the covariance recursion converge.
The remaining frames are compared against the true angle, reporting both the exact match rate and the rate within one grid step (±10°).

Test results:

Metric	Result	Note
Exact match rate	94.0% (609/648)	Estimated angle equals the true angle
Accuracy within ±10°	94.0% (609/648)	Error within one grid step

Resource Consumption

The following table shows typical resource usage and performance data (16 kHz sample rate):

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