Direction of Arrival (DOA)

[中文]

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 by default (optimized for speech); the band is configurable at runtime via esp_doa_capon_embedded_create_with_band() (see Custom Frequency Band below), and the default band can be overridden at compile time via the DOA_LOW_FREQ / DOA_HIGH_FREQ / DOA_FREQ_SPACING macros

• 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:

1. 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},
   };
   

2. 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);
   

3. 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.

4. (Optional) Reset the processor state

   Resets the covariance matrix and smoothing filters, e.g., after a long pause:

   esp_doa_capon_embedded_reset(doa);
   

5. 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.

Custom Frequency Band

By default, the Capon spectrum is evaluated over 1500–4500 Hz with 100 Hz spacing (31 bins). To tune the band at runtime, create the instance with esp_doa_capon_embedded_create_with_band() instead of esp_doa_capon_embedded_create():

esp_doa_capon_embedded_handle_t *doa =
    esp_doa_capon_embedded_create_with_band(mic_coords, 4,
                                            2000,  /* low_freq (Hz) */
                                            6000,  /* high_freq (Hz) */
                                            200);  /* freq_spacing (Hz) */

The band is validated at creation time; NULL is returned if any of the following constraints is violated:

• 0 < low_freq < high_freq <= 8000 (Nyquist at 16 kHz)

• freq_spacing >= 63 Hz (the FFT bin resolution is 62.5 Hz)

• (high_freq - low_freq) / freq_spacing + 1 <= 129 frequency bins

Band selection guidance (speed of sound c = 340 m/s):

• low_freq >= c / (2 * array_aperture) for useful directivity

• high_freq <= c / (2 * min_mic_spacing) to avoid grating lobes

Note

Processing time scales linearly with the number of evaluated frequency bins.

The default band used by esp_doa_capon_embedded_create() can also be changed at compile time by defining DOA_LOW_FREQ, DOA_HIGH_FREQ and DOA_FREQ_SPACING (e.g., as compile definitions).

Memory Configuration

• On ESP32-P4, the DOA memory pool is split into two parts (about 206 KB in total for 4 microphones):

  • Per-frame hot buffers (about 57 KB) are always allocated in internal RAM for fast access.

  • The large read-only steering-vector tables (about 149 KB) are allocated in PSRAM by default.

• To place everything 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 data_4mic_r5cm_quite 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	100% (648/648)	Estimated angle equals the true angle
Accuracy within ±10°	100% (648/648)	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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