drupal 7, entity query by date and entity reference field.

gistfile1.txt

  $q = new EntityFieldQuery;
  $exam_id = $exam_wrp->field_event_exan_id->value();

  $assignee_user = $q->entityCondition('entity_type', 'event')
    ->propertyCondition('type', 'exam_event')
    ->fieldCondition('field_start_event_date', 'value', date('Y-m-d'), '>')
    ->fieldCondition('field_event_exan_id', 'value', $exam_id, '=')
    ->fieldCondition('field_assignee', 'target_id', array($GLOBALS['user']->uid), 'IN')
    ->execute();