How to map type when map keys are not in the entity table with Doctrine?

Question

Can the discriminator mapping strings of a Doctrine entity be fetched from a database foreign table field? If not, how to handle inheritance type mapping in such a situation?

Considering a Doctrine 2.7.2 abstract entity Person with concrete entities A and B like:

/**
 * @MappedSuperclass
 * @Table(name="PERSON")
 */

abstract class Person {
    /**
     * @Id
     * @GeneratedValue
     */
    protected $id;

    /**
     * @Column(name="name",type="string")
     */
    protected $name;

     /**
     * @OneToOne(targetEntity="PersonType")
     * @JoinColumn(name="type", referencedColumnName="id")
     */
    protected $type;
}

/**
 * @Entity
 * @Table(name="PERSON")
 */
class A extends Person {}

/**
 * @Entity
 * @Table(name="PERSON")
 */
class B extends Person {}

A Person has a type bound to a PersonType entity like:

/**
 * @Entity
 * @Table(name="PERSON_TYPE")
 */
class PersonType {
    /**
     * @Id
     * @GeneratedValue
     */
    protected $id;

    /**
     * @Column(name="code",type="string")
     */
    protected $code;

    /**
     * @Column(name="name",type="string")
     */
    protected $name;
}

How to get the right class instantiated by repository query methods like find(), findBy(), findById(), etc?

Database set:

SELECT * FROM PERSON:
id name type
1  John 1
2  Tom  2

SELECT * FROM PERSON_TYPE:
id code name 
1  A    Type A
2  B    Type B

Expected results:

$entityManager->getRepository("A")->findOneById(2); // null
$entityManager->getRepository("B")->findOneById(2); // B object (Tom)
$entityManager->getRepository("A")->findOneById(1); // A object (John)

I can't find how to specify this using a discriminator.

Alternatively I have a working solution implementing a SQLFilter with the inconvenience to have to enable or disable filter.

An alternative solution may be to populate $discr?

(I can of course use the Person::findByType() method but it would be nice to have this feature directly managed by the respective repositories).