A Mexican man pleaded guilty today to raping and strangling an 84-year-old retired psychiatrist during a 2001 break-in at her

Carlsbad senior housing complex, and trying to rape a woman in Los Angeles three years later.

Alejandro Avalos Fernandez will be sentenced to 34 years to life in state prison at a Jan. 6 hearing before Judge Daniel Goldstein at the Vista Courthouse.

The 34-year-old defendant pleaded guilty to first-degree murder and rape in the death of Gladys Conrad and assault with intent to commit rape in the April 2004 assault of a 64-year-old woman in Los Angeles.

A friend found Conrad's body the afternoon of Sept. 1, 2001. Carlsbad police said she had been sexually assaulted and strangled early that morning or late the previous night by a man who apparently entered her home at the Carlsbad-by-the-Sea retirement village through an unlocked door or window.

There was no indication that the victim knew Fernandez, who worked odd jobs in the area and may have been staying with friends in the vicinity, said Carlsbad police Lt. Kelly Cain.

Investigators had no solid leads in the case until late 2004, when a DNA database matched the genetic profile of Conrad's killer to that of the perpetrator in the Los Angeles attempted rape.

The victim in the Los Angeles case testified at a preliminary hearing in June that she was attacked about 11 p.m. as she walked two blocks home after leaving work at a convalescent home.

She said the defendant started asking her questions as she walked.

"When I looked back, he punched my face,'' the witness said.

The woman, who was 64 at the time, said she fell to the ground, stood back up, and was punched again.

"He tried to strangle me with his right hand and with his left hand tried to pull down my pants,'' the woman testified.

The witness said she bit her attacker's hand and he walked off after punching her again.

"I was so scared that night that he might kill me,'' she testified.

In 2007, Fernandez was arrested on a narcotics charge in Los Angeles and a DNA sample was taken. He was released, however, before his DNA was entered into the national database.

The defendant was re-arrested in January 2009 in Mexico City when a DNA check tied him to Conrad's death. It took 13 months to get him extradited to

San Diego.