What are the requirements for a custodial interrogation under the Miranda Rule?

A custodial interrogation must be preceded by the familiar Miranda warnings and by the suspect's waiver of them.⁷ (Elizalde, supra, 61 Cal.4th at pp. 527, 530-531.) The prosecution has the burden to prove, by a preponderance of the evidence, that the accused's rights under Miranda were not violated. (People v. Villasenor (2015) 242 Cal.App.4th 42, 59; People v. Dykes (2009) 46 Cal.4th 731, 751 [prosecution has the burden to prove the validity of defendant's waiver of his rights].)