Camera moves with player in doom-like

I'm attempting to make a game with the same camera controls and movement as Doom, basically the ability to move forward and backward, strafe, and rotate the view left or right. But I can't seem to figure out how to go about aligning the player with it's child, the main camera. I can turn the camera left and right, but I don't move in the direction the camera is facing. Would it be possible to cast a ray from the camera and use it's direction to orient the player? Here's my movement code so far

 using UnityEngine;
 using System.Collections;
 
 public class PlayerMovement : MonoBehaviour
 {
 
     public float runSpeed = 240f;
     public float walkSpeed = 120f;
     public float turnSpeed = 60f;
 
     Vector3 movement;
     //bool isRunning;
     Rigidbody playerRigidbody;
     
 
     void Awake()
     {
         playerRigidbody = GetComponent<Rigidbody>();
     }
 
     void FixedUpdate()
     {
         float h = Input.GetAxisRaw("Horizontal");
         float v = Input.GetAxisRaw("Vertical");
         float t = Input.GetAxisRaw("Turn");
 
         Move(h, v);
 
         Turning(t);
     }
 
     void Move(float h, float v)
     {
         movement.Set(h, 0f, v);
 
         //if(!isRunning)
             movement = movement * walkSpeed * Time.deltaTime;
        // else
             //movement = movement.normalized * runSpeed * Time.deltaTime;
 
         playerRigidbody.MovePosition(transform.position + movement);
     }
 
     void Turning(float t)
     {
         float newRotation = t * turnSpeed;
 
         newRotation *= Time.deltaTime;
 
         transform.Rotate(0, newRotation, 0);
 
     }
 }