Sinon.JS stub for window.location.search

I am trying to test a simple function that makes a call to window.location.search. I'm trying to understand how to stub this call so that I can return a url of my choosing.

function:

getParameterByName: (name) =>    
  name = name.replace(/[\[]/, "\\\[").replace(/[\]]/, "\\\]")
  regexS = "[\\?&]" + name + "=([^&#]*)"
  regex = new RegExp(regexS)    
  results = regex.exec(window.location.search) //Stub call to window.location.search
  if(results == null)
    return ""
  else
    return decodeURIComponent(results[1].replace(/\+/g, " "))

Test case:

describe "Data tests", () ->
  it "Should parse parameter from url", () ->        
    data = new Data()

    console.log("search string: " + window.location.search) //prints "search string:"
    window.location.search = "myUrl"
    console.log("search string: " + window.location.search) //prints "search string:"
    console.log(data.getParameterByName('varName'))

    expect(true).toBe(true)

My original attempt was to return a value directly like so:

sinon.stub(window.location.search).returns("myUrl")

This, of course, doesn't work. I don't think I'm specifying the stub correctly, but it shows my intent.

Any ideas on how to solve this would be greatly appreciated.