Maybe try filling a square with a linear gradient that goes from white to black to white, then do a perspective transform on it.

Layer > New Fill Layer > Gradient and set the Style to Angle. The Fill Layer will have a Layer mask. Create a standard black/white radial gradient on the mask (see image below.)

Convert the Gradient Layer to a Smart Object by right-clicking it in the Layers Panel
Then choose Filter > Noise > Add Noise and adjust to your liking.

Applying the Noise filter as a Smart Filter, means you can adjust the noise further at any time. And having the gradient as a layer inside the smart object also means you can adjust the gradient at any time as well.

Or.. you can simply create an angled gradient using the gradient tool, add a "cover all" (i.e. black filled) layer mask. Then apply the Noise filter to the layer. The Smart Object method is merely non-destructive and keeps everything "live" and further editable.

The difference between an Angle gradient and a standard Radial gradient will be in how the gradient values are laid down. Using the Angle option causes the gradient to get darker in a circular or rotary manner, as opposed to just darker at the center like standard radial gradients.

Additional

The Noise filter creates dark and light pixels to convey noise. If you need this gradient transparent for use on a colored background, you may need to build it on a colored background in Photoshop. Primarily because blending modes, in general, are not going to allow you to maintain the color of the gradient. Photoshop does have features which aren't available in apps such as InDesign.

After creating the gradient and adding noise, it's possible to use Blending Options and the Blend If sliders in Photoshop to remove the white noise pixels....

(Due to the looping in the animation above, it sort of looks like clicking OK for the Blending Options makes the blending reset. It doesn't. That's merely the gif looping.)

Or... add a Layer Mask to the Smart Object and apply the Noise filter to the Layer Mask directly - same general result.

If you want noise more course and larger... Unlink the mask with the Smart Object and then transform the layer mask, enlarging it.

And.. on the mask.. you can apply noise, enlarge the mask, apply noise again, enlarge again, repeat... to get more variation in the size of the noise.