WPC AJAX Search

Free version: Download for free here https://wordpress.org/plugins/wpc-ajax-search/#description

Key Features:

Live search, instant results of products
Set up suggestions for special keywords
Add search to different menus
Show/ hide the overlay effect
Click outside to hide the popup
Add products to the Wishlist & Compare right from the search popup
Automatically show or hide the search popup when search input is possible
Choose a heading for the search popup
Choose a position for the search popup on your site
Enable/ disable the sliding effect of the popup
Show/hide the Close button at the top corner of the popup
Link to individual products in the same or a new tab
Compatible with most common WordPress themes and plugins
Open individual products in a Smart Quick View popup
Set up keywords for one-sale, recent, featured, and popular products
Configure the search settings: by categories or SKU, search limit
(Premium) Smart Search: override normal search with selective output results