1090 antenna

Never tried a 1090 Mhz antenna for 978 Mhz, but theoretically, it will not give optimum performance. However the two frequencies being close to each other, it should not perform too bad either.

If you can make a DIY antenna, try a Spider or Cantenna with whip/radials/can-height 76mm instead of 69mm to tune it to 978 MHz.