Messenger of Allah ﷺ used to pray two light rakʿat before the morning (compulsory) prayer after the day dawned and the Mu'adh-dhin had finished his Adhan. He then would lie on his right side till the Mu'adh-dhin came to pronounce the Iqama.  

كَانَ رَسُولُ اللَّهِ ﷺ إِذَا سَكَتَ الْمُؤَذِّنُ بِالأُولَى مِنْ صَلاَةِ الْفَجْرِ قَامَ فَرَكَعَ رَكْعَتَيْنِ خَفِيفَتَيْنِ قَبْلَ صَلاَةِ الْفَجْرِ بَعْدَ أَنْ يَسْتَبِينَ الْفَجْرُ ثُمَّ اضْطَجَعَ عَلَى شِقِّهِ الأَيْمَنِ حَتَّى يَأْتِيَهُ الْمُؤَذِّنُ لِلإِقَامَةِ  

"When the Muaddhin fell silent after the Adhan for the beginning of Fajr, he would pray two brief rak'ahs, then he would lie down on his right side."  

كَانَ رَسُولُ اللَّهِ ﷺ إِذَا سَكَتَ الْمُؤَذِّنُ بِالأُولَى مِنْ صَلاَةِ الْفَجْرِ قَامَ فَرَكَعَ رَكْعَتَيْنِ خَفِيفَتَيْنِ قَبْلَ صَلاَةِ الْفَجْرِ بَعْدَ أَنْ يَتَبَيَّنَ الْفَجْرُ ثُمَّ يَضْطَجِعُ عَلَى شِقِّهِ الأَيْمَنِ  

"When the Muaddhin fell silent after the Adhan for the beginning of Fajr, he would pray two brief rak'ahs, then he would lie down on his right side." (Using translation from Nasāʾī 1762)  

«كَانَ رَسُولُ اللَّهِ ﷺ إِذَا سَكَتَ الْمُؤَذِّنُ بِالْأَوَّلِ مِنْ صَلَاةِ الْفَجْرِ قَامَ فَرَكَعَ رَكْعَتَيْنِ خَفِيفَتَيْنِ قَبْلَ صَلَاةِ الْفَجْرِ بَعْدَ أَنْ يَتَبَيَّنَ لَهُ الْفَجْرُ ثُمَّ اضْطَجَعَ عَلَى شِقِّهِ الْأَيْمَنِ حَتَّى يَأْتِيَهُ الْمُؤَذِّنُ لِلْإِقَامَةِ»