* Clashes on outskirts of capital
* Damascus streets deserted, celebratory gunfire causes alarm
* Mortars hit old city in Homs
By Oliver Holmes
BEIRUT, Jan 1 (Reuters) - Syrians woke on New Year's Day to countrywide aerial bombardment, while President Bashar al-Assad's forces and rebels fighting to topple him clashed on the outskirts of the capital.
Residents of Damascus entered the new year to the sound of artillery hitting southern and eastern districts that form a rebel-held crescent on the outskirts of the capital, the centre of which is still firmly under government control.
In the centre, soldiers manning checkpoints fired celebratory gunfire at midnight, causing alarm in a city where streets were largely deserted.
"How can they celebrate? There is no 'Happy New Year'," Moaz al-Shami, an opposition activists who lives in the capital's central Mezzeh district, said over Skype, his voice trembling with anger.
He said rebel fighters attacked one checkpoint in the district of Berzeh early on Tuesday. Opposition groups said mortar bombs hit the southwest suburb of Daraya, where the army launched a military offensive on Monday to retake the battered district.
Assad's air force pounded Damascus's eastern suburbs, as well as rebel-held areas in the second city Aleppo, and several rural towns and villages, opposition activists said.
An estimated 45,000 people have been killed in the revolt, which started in early 2011 with peaceful protests demanding democratic reforms but turned into an armed uprising after months of attacks on protesters by security forces.
A resident of the central city of Homs, who asked to remain anonymous, said shells had landed on the Old City early on Tuesday.
Homs lies on the strategic north-south highway and parts of the ancient city have been levelled during months of clashes. Government forces ousted rebels from the city early last year but militants have slowly crept back in.
"The Old City is under siege. There is shelling from all sides," he said.
The opposition-linked Syrian Observatory for Human Rights, a British-based monitoring group, reported 160 people killed on the final day of 2012, including at least 37 government troops. The group's reports cannot be verified.
The civil war in Syria has become the longest and deadliest of the conflicts that rose out of the uprisings that swept through the Arab world over the past two years.
Many Sunni Muslims, the majority in Syria, back the rebellion, while Assad, who hails from the Shi'ite-derived Alawite minority sect, is backed by some minorities who fear revenge if he falls. His family has ruled Syria harshly since his father seized power in a coup 42 years ago.
Assad's forces have lately relied more on aerial and artillery bombardment, rather than infantry. Residential areas where rebels base themselves have been targeted, killing civilians unable to flee. Schools and queues of people buying bread have been hit.
Rebels have taken swathes of the north and the east but have struggled to hold cities, complaining that they are defenceless against Assad's Soviet-built air force.
A year ago, many diplomats and analysts predicted Assad would leave power in 2012. But he has proved resilient and none of his inner circle have defected. He still largely retains control of his armed forces.
Diplomatic efforts to end the war have faltered, with the rebels refusing to negotiate unless Assad leaves power and him pledging to fight until death.
Most Western and Arab states have called for him to leave power. He is supported by Russia and Shi'ite Iran.
In the final days of 2012, international mediator Lakhdar Brahimi called on countries to push the sides to talk, saying Syria faced a choice of "hell or the political process".
One Damascus resident, who asked not to be identified for security reasons, said the usual new year's eve crowds were absent from the increasingly isolated capital.
"There was hardly anyone on the streets, no cars, no pedestrians. Most restaurants, cafes and bars were empty," she said. Some young people gathered at three bars in the old city.
"There was music but nobody was dancing. They just sat there with a drink in their hands and smoking. I don't think I saw one person smile," she said. The midnight gunfire caused alarm.
"It was very scary. No one knew what was going on. People got very nervous and started making phone calls. But then I discovered that at least on my street, the gunfire was celebratory."