Beam training method for a user equipment, hereinafter referred to as UE, and a base station, hereinafter referred to as BS, belonging to a mobile communication network, the BS comprising a memory in which are stored a plurality of beam dictionaries ( BD k,k =1,..,N), wherein the BS is initially provided with an estimate ( d̂) of the position of the UE along with a standard deviation (σ d) of this estimate; the BS uses said UE position estimate and standard deviation to select, in said plurality of dictionaries, an initial beam having the smallest beamwidth while covering the UE and meeting a constraint of predetermined maximum beam selection error probability ( δ BS), the BS and the UE perform a first iterative loop in which: (a) the BS transmits first downlink pilot symbols using its currently selected beam; (b) the UE updates its position estimate and standard deviation thereof from the received first downlink symbols and sends said position estimate and standard deviation to the BS; (c) the BS uses said updated UE position estimate and standard deviation to select a beam having the smallest beamwidth while covering the UE and meeting said constraint of predetermined maximum beam selection error probability ( δ BS); said first loop being repeated until a standard deviation of the position of the UE lies below a predetermined position error threshold ( δ d); the BS and the UE performing a second iterative loop in which: (a') the BS transmits second downlink pilot symbols using its currently selected beam; (b') the UE updates an estimate of direction of arrival ( ψ̂) of the signal received from the BS and a standard deviation of this direction of arrival ( δ ψ); (c') the UE uses said updated direction of arrival and standard deviation thereof to set a beam pointing towards the updated direction of arrival and having the smallest beamwidth meeting a constraint of predetermined maximum beam alignment error probability ( δ MA); the iterations of the first loop and second loops being stopped if the standard deviation of the position of the UE lies below said predetermined position error threshold and standard deviation of direction of arrival lies below said predetermined angular error threshold. the BS is initially provided with an estimate ( d̂) of the position of the UE along with a standard deviation (σ d) of this estimate; the BS uses said UE position estimate and standard deviation to select, in said plurality of dictionaries, an initial beam having the smallest beamwidth while covering the UE and meeting a constraint of predetermined maximum beam selection error probability ( δ BS), the BS and the UE perform a first iterative loop in which: (a) the BS transmits first downlink pilot symbols using its currently selected beam; (b) the UE updates its position estimate and standard deviation thereof from the received first downlink symbols and sends said position estimate and standard deviation to the BS; (c) the BS uses said updated UE position estimate and standard deviation to select a beam having the smallest beamwidth while covering the UE and meeting said constraint of predetermined maximum beam selection error probability ( δ BS); (a) the BS transmits first downlink pilot symbols using its currently selected beam; (b) the UE updates its position estimate and standard deviation thereof from the received first downlink symbols and sends said position estimate and standard deviation to the BS; (c) the BS uses said updated UE position estimate and standard deviation to select a beam having the smallest beamwidth while covering the UE and meeting said constraint of predetermined maximum beam selection error probability ( δ BS); said first loop being repeated until a standard deviation of the position of the UE lies below a predetermined position error threshold ( δ d); the BS and the UE performing a second iterative loop in which: (a') the BS transmits second downlink pilot symbols using its currently selected beam; (b') the UE updates an estimate of direction of arrival ( ψ̂) of the signal received from the BS and a standard deviation of this direction of arrival ( δ ψ); (c') the UE uses said updated direction of arrival and standard deviation thereof to set a beam pointing towards the updated direction of arrival and having the smallest beamwidth meeting a constraint of predetermined maximum beam alignment error probability ( δ MA); (a') the BS transmits second downlink pilot symbols using its currently selected beam; (b') the UE updates an estimate of direction of arrival ( ψ̂) of the signal received from the BS and a standard deviation of this direction of arrival ( δ ψ); (c') the UE uses said updated direction of arrival and standard deviation thereof to set a beam pointing towards the updated direction of arrival and having the smallest beamwidth meeting a constraint of predetermined maximum beam alignment error probability ( δ MA); the iterations of the first loop and second loops being stopped if the standard deviation of the position of the UE lies below said predetermined position error threshold and standard deviation of direction of arrival lies below said predetermined angular error threshold.