A network for handling a transmission in an unlicensed band, the network comprises: a storage unit for storing instructions; and a processing circuit, coupled to the storage unit, wherein the storage unit stores, and the processing circuit is configured to execute, the instructions of: performing a channel access procedure according to a channel access priority class for a downlink transmission on a channel of an unlicensed band, wherein the channel access priority class is defined by contention windows CW min, p and CW max, p, consecutive slot durations, m p, maximum channel occupancy time, T m cot, p, and a subset of [ CW min, p, CW max, p] of allowed sizes for the contention windows in a 3rd Generation Partnership Project, 3GPP, specification; wherein the downlink transmission comprises a physical downlink, DL, control channel, PDCCH, order transmission or an uplink, UL, grant transmission; and performing the downlink transmission to a communication device, after sensing that the channel is idle for at least one sensing interval; and receiving a buffer status report from the communication device, wherein the buffer status report indicates in which of the logical channels or the logical channel groups the communication device has data in a buffer, and determining the channel access priority class according the highest logical channel priority among the logical channel priorities of the logical channels or logical channel groups for which the buffer status report has indicated that the communication device has data in the buffer. a storage unit for storing instructions; and a processing circuit, coupled to the storage unit, wherein the storage unit stores, and the processing circuit is configured to execute, the instructions of: performing a channel access procedure according to a channel access priority class for a downlink transmission on a channel of an unlicensed band, wherein the channel access priority class is defined by contention windows CW min, p and CW max, p, consecutive slot durations, m p, maximum channel occupancy time, T m cot, p, and a subset of [ CW min, p, CW max, p] of allowed sizes for the contention windows in a 3rd Generation Partnership Project, 3GPP, specification; wherein the downlink transmission comprises a physical downlink, DL, control channel, PDCCH, order transmission or an uplink, UL, grant transmission; and performing the downlink transmission to a communication device, after sensing that the channel is idle for at least one sensing interval; and receiving a buffer status report from the communication device, wherein the buffer status report indicates in which of the logical channels or the logical channel groups the communication device has data in a buffer, and determining the channel access priority class according the highest logical channel priority among the logical channel priorities of the logical channels or logical channel groups for which the buffer status report has indicated that the communication device has data in the buffer. performing a channel access procedure according to a channel access priority class for a downlink transmission on a channel of an unlicensed band, wherein the channel access priority class is defined by contention windows CW min, p and CW max, p, consecutive slot durations, m p, maximum channel occupancy time, T m cot, p, and a subset of [ CW min, p, CW max, p] of allowed sizes for the contention windows in a 3rd Generation Partnership Project, 3GPP, specification; wherein the downlink transmission comprises a physical downlink, DL, control channel, PDCCH, order transmission or an uplink, UL, grant transmission; and performing the downlink transmission to a communication device, after sensing that the channel is idle for at least one sensing interval; and receiving a buffer status report from the communication device, wherein the buffer status report indicates in which of the logical channels or the logical channel groups the communication device has data in a buffer, and determining the channel access priority class according the highest logical channel priority among the logical channel priorities of the logical channels or logical channel groups for which the buffer status report has indicated that the communication device has data in the buffer.