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This paper studies adaptive power allocation among sub-carriers in MC-CDMA. Due to intrinsic nature of MC-CDMA; carrier based power allocation schemes cause MAI (multiple access interference) enhancements, hence fail at higher system loads. We propose a band based dynamic link adaptation (BBDLA) scheme that preserves orthogonality (among users) by spreading user's signal only over a band of adjacent N sub-carriers (N < Nsc) lying within coherence bandwidth (Bc) of the channel. Hence, it allows band based power allocation without causing any MAI. However, with only N orthogonal users supported on a particular band, BBDLA essentially proposes a hybrid of FDMA with MC-CDMA where Bands and transmit powers are optimally assigned to users by base station (in accordance with their channel state). Optimum band allocation for BBDLA is found to be computationally intractable hence a sub-optimal heuristic approach is proposed with equal power distribution among all assigned bands for each user. Effect of Bc over choice of N is studied and BBDLA with suitably chosen N, is shown to outperform other published carrier based power allocation schemes while it maintain almost single user BER performance up to 62% of full system loading.