Spectrum auctions are one of the best‐known solutions to improve the efficiency of spectrum use. However, there can be many challenges in the design of a practical spectrum auction. Heterogeneity is one of the most major challenges. Unfortunately, most of the existing auction designs either do not take into account the various aspects of heterogeneity or assume only the scenario where each seller supplies one distinct channel and each buyer wishes to buy merely one channel. The authors propose a spectrum auction mechanism which considers the various aspects of heterogeneity as well as multi‐channel purchasing. They prove that the auction design preserves three important economic aspects including truthfulness, budget balance and individual‐rationality. Moreover, most of the existing works only provide the bidders a simple demand format. Their auction mechanism enables bidders to use diverse demand formats. Furthermore, they propose some novel adaptive grouping algorithms to improve the auction's performance. The simulation results demonstrate good performance of the proposed algorithms on various auction metrics.