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This paper presents simple, exact, and closed-form expressions for the average bit error rate (BER) of M-ary orthogonal signals with noncoherent diversity combining over independent as well as arbitrarily correlated nonidentically distributed Nakagami-m fading channels. The fading channels are allowed to have arbitrary average signal-to-noise ratios (SNRs) as well as arbitrary fading parameters. The derived expressions are given in terms of elementary functions, they do not involve numerical integrals or complicated functional operations, and can easily be evaluated numerically. The results show that the system average BER can be estimated using the derived expressions herein with large computational time savings as compared with those taken by the ones addressed perviously.