Cyclic delay diversity is a simple, yet effective, transmit diversity scheme for multicarrier based transmissions employing coherent digital linear modulation schemes. It is shown that, for satisfactory operation, the scheme requires additional channel estimation overhead compared to single antenna and traditional space-time coded transmissions owing to the inherent increase in frequency selective fading. The authors analyse the additional channel estimation overhead requirement for a Hiperlan #2 style system with two transmit antennas operating in a NLOS indoor environment. The analysis shows that an additional overhead of 500% is required for the candidate system compared to a single antenna system. It is also shown that by employing differential modulation the channel estimation overhead can be eliminated with significant performance improvement compared to a system employing a practical channel estimation scheme. This novel combination, termed 'differentially modulated cyclic delay diversity', is shown to yield a highly spectral efficient, yet simple transmit diversity solution for multi-carrier transmissions.