Bit error rate (BER) performance is studied for a subcarrier differential quadrature phase-shift keying modulated optical wireless communication system over the Gamma-Gamma turbulence channels. A closed-form BER expression is derived using a series expansion approach. Asymptotic analysis shows that the diversity order of the considered system depends only on the smaller channel parameter.Introduction: As an attractive alternative to pulse position modulation (PPM) and on-off keying (OOK), subcarrier intensity modulation (SIM) with direct detection was first proposed for optical wireless communication (OWC) in [1]. It can be shown that SIM can have better error rate performance than PPM and OOK. Although a SIM system with coherent modulations is superior to that with noncoherent or differentially coherent modulations, it requires carrier phase recovery for the subcarrier signal to achieve its optimal performance [2]. Thus, it is difficult to perform coherent detection in applications where the phase of the received subcarrier signal cannot be tracked accurately. In such scenarios, noncoherent frequency shift keying (NCFSK) or differential phase shift keying (DPSK) can be employed at the expense of system performance. In [1], Huang et al. first studied the bit error rate (BER) performance of a subcarrier DPSK modulated OWC system over the lognormal channels. In [3], Popoola et al. studied the BER performance of a subcarrier DPSK modulated OWC link in the negative exponential channels. More recently, Song et al. analysed the BER of a subcarrier DPSK modulated OWC system over the Gamma-Gamma channels and obtained a closed-form BER expression using a series expansion approach [4]. All the aforementioned work has mainly focused on binary DPSK. As a multilevel modulation scheme, differential quadrature PSK (DQPSK) can achieve higher spectral efficiency than binary DPSK. However, to the best of the authors' knowledge, no prior work has been carried out to study the error rate performance of a subcarrier DQPSK modulated OWC system over turbulence channels. In this Letter, we study the BER performance of a subcarrier DQPSK modulated OWC system over the Gamma-Gamma channels and derive a closed-form BER expression.