Signal space cooperative (SSC) system is bandwidth and energy efficient, which can achieve full-rate and full-diversity simultaneously. In this study, the authors first derive accurate bit error rate (BER) of the SSC system with maximum-likelihood detection (MLD), low-complexity linear detection (LD) and combined MLD and LD (MLD&LD). Specifically, closed-form BER expressions for the three detection schemes are derived. Also, asymptotic approximation analysis is performed to show clearly the diversity and coding gains of the three detection schemes. Through the analysis, the authors find out that MLD is optimal in diversity but has a high complexity, whereas LD is of low complexity but only achieves diversity order one. Interestingly, MLD&LD has almost the same BER as the BER-optimal MLD over the whole SNR range when equal power allocation (EPA) is adopted, whereas having lower complexity than MLD at low-to-medium SNR. Then, optimum power allocation for MLD&LD is developed, however, the largest power gain over EPA is proven to be only 0.37 dB. In view of the BER performance of MLD&LD and implementation simplicity of EPA, they conclude that MLD&LD with EPA is a wise choice for the SSC system. Finally, outage probability of MLD&LD with EPA is analysed to characterise the transmission reliability.