Each transmit antenna in spatial modulation (SM) based communication is uniformly activated, which can lead to poor channels for transmission, causing performance degradation. Though antenna selection can be used to tackle this problem caused by uniform antenna activation (U-AA), it requires additional antenna elements, high computational complexity, and signalling overhead. This paper proposes an irregular antenna activation (I-AA) technique, which activates an antenna with a probability that is proportional to a channel with the highest gain. In the proposed method, consecutive equal bits in a bit sequence are exploited to choose an antenna index for transmission. Since different numbers of consecutive equal bits occur with different probabilities, this makes each of the available antennas to be randomly activated with different probabilities. Taking advantage of available channel state information at the transmitter, we develop a rate-optimized I-AA method to utilize better channels for transmission. In prominent variants of SM, the use of I-AA is shown to yield higher throughput and smaller error rates compared to operations with the conventional U-AA. Moreover, a joint rate and Euclidean-distance optimized antenna selection (REAS) and a rate-optimized low-complexity AS (RLAS) for SM with I-AA are proposed. The use of I-AA without AS in prominent variants of the SM technique is shown to achieve better error rate performance compared to U-AA with AS. Also, the use of I-AA in REAS and RLAS yields improvements in the data rates and error rates compared to U-AA with AS, at a negligible extra complexity and signalling overhead.