Stochastic computing (SC) is an alternative computing paradigm that processes data in the form of long uniform bit-streams rather than conventional compact weighted binary numbers. SC is fault-tolerant and can compute on small, efficient circuits, promising advantages over conventional arithmetic for smaller computer chips. SC has been primarily used in scientific research, not in practical applications. Digital sound source localization (SSL) is a useful signal processing technique that locates speakers using multiple microphones in cell phones, laptops, and other voice-controlled devices. SC has not been integrated into SSL in practice or theory. In this work, for the first time to the best of our knowledge, we implement an SSL algorithm in the stochastic domain and develop a functional SC-based sound source localizer. The developed design can replace the conventional design of the algorithm. The practical part of this work shows that the proposed stochastic circuit does not rely on conventional analog-to-digital conversion and can process data in the form of pulse-width-modulated (PWM) signals. The proposed SC design consumes up to 39% less area than the conventional baseline design. The SC-based design can consume less power depending on the computational accuracy, for example, 6% less power consumption for 3-bit inputs. The presented stochastic circuit is not limited to SSL and is readily applicable to other practical applications such as radar ranging, wireless location, sonar direction finding, beamforming, and sensor calibration.

Multiply-accumulate (MAC) operations are common in data processing and machine learning but costly in terms of hardware usage. Stochastic Computing (SC) is a promising approach for low-cost hardware design of complex arithmetic operations such as multiplication. Computing with deterministic unary bit-streams (defined as bit-streams with all 1s grouped together at the beginning or end of a bit-stream) has been recently suggested to improve the accuracy of SC. Conventionally, SC designs use multiplexer (MUX) units or OR gates to accumulate data in the stochastic domain. MUX-based addition suffers from scaling of data and OR-based addition from inaccuracy. This work proposes a novel technique for MAC operation on unary bit-streams that allows exact, non-scaled addition of multiplication results. By introducing a relative delay between the products, we control correlation between bit-streams and eliminate OR-based addition error. We evaluate the accuracy of the proposed technique compared to the state-of-the-art MAC designs. After quantization, the proposed technique demonstrates at least 37% and up to 100% decrease of the mean absolute error for uniformly distributed random input values, compared to traditional OR-based MAC designs. Further, we demonstrate that the proposed technique is practical and evaluate area, power and energy of three possible implementations.