Speech signals captured by a microphone mounted to a smart soundbar or speaker are inherently contaminated by echos. Modern smart devices are usually characterized by low computational capabilities and low memory resources; in these cases, a low-complexity acoustic echo canceller (AEC) may be preferred even though a tolerable degradation in the cancellation occurs. In principle, devices with multiple loudspeakers need an individual AEC for each loudspeaker because the transfer function (TF) from each loudspeaker to the microphone must be estimated. In this paper, we present an normalized least mean square (NLMS) algorithm for a multi-loudspeaker case using relative loudspeaker transfer functions (RLTFs). In each iteration, the RLTFs between each loudspeaker and the reference loudspeaker are estimated first, and then the primary TF between the reference loudspeaker and the microphone. Assuming loudspeakers that are close to each other, the RLTFs can be estimated using fewer coefficients w.r.t. the primary TF, yielding a reduction of 3:4 in computational complexity and 1:2 in memory usage. The algorithm is evaluated using both simulated and real room impulse responses (RIRs) of two loudspeakers with a reverberation time set to 0.3 s and several distances between the loudspeakers.
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