Proposed echo processing scheme

Our problem is to achieve echo cancellation given the two observations signalsyj(n) (with j ∈ {1,2}) and the reference signal x(n). The system introduced here still outputs an estimate of the near-end speech signal s₁(n) (i.e. near-end speech signal picked by the primary microphone) in an equivalent manner. The proposed echo cancellation schemes are composed of adaptive filtering followed by echo postfiltering and are illustrated in

76 5. Echo cancellation for dual channel terminals

ˆh₂(n) hˆ₁(n)

+

+ Echo

Filtering Filter Update

x(n)

y₁(n) y₂(n)

e₁(n) e₂(n)

−

− dˆ₂(n) dˆ₁(n)

s(n)

ˆ s₁(n)

Figure 5.5: Proposed echo processing scheme

figures 5.5 and 5.6. The choice and position of each module is explained in the following.

5.2.1 Adaptive echo cancellation

In the system illustrated in Figure 5.5, adaptive echo cancellation (AEC) is composed of two adaptive filters: one adaptive filter per microphone path. The echo signal recorded by the each microphone is generated by the same loudspeaker. This means for each micro-phone signal, an estimate of the echo signal can be obtained through existing approaches to AEC. Similar use of the AEC for multi-microphone terminals can be found in the lit-terature [Guo et al., 2011, Jeannes et al., 2001, Kellermann, 1997]. AEC can be achieved through well-known existing approaches such as least mean square (LMS) or normalized LMS (NLMS) algorithms [Hänsler and Schmidt, 2004, Haykin, 2002]. Subband or fre-quency domain AEC algorithms can also be used.

The proposed DM echo processing scheme is designed such as to output an estimate of the near-end speech signal with an echo postfilter which is solely applied to one microphone path. AEC typically places high demand on memory and computational capacity. One could reduce the computational complexity of the system in Figure 5.5 by using one AEC instead of two as showed in Figure 5.6. The secondary microphone is directly input to the echo postfilter. In this way, the computational complexity is reduced however, the postfilter still exploits the dual-microphone architecture.

For the same reasons as in the SC case, some residual echo is present at the output of the AECs. The errors signals from the AEC can be expressed as follows:

e_j(n) =s_j(n) + ˜d_j(n) (5.6) wherej ∈ {1,2}and ˜d_j(n) represent the residual echo signal.

5.2.2 Echo postfiltering

As explained in Section 2.2.1.2, the postfilter is required to achieve further echo suppres-sion. As schematized in Figures 5.5 and 5.6 and similarly as in SM terminals a frequency domain echo postfilter is used for residual echo suppression. Most frequency domain post-filters can be subdivided into two blocks: the filter update, in which the echo suppression

ˆh₁(n)

+ Echo

Filtering Filter Update

x(n)

y₁(n) y₂(n)

e₁(n)

− dˆ₁(n)

s(n)

ˆ s₁(n)

Figure 5.6: Alternative echo processing scheme with one AEC

filter is computed, and the echo suppression itself through filtering. The computation of the echo suppression filter use the input signals (loudspeaker and microphone signals) to compute an attenuation gain. This attenuation gain is then applied to the microphone path in the frequency domain or time domain to completely suppress the residual echo.

In our case, echo suppression is still applied only to the primary microphone path.

This means existing echo suppression gain rules can still be used. Some example of gain rules which can be used in our case include [Hänsler and Schmidt, 2004, Haykin, 2002, Yemdji et al., 2010a]:

W_a(k, i) = ξ(k, i)

1 +ξ(k, i), W_b(k, i) = Φ^s1s1(k, i)

Φ^s1s1(k, i) + Φ^d˜1d˜1(k, i) (5.7) where Φ^s1s1 is the PSD of the near-end speech, Φ^d˜1d˜1 is the PSD of the residual echo at the primary microphone and ξ is the signal-to-echo ratio (SER) at the primary microphone.

As explained in Chapter 2, both equations are mathematically equivalent but do not necessarily lead to the same results and speech quality.

In the postfilter used in the echo processing schemes in Figures 5.5 and 5.6, two microphone signals are used as inputs to the filter update module. Existing approaches to compute the echo suppression filter are based on single microphone. There is a need to design new estimation methods to compute the quantities involved in the computation of the echo postfilter gains. This can be done in two different ways:

• one simple option consists of keeping the existing gain rule computation unchanged (i.e. based on one microphone path) and simply use the microphones to add addi-tional control on variables such as the gain values or echo PSD estimate. In this logic, the microphone signals can be used to design a double-talk detector(DTD). A DTD based on the level difference between the microphone signals is presented in Section 5.3.

• another option consists of using the dual microphone observations to design new esti-mations rules for the quantities involved in the computation of the echo suppression gain. In Section 5.4, we propose to use the level difference between the microphone signals to design new gain rule. Another approach to DM echo postfilter is presented in Chapter 6.

78 5. Echo cancellation for dual channel terminals 5.2.3 Synthesis

The target of the study of DM echo cancellation is to propose algorithms which improve echo cancellation performance while being implemented on real mobile devices. In the remainder of this thesis, only the echo processing in Figure 5.6 will be used because of its computational simplicity. Nevertheless, the proposed algorithms can be extended so to be used with two AECs. In the contributions presented in the remainder of this thesis, we consider that there is no ambient noise. The microphone signals only are only composed of the near-end speech and of the echo signals. This consideration permits a full in depth assessment of the behavior of proposed algorithms for echo processing.