**3.4. Performance of advanced detection schemes for uncoded IR-UWB transmission**

In Fig. 2 the presented ACR-based detection schemes are compared with respect to bit error rate of uncoded IR-UWB transmission and a time-bandwidth product of *N* = 400. This parameter setting is based on the reasoning in Footnote 2; the Gaussian approximation as described in Sec. 2.3 is employed assuming that the integration interval captures the entire pulse energy, i.e., *E*<sup>i</sup> = *E*s). It can be observed, that i) with increasing blocksize performance improves over traditional DD (the significant loss compared to coherent detection is mainly caused by the squared original noise variance *σ*<sup>2</sup> *<sup>n</sup>* in the equivalent noise variance *σ*<sup>2</sup> *<sup>η</sup>* ) and approaches coherent detection with perfect channel estimation, ii) DF-DD with optimized decision order (dashed lines) achieves almost the performance of MSDD (solid lines, exactly the same performance for *L* = 2 with minimum overlap, and iii) combining multiple observations obtained by introducing a maximum block-overlap, but using the same ACR front-end (right hand side of Fig. 2) leads to significant gains over traditional blockwise processing without overlapping blocks (left hand side of Fig. 2), for both soft-output MSDD and hard-output DF-DD (except for *L* = 2) as blockwise detection scheme. This gain comes at the cost of an increased computational complexity (roughly proportional to *L*).

**Figure 2.** BER of uncoded BPSK IR-UWB transmission with autocorrelation-based detection with *L* = 2, 3, 5, and 10 (right to left). Solid: MSDD, dashed: DF-DD, left: processing of non-overlapping blocks, right: combining of multiple observations obtained by processing of maximum-overlapping blocks.

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detection, is depicted in Fig. 3 (using the same parameter setup as in Sec. 3.4). Since an exact evaluation of the BICM capacity of the IR-UWB system at hand is overly complex, the equivalent discrete-time channel model and the Gaussian approximation, as derived in Sec. 2.3, have been applied [16]. Soft-output MSDD with *L* = 2, 5, and 10 (solid black), DF-DD with *L* = 2 and 5 (dashed black), and soft- and hard-output DD (solid gray/dashed gray) are

In line with the BER results, the ACR operation causes a significant gap compared to coherent detection; the capacity improves with increasing blocksize. As expected for noncoherent detection schemes, cf., e.g., [20], the capacity curves of IR-UWB with ACR-based detection plotted vs. *E*b/*N*0, with *E*<sup>b</sup> denoting the energy per information bit, have a C-like shape. Thus, as opposed to coherent detection, the minimum ratio *E*b/*N*0, which still guarantees reliable transmission, is obtained at non-zero rates (indicated with markers). At the operating point of minimum *E*b/*N*<sup>0</sup> and optimum rate, both options, decreasing and increasing the code rate, lead to operating points which do not allow reliable transmission. Consequently, as known from other noncoherent detection schemes [20], also in realistic BICM IR-UWB systems the code rate should be carefully selected. Especially for increasing *L* this minimum gets more and more pronounced, and higher code rates should be favored compared to the probably more common choice of *R*<sup>c</sup> = 0.5 [4]. In all cases, the optimum rate for the hard-output schemes DD and DF-DD is larger than the respective optimum rate of soft-output MSDD. These effects are also observed for noncoherent detection (energy detection) of pulse-position modulation [20]. However, in this case already the application of BICM in combination with

shown; for comparison the capacity of BPSK with coherent detection is included.

coherent detection leads to optimum operating points at non-zero code rates [13].

Gaussian approximation with time-bandwidth product *N* = 400.
