**4.1. Capacity of IR-UWB with MSDD**

In contrast to coded modulation using multi-level codes [22], common IR-UWB systems adopt the conventional serial concatenation of coding and modulation at transmitter, and detection and decoding at receiver side, as shown in Fig. 1, i.e., restrain to the BICM philosophy. This approach offers increased flexibility and robustness in fading scenarios. The BICM capacity of the overall transmission chain composed of mapping, differential encoding, and ACR-based

6 Will-be-set-by-IN-TECH

**3.3. Low-complexity soft-output detection via combining multiple observations** The blockwise processing of the receive symbol stream enables a further possibility to improve the performance without increase of the maximum delay of the ACR [17]. This method utilizes an overlapping block-structure. Since multiple blocks thus contain the same symbol, processing of each block delivers (possibly different) beliefs on the same symbol, i.e., multiple observations are available. Suitably combining the observations obtained from processing of each block, results in a (possibly more reliable) final decision. Depending on the applied blockwise decision scheme (here SO-MSDD and DF-DD are considered), there are different options how to combine multiple soft/hard observations to deliver a final hard and/or soft decision for the respective symbol [17]. The most interesting option is to combine multiple hard decisions, e.g., obtained from DF-DD, of the same symbol to form a single soft decision. This method can be implemented by using the sum of the individual hard-decisions as (quantized and scaled) "soft-output"; it preserves the low complexity of blockwise DF-DD,

yet enables to exploit the additional gain of soft- vs. hard-decision channel decoding.

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

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

Based on an information theoretic performance analysis of IR-UWB in combination with ACR-based detection [16], in this section design rules for coded IR-UWB transmission systems are derived and verified by means of numerical results employing convolutional codes.

In contrast to coded modulation using multi-level codes [22], common IR-UWB systems adopt the conventional serial concatenation of coding and modulation at transmitter, and detection and decoding at receiver side, as shown in Fig. 1, i.e., restrain to the BICM philosophy. This approach offers increased flexibility and robustness in fading scenarios. The BICM capacity of the overall transmission chain composed of mapping, differential encoding, and ACR-based

*<sup>n</sup>* in the equivalent noise variance *σ*<sup>2</sup>

*<sup>η</sup>* ) and

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

the cost of an increased computational complexity (roughly proportional to *L*).

caused by the squared original noise variance *σ*<sup>2</sup>

**4. Design rules for coded IR-UWB systems**

**4.1. Capacity of IR-UWB with MSDD**

**transmission**

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

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

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

is quantized to *R*<sup>c</sup> = 2/3. Note that due to the increased decoder complexity of high-rate convolutional codes, for MSDD/DF-DD *R*<sup>c</sup> = 3/4 is selected for all *L*, although higher rates are suggested by Fig. 3. ACR-based detection using soft-output MSDD (left) and DF-DD (right) with multiple observations combining is applied. It can clearly be observed that the performance is significantly improved with an optimized choice of the code rate, although the optimum code rates are larger than the default setting of *R*<sup>c</sup> = 0.5 for all *L*—of course the relations are exactly opposite for coherent detection. As expected from the shape of the curves in Fig. 3, this effect is emphasized for larger blocksizes, yielding gains of almost 1 dB

Coding, Modulation, and Detection for Power-Effi cient Low-Complexity Receivers

in Impulse-Radio Ultra-Wideband Transmission Systems

131

Similar results are obtained for different coding schemes, such as LDPC codes with belief-propagation decoding [16], and also for coded IR-UWB pulse-position modulation in

In this chapter we have presented a comprehensive review of coding, modulation, and detection for IR-UWB binary phase-shift keying. We conclude that noncoherent autocorrelation-based receivers in combination with blockwise detection constitute a power-efficient low-complexity reference for uncoded, as well as coded transmission. We derived and verified design rules for coded IR-UWB systems, in particular optimum code

*Lehrstuhl für Informationsübertragung, Friedrich-Alexander-Universität Erlangen-Nürnberg,*

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[3] Guo, N. & Qiu, R. C. [2006]. Improved Autocorrelation Demodulation Receivers Based on Multiple-Symbol Detection for UWB Communications, *IEEE Trans. Wireless Commun.*

[4] *IEEE Std 802.15.4a-2007, IEEE Standard for PART 15.4: Wireless MAC and PHY Specifications*

[5] Leib, H. & Pasupathy, S. [1988]. The Phase of a Vector Perturbed by Gaussian Noise and

[6] Lottici, V. & Tian, Z. [2008]. Multiple Symbol Differential Detection for UWB

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*Institut für Nachrichtentechnik, Universität Ulm, Germany*

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for *L* = 10 compared to *R*<sup>c</sup> = 0.5.

combination with energy detection.

**5. Summary and conclusions**

**Author details** Andreas Schenk

Robert F.H. Fischer

**6. References**

5(8): 2026–2031.

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*Germany*

**Figure 3.** Capacity of BICM BPSK IR-UWB for soft/hard-output DD (solid gray/dashed gray), soft-output MSDD with *L* = 2, 5, and 10 (solid black), and DF-DD with *L* = 2 and 5 (dashed black). Gaussian approximation with time-bandwidth product *N* = 400.

In addition, a more detailled analysis shows that in non-fading scenarios an interleaver is not required for BICM IR-UWB [16].

### **4.2. Performance of advanced detection schemes for coded IR-UWB transmission**

Finally, the design rules derived above are verified by means of numerical simulations. Fig. 4 depicts the BER of coded IR-UWB transmission using convolutional codes with optimized code rate compared to the default rate choice of *R*<sup>c</sup> = 0.5. We apply the same channel model as in Sec. 3.4), and nonrecursively nonsystematically encoded maximum-free-distance convolutional codes with constraint length *ν* = 4. For soft-output DD, the optimum rate

**Figure 4.** BER of convolutionally-coded BICM BPSK IR-UWB with autocorrelation-based detection with *L* = 1, 2, 5, and 10 (right to left). Solid: optimum code rate (*R*<sup>c</sup> = 2/3 for DD with *L* = 1 and *R*<sup>c</sup> = 3/4 for *L* = 2, 5 and 10), dashed: *R*<sup>c</sup> = 1/2, gray: DD uncoded, left: soft-output MSDD, right: DF-DD, both using multiple-observations combining with maximum overlap. Gaussian approximation with time-bandwidth product *N* = 400.

is quantized to *R*<sup>c</sup> = 2/3. Note that due to the increased decoder complexity of high-rate convolutional codes, for MSDD/DF-DD *R*<sup>c</sup> = 3/4 is selected for all *L*, although higher rates are suggested by Fig. 3. ACR-based detection using soft-output MSDD (left) and DF-DD (right) with multiple observations combining is applied. It can clearly be observed that the performance is significantly improved with an optimized choice of the code rate, although the optimum code rates are larger than the default setting of *R*<sup>c</sup> = 0.5 for all *L*—of course the relations are exactly opposite for coherent detection. As expected from the shape of the curves in Fig. 3, this effect is emphasized for larger blocksizes, yielding gains of almost 1 dB for *L* = 10 compared to *R*<sup>c</sup> = 0.5.

Similar results are obtained for different coding schemes, such as LDPC codes with belief-propagation decoding [16], and also for coded IR-UWB pulse-position modulation in combination with energy detection.
