**3. Analog receiver implementations**

### **3.1. Feasibility of analog differential detection**

ISI will degrade the BER performance of DPSK systems, if the symbol interval is considerably smaller than the channel excess delay. However, it is crucial to realize delays on the order of 50 ns or more in the analog domain, if the ultra-wideband nature of the signals is taken into account. Fig. 7 shows the normalized group delay of a Bessel-Thomson all-pass filter with a maximum flat group delay *t*g(*f*). If a 5 % group delay error is chosen to define the cut-off frequency, it is clear that a 5th order filter can provide a usable frequency range of ≈ 1/*t*g(0), i.e., for a desired cut-off frequency of *f*<sup>g</sup> = *B*6/2 = 250 MHz, the delay is only 4 ns. Even a huge and completely unrealistic filter order of 20 could only provide a delay of 5.6 · 4 = 22 ns, if *f*<sup>g</sup> = 250 MHz. It should be noted that two of these analog delay lines have to be implemented, if a quadrature down-conversion stage as shown in Fig. 4 is used.

A basic motivation of impulse radio based on transmitted reference (TR) signaling is that shorter delays can be used. This is possible, since the autocorrelation does not take place with the previous modulated symbol but rather with an additional reference pulse. Our results show that the performance of TR-signaling varies extremely from channel realization

<sup>2</sup> At a total transmission bandwidth *B*, multipath components can be resolved down to 1/*B* in the time domain.

8 Will-be-set-by-IN-TECH 116 Ultra-Wideband Radio Technologies for Communications, Localization and Sensor Applications Non-Coherent UWB Communications <sup>9</sup>

to channel realization, since the autocorrelation process is disturbed by intra-symbol interference. Additionally, if a reference pulse is periodically inserted prior to each modulated pulse, a 3 dB loss occurs. Delay hopping techniques or reference symbol averaging may reduce this 3 dB loss, but require even more (and longer) delay lines.

ADC TH

*f*<sup>s</sup> = 1/*T*int

analog


existing code correlation function based analysis.

**4. Digital receiver implementations**

on soft-limiting [13].

*N*s.

 *T*int · d*τ*

**Figure 8.** Block diagram of a TH code division multiple access receiver with analog multipath

combining. Differential detection is not considered since analog wide band delays are difficult to realize.

is based on the statistics of the total code collisions (or "hits", determined by *N*<sup>s</sup> and *N*h) as well as the first- and second-order moments of the multipath channel's energy within the integration window. For non-coherent TH-PPM systems, the proposed method provides a more accurate and comprehensive evaluation of the multiple access performance than the

In [12], we have investigated various MA codes to be applied for a non-coherent TH-PPM system. It can be concluded that for a moderate number of users, optical orthogonal codes (truncated Costas codes, prime codes) with low code weights ensure a good multiple access performance while adding only a very small additional non-coherent combining loss.

Digital receiver implementations according to Fig. 9 have several advantages. First of all, they offer a superior interference rejection capability [11, 16], since user specific filtering can take place prior to the non-coherent signal processing. This restricts the non-coherent combining loss to the multipath arrivals (which exhibit stochastic path weights), whereas that part of the signal energy, which is already spread by a user-specific code at the transmitter, is coherently summed up. Furthermore, digital receiver implementations enable advanced modulations such as Walsh-modulation [15, 17] or advanced NBI-suppression strategies based

The block diagram of a receiver with a "digital code matched filter" (DCMF) is shown in Fig. 9. The ADC operates with a sampling rate, which is not smaller than the UWB signal bandwidth, where the ADC resolution has been chosen between 1 and 4 bits. Regarding the

Fig. 10 shows the *E*b/*N*<sup>0</sup> improvement of a DCMF-based receiver as a function of *N*s, where *N*s depicts the number of non-zero elements of the user-specific code. As the DCMF combines the corresponding pulses coherently, the benefit compared to an analog receiver increases with

In [14] we have shown that in the 2-PPM case and under certain conditions, low-resolution ADCs can almost achieve the full resolution *E*b/*N*0-performance. One important condition is the number of pulse repetitions *N*s within one modulated symbol, which should not be too small. For the one bit ADC case, *N*<sup>s</sup> = 8 and *N*<sup>s</sup> = 20 just correspond to quantization penalties of 2 dB and 1.5 dB, respectively, cf. Fig. 11(a). If the resolution is increased from 1 bit to 2 or 4 bits, the penalty may decrease, but only if the input level of the ADC is well controlled by an additional gain-control circuit. In [14] we have also proven that a 1 bit ADC with its inherent

following results, we have always assumed TH impulse radio transmission.

**4.1. Applicability of low-resolution ADCs (single user case)**

clipping characteristic offers a superior interference rejection capability.

Decoder

Non-Coherent UWB Communications 117

It is more than unlikely that analog implementations of differential receivers will have a chance to be applied in low cost products. For the multi-user case with analog multipath combining (next section), we have therefore focused on energy detection combined with time-hopping (TH) impulse radio.

**Figure 7.** Normalized group delay of a Bessel-Thomson all-pass filter of order *N*.

### **3.2. Multiple access for analog multipath combining**

As mentioned above, the transmitted pulse *ψ*1(*t*) may be also a chirp or direct-sequence spread spectrum waveform. To realize the filter *g*T(*t*) in the analog domain, SAW-filters (SAW: surface acoustic wave) could be a solution, but only if *ψ*1(*t*) is a fixed, user independent waveform. Therefore, as long as the non-coherent signal processing (or a part of it) takes place in the analog domain, we assume a user independent *ψ*1(*t*).

To still enable multiple access (MA) communications, we assume that each symbol to be transmitted is represented by several short pulses which are generated at distinct times according to a user specific TH-code. The decoding will be carried out digitally, i.e., after the non-coherent signal processing took place, cf. Fig. 8.

Compared to direct sequence MA codes which contain a large number of (non-zero) chips, the sparseness of TH codes facilitates the receiver processing, reduces the complexity and keeps the additional loss due to the non-coherent combining of the code elements within limits. A TH code is determined by two parameters: the number of pulse repetitions *N*s, which is equivalent to the code weight, and the number of hopping positions<sup>3</sup> *N*h. In [12], we have presented a semi-analytical method to assess the multiple access performance. It

<sup>3</sup> One symbol interval can be divided into an integer number *N*<sup>s</sup> of equally spaced intervals (named frames), where each frame contains one pulse. Within each frame, *N*<sup>h</sup> positions are possible.

**Figure 8.** Block diagram of a TH code division multiple access receiver with analog multipath combining. Differential detection is not considered since analog wide band delays are difficult to realize.

is based on the statistics of the total code collisions (or "hits", determined by *N*<sup>s</sup> and *N*h) as well as the first- and second-order moments of the multipath channel's energy within the integration window. For non-coherent TH-PPM systems, the proposed method provides a more accurate and comprehensive evaluation of the multiple access performance than the existing code correlation function based analysis.

In [12], we have investigated various MA codes to be applied for a non-coherent TH-PPM system. It can be concluded that for a moderate number of users, optical orthogonal codes (truncated Costas codes, prime codes) with low code weights ensure a good multiple access performance while adding only a very small additional non-coherent combining loss.
