Application Note AN143 Nov 6, 23 Performance Analysis of Different Ultra Wideband Modulation Schemes in the Presence of Multipath Maurice Schiff, Chief Scientist, Elanix, Inc. Yasaman Bahreini, Consultant Abstract Over the recent years, different modulation schemes have been proposed and considered for Ultra Wide-Band (UWB) communication systems. Unlike narrowband technologies, this technology benefits from the inherent wideband characteristics and, if designed properly, can gain from multipath processing. Just recently, the IEEE 82.15.3a Channel Modeling Subcommittee has finalized a UWB channel model description for indoor Personal Area Network (PAN) ranges in three categories -- line of site, non-line-of-site, and harsh multipath conditions. This paper will provide simulation analysis and results on the performance of different proposed UWB modulation schemes based on this indoor channel model. The modulation schemes under study will include On-Off Keying (OOK), Binary Phase Shift Keying (BPSK), and Pulse Position Modulation (PPM) schemes. Each modulation scheme has its advantages and disadvantages when compared in the categories of bandwidth efficiency, sensitivity to jitter and synchronization offset, and receiver cost and complexity. The main performance evaluation metric will be Bit Error Rate (BER) versus Signal-to-Noise Ratio (SNR) in the presence of multipath. The simulation results will help define the bounds on the achievable maximum data rate, the synchronization offset tolerance, and the complexity of multipath-combining at the receiver for all modulation schemes under consideration. The simulation tool used is SystemView by Elanix. technology was primarily used for military radar applications [2, 3]. The late 199 s have witnessed a wave of new UWB implementation designs targeting a multitude of commercial high performance communication and position/location applications. In February 22, the Federal Communications Commission s (FCC) First Report and Order for UWB was issued, authorizing and defining UWB spectrum masks for different applications [4]. According to the definition put forth by the FCC, UWB is now defined as any signal that occupies more than 5 MHz of bandwidth in the authorized frequency band, or a signal with 2% fractional bandwidth, both defined at the 1 db point. In the United States, operation of UWB communication applications is regulated in the 3.1 GHz to 1.6 GHz frequency band. UWB spectrum regulation in other parts of the world is still pending. II. Introduction UWB has fostered growing interest in standard bodies. Currently UWB is being considered as an alternate Physical Layer to high rate IEEE 82.15.3 Personal Area Network (PAN) standard. Just recently the channel model subcommittee of IEEE 82.15.3a has finalized and published UWB channel models, backed up by measurement data, that characterize UWB propagation in three categories; line-of-site, non-line of site, and harsh multipath in the PAN ranges [5]. Different UWB modulation schemes have been proposed and analyzed in the literature. This paper considers three most commonly proposed modulation schemes and analyzes the effect of mentioned channel conditions. In section III, the system model assumptions I. Background The origin of Ultra Wideband (UWB) technology goes back to the early days of wireless engineering [1]. Originally, UWB or commonly called impulse radio are described. Section IV presents simulation analysis was defined as a communication method where short and results. Section V concludes the paper by impulses carry information bits. In this technology, unlike summarizing achievable bounds and limits on data rate, carrier based modulation techniques, short pulses that synchronization offset tolerance, and the complexity of possess a wide frequency-content are modulated using multipath-combining at the receiver for all modulation position, phase, or amplitude modulation techniques. The schemes under consideration. wider the spectrum content, the shorter the impulse in time III. System Model needs to be. Starting in the 196 s, because of the This section describes system model parameters and reduced probability of jamming characteristics, UWB assumptions. Three modulation techniques -- Binary AN143 Nov 6, 23 Page 1 of 9
Phase Shift Keying (BPSK), On-Off Keying (OOK), and Pulse Position Modulation (2-PPM) will be considered. Pulse shaping, and channel models are defined in subsections III.a, III.b. Subsection III.c provides the details on modulation and detection of the considered schemes. III.a) Pulse Shaping In all cases presented here, the transmitted signal is derived via a unit impulse function exciting a band pass filter. The band pass filter that assures FCC compliant transmission is selected to be a 3 rd order Elliptic filter with high-pass 3 db cut-off frequency of 3.5 GHz, and lowpass 3 db cut-off frequency of 4.5 GHz. This translates to 1.2 GHz 1 db bandwidth. Figure 1 shows the impulse response of the filter, and Figure 2 gives the frequency response. SystemView Pulse Shape in Time 1.e-9 2.e-9 3.e-9 4.e-9 5.e-9 1 5.e-3 Amplitude -5.e-3-1 1.e-9 2.e-9 3.e-9 4.e-9 5.e-9 Time in Seconds Figure 1. Pulse Shape in Time SystemView Power Spectrum of p(t) in 5 ohms 3e+9-3 3.4e+9 3.8e+9 4.2e+9 4.6e+9 5e+9 5.4e+9 5.8e+9-4 -5 Power dbm -6-7 -8-9 -1 3e+9 3.4e+9 3.8e+9 4.2e+9 4.6e+9 5e+9 5.4e+9 5.8e+9 Frequency in Hz Figure 2. Power Spectrum of Pulse Shape AN143 Nov 6, 23 Page 2 of 9
III.b) Channel Mode Three channels models (Table 1) based on the IEEE 82.15.3a recommendation are considered. Channel model 1 represents line-of-site (LOS) -4m scenarios, channel model 2 represents non-line-of-site (NLOS) -4m scenarios, and channel model 3 represents NLOS 4-1m scenarios. Main parameters of these channel models are provided below [5]. All models are modified Saleh- Valenzuela models [6]. The general assumptions for these models are: (a) lognormal distribution for the multipath gain magnitude, (b) independent fading for each cluster, and (c) independent fading for each ray within the cluster. The overall group delay of the channel can vary from one statistical representation to the next. This forces the need for a receiver to track this variation in order to obtain the timing and/or phase information for demodulation. Such a tracking mechanism is beyond the scope of this simulation. We therefore fixed the arrival rates of the clusters and rays to their mean value. This fixes the group delay. The amplitude statistics were not changed. Figure 3 shows the impulse of the CM1 under this constraint. The rays are then spaced by.4 ns, and the clusters are spaced by 42.9 ns. There are two clusters of significance in this case. For presentation only we rectified the negative pulses. Figure 4 represents autocorrelation of CM1. The impulse coefficients were normalized so that the sum-squared is unity. It is assumed that the fade dynamics is slow enough to enable the receiver to make periodic measurements via some form of training sequence as is done in the GSM system. The receiver then implements a matched filter to this measured model. In practice, digital approximation of the mentioned channel model filter introduces truncation errors. We assumed ideal approximation and no truncation errors. Channel Characteristics CM 1 CM 2 CM 3 Mean Excess Delay (ns) ( τ m ) 5.5 1.38 14.18 RMS Delay (ns) ( τ rms ) 5.28 8.3 14.28 Model Parameters Cluster Arrival Rate Λ (1/ns).233.4.67 Cluster Arrival Period (ns) 42.9 2.5 149.3 Ray Arrival Rate λ (1/ns) 2.5.5 2.1 Ray Arrival Period (ns).4 2.48 Cluster Decay Factor Γ 7.1 5.5 14. Ray Decay Factor γ 4.3 6.7 7.9 Table 1. Channel Model Parameters AN143 Nov 6, 23 Page 3 of 9
SystemView Channel Response 2e-9 4e-9 6e-9 8e-9 C M 1 C hannel Im pulse R esponse F irs t C lu s te r 1.e-1 Second Cluster Amplitude 1.e-2 1.e-3 1.e-4 2e-9 4e-9 6e-9 8e-9 Time in Seconds Figure 3. Channel Model 1 Impulse Response SystemView CM1 Correlation 68e-9 78e-9 88e-9 98e-9 1e+9 8e+9 C M 1 A utocorrelation F unction 6e+9 Amplitude 4e+9 2e+9-2e+9-4e+9 68e-9 78e-9 88e-9 98e-9 Time in Seconds Figure 4. Channel Model 1 Autocorrelation Function AN143 Nov 6, 23 Page 4 of 9
III.c) Modulation & Coding In all cases, a forward error correction rate r = 1/2, constraint length L = 7 convolutional code is used. The decoder is a hard-decision Viterbi decoder with a 15-bit path memory. The information bit rate is 5 Mbps, and the channel rate is 1 Mbps. It is important to note the level of system s inherent Inter-Symbol Interference (ISI) by comparing the cluster arrival period, as shown in Table 1, to the average symbol period of 1 ns over the air. Binary Phase Shift Keying (BPSK) The simulation model is shown in Figure 5. In BPSK, the phase of a reference template carries the information data. In other words, is modulated to a pulse shape p(t), where p(t) is the impulse response of pulse shape shown in Figure 1. A 1 is mapped to -p(t). In order to bypass carrier phase estimation, differential encoded modulation/demodulation was implemented. The detector has two steps of filtering. First is a band pass filter identical to the one in the transmitter. This approximates a matched filter for the transmit pulse. The second is the channel matched filter as previously explained. The DPSK demodulator is a simple complex delay and multiply operation. Figure 5. Differential BPSK (DPSK) System Simulation Diagram On-Off Keying (OOK) The simulation model is shown in Figure 6. In OOK, presence or absence of energy at the pulse reoccurrence period carries information data. In other words, presence of pulse shape p(t) denotes a 1, and absence of pulse energy denotes a. As before, the detector is a two step matched filter receiver with a template that takes into account the distortions introduced by transmit and receive pulse shaping filters as well as each propagation channel. The demodulation of OOK is performed using noncoherent envelope detection. In this model, a threshold must be set to differentiate a 1 from a. We set this threshold by using a long time average of the received signal power. AN143 Nov 6, 23 Page 5 of 9
Figure 6. OOK System Simulation Diagram Pulse Position Modulation (2-PPM) The simulation model is shown in Figure 7. In PPM, the position of a reference pulse shape in time carries the information bits. In other words, a is mapped to a reference pulse shape at zero time offset from a reoccurrence period, and 1 is mapped to a reference pulse shape p(t) with a time offset from the reoccurrence period. A is represented by p(t) delayed by a time offset representing a 1 is half of the reoccurrence period. As before, the detector is a two-step matched filter receiver is considered. The PPM detector is implemented by delaying the received signal by ½ of a bit period and then subtracting it from the original signal. The output decision is based on a test statistic that maps +1 for a data bit, and a 1 to a 1 data bit. Continued on the next page. AN143 Nov 6, 23 Page 6 of 9
Figure 7. PPM System Simulation Diagram IV. Simulation Analysis & Results We made no attempt to fully optimize the performance of any of the proposed models. By way of calibration, the channel effect was removed to first test the validity of simulation models in Additive White Gaussian Noise (AWGN) channels. It is well known theoretically that in AWGN conditions, DPSK performs 3dB poorer than coherently detected BPSK, and non-coherently detected OOK and PPM perform 6dB worse than coherently detected BPSK. Our simulation performance for non-coherent detection of OOK and 2-PPM followed the theoretical results. However, the performance of DPSK in AWGN was about.5 db worse than the theoretical value. The reason is that the receive band-pass filter is not the ideal matched filter for the transmit band-pass filter. This simulation exercise is a two dimensional problem, (1) the AWGN, and (2) the fading channel. In all cases, a specific per bit signal to noise ratio (Eb/N) was chosen, and the simulation was run for 1 trials of the channel in order to get the average BER. The amount of computing required to accomplish the overall task for three channel models and several receivers is enormous. Our results are preliminary in nature, and serve to present a first cut at the system performance. The following plots present bit error rate (BER) performance of the considered modulation schemes in channel models 1-3. Eb/N in these plots is the standard definition as measured against AWGN. It can be observed that only in CM1 (Figure 8), and CM3 (Figure 1) that are similar to narrow band flat fading scenarios, DPSK performs around 3dB better than PPM and OOK. By taking a closer look at these two channel conditions, it is observed that in CM1 (LOS less than 4 m) and CM3 (NLOS 4-1 m) the cluster arrival rate is much less than the ray arrival rate. The ray amplitude decay factor is about half of the cluster amplitude decay factor. In CM2 (Figure 9), the cluster arrival rate and the ray arrival rate are in the same order of magnitude, and the same is true for the ray and cluster amplitude factors. This observation explains the poor performance of DPSK in CM2, where phase stability over even two consecutive signaling intervals is not maintained, and the poor performance of PPM, where the packed density of the rays introduces time jitter. AN143 Nov 6, 23 Page 7 of 9
Channel Model 1 Ave. BER 1.E+ 1.E-1 1.E-2 1.E-3 1.E-4 1.E-5 1.E-6 9 1 11 12 13 Eb/N [db] OOK PPM DPSK Figure 8. BER Performance for Channel Model 1 Channel Model 2 1.E+ Ave. BER 1.E-1 OOK PPM DPSK 1.E-2 13 14 15 16 17 Eb/N [db] Figure 9. BER Performance for Channel Model 2 Channel Model 3 1.E+ Ave. BER 1.E-1 OOK PPM DPSK 1.E-2 6 7 8 9 1 Eb/No [db] Figure 1. BER Performance for Channel Model 3 AN143 Nov 6, 23 Page 8 of 9
V. Conclusions In this paper, we have shown preliminary results on the effect of multipath for a 1MHz UWB system employing OOK, BPSK, and 2-PPM. These results put limits on achievable data rates and complexity of ISIproof receiver. Future simulations will consider performance of the multi-band approach [7]. In this approach the spectrum is divided into sub-bands and the symbols are time multiplexed across different bands of operation. Inherently due to the lower symbol rate per band, this approach introduces less ISI. A comparison of the two approaches will be drawn upon completion of the simulation runs. For more information on SystemView simulation software please contact: ELANIX, Inc. 5655 Lindero Canyon Road, Suite 721 Westlake Village CA 91362. Tel: (818) 597-1414 Fax: (818) 597-1427 Or visit our web home page ( www.elanix.com ) to down load an evaluation version of the software that can run this simulation as well as other user-entered designs. Acknowledgement The authors wish to thank Pulse Link, Inc. for the use of their computers for the long BER runs. References [1] IEEE P82.15.3 Tutorial: Understanding UWB- Principles and Implications for Low-Power Communications, R. Aiello, J. Ellis, U. Kareev, K. Siwiak, L. Taylor, March 23. [2] C. Leonard Bennett and Gerald F. Ross, Time- Domain Electromagnetic and Its Applications, Proceedings of the IEEE, Vol. 66, No.3, March 1978. [3] Henning F. Harmuth, Introduction to Large Relative Bandwidth Radio Transmission, Antennas and Waveguides for Non-sinusoidal Waves, Academic Press: 1984. [4] US 47 CFR Part15 Ultra-Wideband Operations FCC Report and Order, April 22, 22. [5] IEEE 82.15.3a Channel Model Sub-committee Final Report, February 23. [6] A. Saleh and R. Valenzuela, A Statistical Model for Indoor Multipath Propagation, IEEE JSAC, Vol. SAC-5, No.2, February 1987. [7] www.uwbmultiband.org AN143 Nov 6, 23 Page 9 of 9