Degradation of BER by Group Delay in Digital Phase Modulation

Transcription

1 The Fourth Advanced International Conference on Telecommunications Degradation of BER by Group Delay in Digital Phase Modulation A.Azizzadeh 1, L.Mohammadi 1 1 Iran Telecommunication Research Center (ITRC) azad@itrc.ac.ir, mohamady@itrc.ac.ir Abstract One of the most important destructive factors in digital phase modulation is group delay variations (GDV) over frequency. This factor causes a larger bit error rate (BER) from expected BER at specific Eb/N0 values. Thus, the effect of group delay degradation must be compensated. GDV is difficult to analyze exactly for modulation purposes in practical systems, but it is relatively simple to simulate. In this paper, we focus on the effect of group delay on digital phase modulation and simulate the effects of, Linear, and Parabolic group delays on BER to identify a suitable criterion by which the acceptable variations of group delay can be determined before the demodulator. 1. Introduction Data sheets for demodulators provide expected BER at specific Eb/N0 values. This information is valid only for a laboratory environment where the modulator is connected bac to bac with the demodulator at IF, i.e. alterations of the signal shape that are caused by numerous factors such as group delay, amplitude distortion, and Doppler shift must be compensated. Among these factors, conceptually group delay is one of the simplest, although it is probably a more difficult factor to be analyzed. Since transmission data in the phase modulation resides in the phase, therefore group delay modifies signal constellation and causes BER degradation. This investigation focuses on the effects associated with group delay, in order to find a criterion by which the acceptable variations of the group delay before the demodulator can be determined. Thus the generated group delay in the pervious component will be measured and equalized to the defined value. In this paper, at first we discuss group delay followed by discussion of its different types and effects on digital phase modulation. Finally the simulated results of the effects of, Linear, and Parabolic group delays on BER are given. These include identification of a suitable criterion for calculating the acceptable variations of the group delay before the demodulator. 2. Group delay and its effects Group delay response is the difference in transit time versus frequency for signals going through a communications channel. Ideally, group delay is constant (straight line with no til so that that all frequencies of the transmitted carrier experience the same time lag through the system. If not, the recovered symbols interfere with one another causing difficulties in distinguish different symbols and thus errors occur. Consider a digitally modulated waveform with its spectrum placed within a filter that just fits it. There will be frequency components at the band edges and where the frequency components of the modulation envelope will be delayed relative to the mid-band components, resulting in group delay distortion. In the time domain, the impact can be viewed as dispersion on an oscilloscope. The time domain waveform spreads itself out for each symbol. For a digital communication system, the detection mechanism will include a matched filter, followed by sampling of the filter output at the optimum point. The effect of dispersion is to create inter symbol interference (ISI). Adjacent symbols run into one another and energy may exist at the sample instant of one symbol that's actually energy associated with an adjacent symbol, which contributes to symbol errors [1]. The frequency spectrum of a digital carrier is shown in Fig. 1(3rd from top). For convenience the symbol rate bandwidth, also the 3 db bandwidth is identified. Above the transmitted carrier are plotted several types of group delay that are used for simulation. At the top of the figure linear and parabolic delays are indicated. Parabolic group delay is usually associated with bandpass filters found in communication devices. The sinusoidal delays are often caused by impedance mismatches in the system [2] /08 $ IEEE DOI /AICT

2 transmitted information [5]. Now suppose that s ( is required to be transmitted over the AWGN channel. The received symbol is modified by both noise and group delay relative to the transmitted symbol. We consider ( α, β ) as the displacement of transmitted symbol caused by the group delay. As such the received symbol vector r can be written as: [ n2 r = r r ] = [ s + α + n s + β ] (4) Figure 1. Several types of group delay and transmitted spectrum 3. Effect of group delay on digital phase modulation where n1 and n 2 are the noise components. It can now be concluded that the received vector r is the transmitted vector s, which has been modified by noise and group delay during the transmission in the channel. Fig. 2 illustrates the displacement of the transmitted vector through the noise and GDV. Since GDV is considered to cause signal distortion, it can be concluded that the pulse shape for each bit is distorted. Suppose a pulse shape g( with duration T S, is allowed to pass through the system with the impulse response H ( f ) = exp( jφ( f )) having constant amplitude and non-linear phase. The output pulse g ˆ( is then as follows: gˆ ( = g( h( = + G( f ) e e j 2πf t jφ( f ) df (1) where G ( f ) and H ( f ) are the Fourier transforms of g ( and h (, respectively. In general, the distorted pulse g ˆ( consists of the original pulse and several scattered pulses each having different amplitudes, phases and delays with respect to the original pulse. It may be a complex signal, and may have a value outside the interval [0, T s ]. Consequently it can be concluded that GDV cause the inter symbol interference (ISI) leading to distortion in the pulse [3], [4]. In MPSK, the M base-band signal waveforms can be written as: jθ 2π s ( = g ( e, θ = ( i 1), i = 1,2,..., M (2) M having vector representation as follows: s = [ E g cosθ E g sinθ ] (3) where E g is the energy of the pulse shape and θ indicates the M possible phases that convey the Figure 2. Displacement of the transmitted vector through the noise and group delay variations The particular values of α and β depend on type of group delay, value of GDV, type of pulse shape and disposition of transmitted symbols (or bits). By calculating ( α, β ), BER degradation through GDV can be computed. However, owing to the presence of complex integral in (1) for linear and parabolic group delay, ( α, β ) can be computed using numerical methods only. But for ripple group delay, ( α, β ) can be calculated analytically (for details refer to [6]). Therefore BER degradation is obtained from simulation. In the following, the simulated results are introduced. 351

3 4. Simulated results An exact analysis of GDV for modulations in practical systems is rather difficult while it is relatively simple to perform simulation studies. In this paper, we use simulations, for evaluating the amount of the displacement of the transmitted symbol and BER degradation, caused by each type of group delay (Linear, Parabolic and ) for BPSK and QPSK modulation. Fig. 3 indicates a bloc diagram of simulation steps. At the first stage, a zero delay was considered and a reference Eb/N0 was determined for a BER of approximately Additional data was obtained with varying group delay to determine the required added Eb/N0 to achieve the same BER. As such, the group delay value considered was the total variation measured over the symbol bandwidth. We evaluated the BER degradation in terms of a factor that was normalized to the product of symbol rate (SR) and group delay (GD). Figure 4. Displacement of symbols by Linear group delay at GD.SR=0.5 in a) QPSK, b) BPSK Figure 5. Displacement of symbols by Parabolic group delay at GD.SR=0.5 in a) QPSK, b) BPSK Figure 3. The bloc diagram of simulation Fig. 4 through Fig. 7 illustrate the simulation results of the amount of the displacement in BPSK and QPSK for each type of group delay with GD.SR =0.5. Fig. 8 through Fig. 11 indicate graphic representations of the simulated results as well as polynomial equations that are fitted to represent the data. The input data on the X axis is normalized to the symbol rate (SR) multiplied by the group delay (GD). The symbol rate is in symbols/second (sym/s) and the group delay is in seconds (s). The dependent data on the Y axis represent BER degradation and is the added Eb/N0 or required power to overcome the effects of group delay as compared to the reference with no group delay. The polynomial equations used to produce the graphs are shown in the Table (1) where B.D indicates BER degradation and x is GD.SR. Figure 6. Displacement of symbols by group delay (1 cycle) at GD.SR=0.5 in a) QPSK, b) BPSK Figure 7. Displacement of symbols by group delay (2 cycles) at GD.SR=0.5 in a) QPSK, b) BPSK 352

4 Table 1. Polynomial equations fit to simulated data Group Delay Modulation BER Degradation Curve Linear BPSK B.D= x x Linear QPSK B.D= x x Parabolic BPSK B.D= x x Figure 8. BER degradation through Linear group delay versus GD.SR Parabolic QPSK B.D= x x (1 cycle) (1 cycle) (2 cycles) (2 cycles) BPSK B.D= x x QPSK B.D= x x BPSK B.D= x x QPSK B.D= x x Figure 9. BER degradation through Parabolic group delay versus GD.SR Figure 10. BER degradation through group delay (1 cycle) versus GD.SR Table (1) provides the maximum permissible x (i.e. GD.SR) for a given level of B.D. This Table can be used as a design aid to identify the condition under which equalization should be considered. The value GD.SR is dimensionless since the symbol rate has a dimension of 1/time and group delay is measured in second. For example, in general up to B.D=0.5 db of the added BER degradation is acceptable for QPSK. If it is desired to carry a 50 Msym/s QPSK signal with under 0.5 db of added degradation, it can be determined using Table (1). The Table indicates GD.SR =1.15 for QPSK parabolic and GD.SR =0.43 for linear QPSK. Given SR, the maximum GD is calculated as follows: 1.15/ (50 Msym/s) =23 ns Parabolic 0.43/ (50 Msym/s) =8.6 ns Linear Therefore if the group delay of the entire channel including uplin, transponder and receiver exceeds either of these values, an equalizer should be used. Thus the overall parabolic group delay must be under 23 ns and the overall linear group delay must be under 8.6 ns. 5. Conclusion Figure 11. BER degradation through group delay (2 cycles) versus GD.SR In this paper the effect of GDV on BER was derived by carrying out simulation. The results obtained from above simulation show that degradation caused by ripple group delay is dependent on the quantity of ripples. Fewer ripples cause more degradation. Also 353

5 linear group delay causes greater degradation than parabolic group delay. Furthermore, with increasing modulation index M, BER degradation is increased. Ultimately, BER degradation was calculated through GDV as a function of GD.SR. By using these results for BPSK and QPSK with the defined symbol rate and acceptable BER degradation, a suitable GDV variations before demodulator can be determined. These results can be used as a design aid to determine if equalization should be used. 5. References [1] R. Howald," A delay in the (fourier) proceedings ", Jul 27, 2006, [2] S. Bac, M. Weigel,"Degradation of digital satellite signals by group delay", Globecomm System Inc & EFDATA Corporation, Appeared In world Broadcast News, November [3] X. Liu, L. Mollenauer, X. Wei," Impact of group-delay ripple in transmission systems including phasemodulated formats ", IEEE Photonics Technology Letters, VOL. 16, NO. 1, January 2004,pp [4] C. Scheerer, C. Glingener, G. Fischer, M. Bohn, and W. Rosenranz, "System impact of ripples in grating group delay" in Proceedings of IEEE Conference on Transparent Optical Networs (Institute of Electrical and Electronics Engineers, Kielec, 1999), pp [5] John G. Prois, Digital communication. McGraw-Hill Science Engineering, 2000 [6] A. Azizzadeh, L. Mohammadi, "Effect of group-delay ripple on BER in digital phase modulation ", unpublished. 354