Microwave Seminar. Noise and Bit Error Ratio. J. Richie. Spring 2013

Transcription

1 Microwave Seminar Noise and Bit Error Ratio J. Richie Spring 2013

2 Outline Noise Noise and Equivalent Temperature Noise Figure Small Scale Fade and Multipath Impulse Response Model Types of Fading Modulation Performance in Fading and MP Channels Conclusions

3 Noise Sources of Noise Thermal noise, thermal vibration of bound charges Shot noise, random fluctuations of charge carriers Flicker or 1/f noise (larger at lower frequencies) V n = 4hfBR e hf/kt 1 rms value, from Q/M h: Planck s constant k: Boltzmann s constant T: temp. in K B: bandwidth in Hz f: center frequency R: resistance T(K) R v(t)

4 Noise Noise and Equivalent Temperature Outline Noise Noise and Equivalent Temperature Noise Figure Small Scale Fade and Multipath Impulse Response Model Types of Fading Modulation Performance in Fading and MP Channels Conclusions

5 Noise Noise and Equivalent Temperature Microwave Noise Power At microwave frequencies (Rayleigh-Jeans approximation): V n = 4kTBR which is independent of frequency (white noise) If we model R at T K as R at 0 K with a source voltage of value V n and we match the circuit with another resistor, P n = ktb If B 0, narrower bandwidth means less noise If T 0, cooler devices mean less noise If B, Rayleigh-Jeans approximation breaks down.

6 Noise Noise and Equivalent Temperature Equivalent Noise Temperature An arbitrary white noise source can be modeled with an equivalent noise temperature (this implies a fixed bandwidth). Consider an amplifier: T = 0K s Noisy Amp, BW=B N o =GkT B e only due to amplifier T e= N o/(gkb) Noisless Amp, BW=B N o =GkT B e R Gain is G R R Gain is G R

7 Noise Noise Figure Outline Noise Noise and Equivalent Temperature Noise Figure Small Scale Fade and Multipath Impulse Response Model Types of Fading Modulation Performance in Fading and MP Channels Conclusions

8 Noise Noise Figure Noise Figure NF: a measure of the degredation in the SNR between the input and output of the component: Ni = kt o B No = kgb(t o + T e ) Therefore, Notes: F = SNR i SNR o 1 F = 1 + T e T o or T e = (F 1)T o NF (or F) defined for a matched source initial input noise source is at To = 290 K FdB = 10 log 10 F since SNR is power ratio.

9 Noise Noise Figure example see seminarex1.pdf

10 Small Scale Fade and Multipath Wireless Environment In addition to the typical noise of closed systems, the wireless channel has additional considerations: channel varies over time due to changes in surroundings channel varies over time due to relative motion of XMT/RCVR The channel rings transmit one pulse. At the receiver, one will receive multiple copies of the pulse at different times, amplitudes, and phases.

11 Small Scale Fade and Multipath Impulse Response Model Outline Noise Noise and Equivalent Temperature Noise Figure Small Scale Fade and Multipath Impulse Response Model Types of Fading Modulation Performance in Fading and MP Channels Conclusions

12 Small Scale Fade and Multipath Impulse Response Model Impulse Response Model Mobile radio channel is modeled as a linear filter with a time-varying impulse response: h b (t, τ) t represents time variation of h due to motion τ represents channel multipath delay for a fixed t. hb is the complex, baseband impulse response (we track the complex envelope of the signal). N 1 h b (t,τ) = a i (t,τ)e j[2πfcτi(t)+φ(t,τ)] δ(τ τ i [t]) i o=0 often, 2πfc τ i (t) + φ(t,τ) = θ i (t,τ) If channel is assumed time invariant or wide sense stationary (WSS), then N 1 h b (τ) = a i e jθ i δ(τ τ i ) i=0

13 Small Scale Fade and Multipath Impulse Response Model example see seminarex2.pdf

14 Small Scale Fade and Multipath Types of Fading Outline Noise Noise and Equivalent Temperature Noise Figure Small Scale Fade and Multipath Impulse Response Model Types of Fading Modulation Performance in Fading and MP Channels Conclusions

15 Small Scale Fade and Multipath Types of Fading Time Dispersion Parameters From the impulse response model, we can determine the mean excess delay ( τ) and the rms delay spread (σ τ ): a 2 k τ k k τ = σ τ = τ 2 ( τ) 2 k a 2 k where τ 2 = a 2 k τ k 2/( a 2 k ) k k Coherence bandwidth is a measure of the range of frequencies where channel is flat: B c 1/(50σ τ ) note how this gives an estimate of the channel bandwidth

16 Small Scale Fade and Multipath Types of Fading Frequency Dispersion Parameters Frequency dispersion is due to relative motion, i.e., Doppler effects Doppler Spread: B D = 2f m where f m is the maximum Doppler shift, f m = v/λ If signal bandwidth is much greater than B D, then the effects of frequency dispersion are negligable. Coherence Time: time over which the channel characteristics remain relatively constant: T c f m (formally, the time duration over which 2 signals have strong potential for amplitude correlation) If symbol period is smaller than T c, then frequency dispersion is negligable.

17 Small Scale Fade and Multipath Types of Fading Types of Fading Frequency Dispersion If frequency dispersion is not negligable, then have Fast Fade If frequency dispersion is negligable, then have Slow Fade (more typical except with very low data rates) Time Dispersion If bandwidth of signal is smaller than bandwidth of channel, then have Flat Fade If bandwidth of signal is larger than bandwidth of channel, then have Frequency Selective Fade

18 Small Scale Fade and Multipath Types of Fading Bit Error Ratio (BER) Bit errors: number of received bits of a data stream that have been altered due to noise, interference, etc. Bit error ratio (it is a ratio, not a rate): # of bit errors Total bits transferred BER is dimensionless, and somtimes expressed as a percentage Example Transmitted bits: Received bits: bit errors is 3, total bits is 10 BER=0.3 or 30%

19 Modulation Performance in Fading and MP Channels Digital Modulation Techniques Phase Shift Keying PSK DPSK QPSK, π/4-qpsk Frequency Shift Keying FSK MSK GMSK

20 Modulation Performance in Fading and MP Channels Flat vs. Frequency Selective Fading Flat Fading hb (τ) has only one term the amplitude varies by Rayleigh or Rice distribution. Performance can be studied analytically. Frequency Selective Fading hb (τ) has multiple terms ISI is possible Performance must be simulated to analyze Remainder of talk is a series of graphs illustrating the performance of some digital modulation methods when subjected to the wireless channel and additive white Gaussian noise (AWGN).

21 Modulation Performance in Fading and MP Channels Performance see seminarex3.pdf

22 Conclusions Conclusions Noise and equivalent temperature, noise figure wireless communication and small-scale fade BER Modulation performance in wireless channel