WIRELESS COMMUNICATIONS PRELIMINARIES

Transcription

1 WIRELESS COMMUNICATIONS Preliminaries Radio Environment Modulation Performance PRELIMINARIES db s and dbm s Frequency/Time Relationship Bandwidth, Symbol Rate, and Bit Rate 1

2 DECIBELS Relative signal strengths are measured on a log scale to facilitate the comparison of large differences Relative power (e.g., loss or gain) gain or loss in db = 10 log (P 2 /P 1 ) Power relative to P 0 P (dbw) = 10 log (P/1 Watt) P (dbm) = 10 log (P/1 mwatt) 0 dbw = 30 dbm FREQUENCY-TIME RELATIONSHIP Signal uniquely represented in time or frequency domain Fourier coefficients are frequency components of signal j πnft X ( f ) x( t) e 2 j πft = dt x( t) = X ( f ) e 2 df A -.5T.5T t Time-limited signals have infinite frequency content Band-limited signals have infinite time duration Uncertainty Principle f 2

3 SIGNAL BANDWIDTH For bandlimited signals, bandwidth B defined as range of positive frequencies for which X(f) >0. In practice, all signals are time-limited, not band-limited Need alternate bandwidth definition X(f) Bandlimited X(f) Null-to-Null X(f) 3dB -3dB 0 2B 0 2B 0 2B BANDWIDTH AND TRANMISSION RATE A -1/T 1/T -.5T.5T t Symbol Rate = 1/T Bandwidth = 1/T f Bit Rate = Symbol Rate X Number of Bits/Symbol k = Number of Bits/Symbol = log 2 (M) 3

4 COMMUNICATION SYSTEM Text Images Video Source Encoder Transmitter Channel Receiver Source Decoder Source encoder converts message (or bits) into bits. Transmitter converts bits into a transmitted signal at some carrier frequency modulation Channel introduces distortion, noise, and interference. Receiver detects the signal and converts to bits. Source decoder converts back to original format. RADIO ENVIRONMENT Path Loss Shadow Fading Multipath Flat fading Doppler spread Delay spread Interference 4

5 PATH LOSS MODEL Different, often complicated, models are used for different environments. A simple model for path loss, L, is P r L = = Pt 1 K α d where P r is the local mean received signal power, P t is the transmitted power, and d is TX/RX distance. The path loss exponent α = 2 in free space; 2 α 4 in typical environments. PATH LOSS LIMITATIONS The received signal-to-noise power ratio, SNR, is P r KP t 1 SNR = = P n d α N o B where N o is the one-sided noise spectrum and B is the signal bandwidth. Given the performance requirement SNR SNR o, the path loss imposes limits on the bit rate and the signal coverage. B KP t d α N o SNR o or d KP ( t ) N o BSNR o 1/α 5

6 EXAMPLE OUTDOOR SNR o = 8 db K = -38 db N o = -204 db/hz α = 4 P t = 0 db (1 Watt) Suppose it is desired to provide coverage for cells with 1 km radius B 6.3 khz Alternatively, suppose B = 200 khz, d 420 meters EXAMPLE INDOOR SNR o = 12 db K = -45 db N o = -204 db/hz α = 3.5 B = 100 MHz d = 100 meters P t = N o B SNR o d α K = 200 mw 6

7 SHADOW FADING The received signal is shadowed by obstructions such as hills and buildings. This results in variations in the local mean received signal power, P where G S r ( db) = P ( db) ~ N r + G 2 ( 0, σ ),4 σ 10dB. S S S Implications nonuniform coverage increases the required transmit power MULTIPATH Received Power Delay Spread t j () t = a e θ δ ( t t ) h i i Constructive and destructive interference of arriving rays i i 0.5λ t, in seconds db With Respect to RMS Value x, in wavelength 7

8 FLAT FADING The delay spread is small compared to the symbol period. The received signal envelope, r, follows a Rayleigh or Rician distribution. Received Signal Power (db) P r ( db) = P (db) + G + 20 log r r path loss S shadow fading Rayleigh fading log (distance) Implications increases the required transmit power causes bursts of errors DOPPLER SPREAD A measure of the spectral broadening caused by the channel time variation. v f D λ Example: 900 MHz, 60 mph, f D = 80 Hz 5 GHz, 5 mph, f D = 37 Hz Implications signal amplitude and phase decorrelate after a time period ~ 1/f D 8

9 Received Power DELAY SPREAD TIME DOMAIN INTERPRETATION 2τ Two-ray model τ = rms delay spread Delay Channel Input Channel Output 0 1 T 1 2T 0 T 2T 0 T 2T τ small negligible intersymbol interference T τ large significant intersymbol interference, T which causes an irreducible error floor DELAY SPREAD FREQUENCY DOMAIN INTERPRETATION H(f) B s = signal bandwidth 1/T B s 1 2τ f τ small T flat fading τ large T frequency-selective fading 9

10 BIT RATE LIMITATIONS Irreducible P b ISI causes an irreducible error floor x + x + x + Coherent Detection + BPSK QPSK OQPSK Modulation x MSK x + x rms delay spread τ = symbol period T The rms delay spread imposes a limit on the maximum bit rate. For example, for QPSK Mobile (rural) Mobile (city) Microcells Large Building τ 25 µsec 2.5 µsec 500 nsec 100 nsec Maximum Bit Rate 8 kbps 80 kbps 400 kbps 2 Mbps INTERFERENCE Frequencies are reused often to maximize spectral efficiency. BASE STATION For interference-limited systems, the noise floor is dominated by co-channel D interference. α S S 1 D = I + N I 6 R Implications high reuse efficiency requires interference mitigation R 10

11 PASSBAND DIGITAL MODULATION s( t) = An ( t)cos(2π fct + θn( t)) = n Bits encoded in amplitude, phase, or frequency of s(t). A n and θ n (t) are constant over a bit time T b These values change every T b ASK, PSK, AND FSK Amplitude Shift Keying (ASK) Ac cos(2πf ct) s( t) = t) Ac cos(2πf ct) = 0 Phase Shift Keying (PSK) Ac cos(2πf ct) s( t) = Ac t)cos(2πf ct) = Ac cos(2πf ct + π ) Frequency Shift Keying Ac cos(2πf1t ) s( t) = Ac cos(2πf 2t) nt ) = 1 nt ) = 1 b b nt ) = 1 b nt ) = 0 b nt ) = 1 nt ) = 1 b b t) AM Modulation AM Modulation t) FM Modulation 11

12 PERFORMANCE AWGN PERFORMANCE FLAT FADING 12