OR
S MSK (t ) A cosct an 2T t b
• Assume that the initial phase is xn. the general form of MSK expression also can be presented as:
Classification
Analog
AM FM PM
Continuous
ASK FSK digital Modulation PSK Other efficient: MSK,QAM,OFDM PAM Analog Pulse PCM PDM PPM
digital
DM
Other: ADPCM, LPC
Phase changing in MSK
• Because MSK is a special type of continuous phase-frequency shift keying. • So when t nTb
n 1 (nTb ) n (nTb )
n xn xn 1 (an 1 an ) 2
Binary Frequency Shift Keying (BFSK)
• The frequency of a constant amplitude carrier signal is switched between two values according to the two possible message states (“0” or “1”). • The expression in time domain:
S MSK (t ) A cosct an 2T t xn b
In the expression,
n (t ) an 2T t xn b
Is called excess phase or Instantaneous phase.
Modulation techniques in Cellular System
Signaling AMPS 1G TACS GSM IS-95 Systems 2G DAMPS PDC CDMA2000 3G TS-SCDMA WCDMA Pi/4-DQPSK Pi/4-DQPSK data ss QPSK, 16PSK, 16QAM data ss U:BPSK, D:QPSK QPSK/OQPSK U:BPSK, D:QPSK QPSK/OQPSK Voice 2FSK FM
Eb p n0
Performance of a modulation scheme
• Bandwidth efficiency
– Describes the ability of a modulation scheme to accommodate data within a limited bandwidth. – Is defined as the ratio of the throughput data rate per Hertz in a given bandwidth.
ak
ak 1 时，减小 2
信息发射速率为1000Baud，载波频率为2000Hz，试画出MSK已 调调制信号波形及相位轨迹图。
s1 (t ) A cos 2f1t S FSK (t ) s2 (t ) A cos 2f 2t 传“1”时(an 1) 传“0”时(an 1)
(n 1)Tb t nTb
Tb为码元宽度
• Wave forms
f 2 2 f1
Spectrum and bandwidth of BFSK signals
Constant Envelope Modulation
• The constant envelope family of modulation has the advantage of satisfying a number of conditions, some of which are:
– Power efficient Class C amplifiers can be used – Low out-of-band radiation of the order of -60 dB to -70 dB can be achieved
B max
C S log 2 1 B N
Note that C is the capacity in bps, B is the RF bandwidth in Hz, and S/N is the signal-to-noise ratio (not in dB) Example: p280 6-6 and 6-7
an an 1 xn 1 xn an an 1 xn 1 k
。
n (t ) an
t xn 2Tb
Assume x0=0, then xn=0 or ±п
t 在任一个码元期间内，
的变化量总是 2 1 时，增大 2
Signaling
Voice GMSK
2FSK
FM Down lnk Up lnk QPSK OQPSK
Factors that influence the choice of digital modulation • Low bit error rates at low received signal-to-noise ratios • Occupies a minimum of bandwidth • Easy and cost-effective to implement Existing modulation schemes do not simultaneous satisfy all of these requirements. Tradeoffs must be made.
Pulse Shaping Techniques
• Band limited • ISI free or minimum
Nyquist Pulses for zero-ISI
Raised Cosine Spectrum
RF signal using Raised Cosine
Gaussian pulse-shapes
The upper bound on bandwidth efficiency
• Shannon’s channel coding theorem states that for an arbitrary small probability of error, the maximum possible bandwidth efficiency is limited by the noise in the channel, and is given by the channel capacity formula.
• The transmission bandwidth BT of an FSK signal is:
BT 2f 2B 2(f R)
• If a raised cosine pulse-shaping filter is used, the bandwidth reduces to:
– VLSI & DSP have made digital modulation more cost effective than analog transmission systems.
– More advantages in digital modulation • Greater noise immunity • Robustness to channel impairments • Easier multiplexing of various forms of information • Greater security • Digital modulation offers error controlling • Can use equalization techniques to improve the performance of the overall communication link • New techniques made it possible to implement digital modulator and demodulator completely in software
R B B
(bps / Hz )
The system capacity of a digital mobile communication system is directly related to the bandwidth efficiency of the modulation scheme. Since a modulation with a greater value of ηB will transmit more data in a given spectrum allocation.
Two FSK signals vH(t) and vL(t) are said to be orthogonal if T
v
0
H
(t )vL (t )dt 0
The expressions of MSK signal in time domain
1 s1 (t ) A cos 2 ( f c 4T )t b S FSK (t ) s (t ) A cos 2 ( f 1 )t 2 c 4Tb 传“1”时(an 1) 传“0”时(an 1)
Performance of a modulation scheme
• Power efficiency