2. MC

* By measuring the SNR in each subchannel, one can optimize the allocation of Pk and n k for each subcarrier by using the water - pouring rule.
2 SNR k TPk Ck / nk 2
•A s/p buffer segments the information sequence into frames of Nf bits. The Nf bits in each frame are parsed ~ into N groups, where the ith group is assigned ~ ni bits, and n N , each group may be ch-encoded separately so the output from the encoder for the ith group ~ is ni ni . Because there are ni information bits in ith group, they are mapped into modulation space with Mi 2n signal points to be denoted by information ~ symbol {Xk}, k 0,1,N 1 .We employ the inverse ~ DFT(IDFT) to modulate the N subcarriers by the information symbol {X k} .
N k k
and X '0 =Re(X 0 ), X N Im( X 0 ). Thus the symbol X 0 is split into two parts, both real. Then the N-point IDFT yields the real -valued sequence 1 xn N X k e j 2 nk / N ,
CP的插入
G b ACP
b
G G+L CP G+2L
( f W ) ( f W )
It is interesting to point out that in order to get maximum capacity, the signal power should be high when the channel SNR, | C( f ) |2 / nn ( f ), is high (Shannon, 1949). ---------------Water Pouring
Capacity of a Non-ideal Linear Filter channel
*For ideal band-limited AWGN channel
fP ( f i ) | C ( f ) |2 Ci f log 2 1 f nn ( fi ) N N P ( f i ) | C ( f ) |2 C Ci f log 2 1 nn ( fi ) i 1 i 1 P ( f i ) | C ( f ) |2 f 0 log 2 1 df nn ( fi ) W
f k k / N and the demodulated sequence (DFT out) are
* The Ck (or cn ) can be estimated by using either a known modulated sequence on each of the subcarriers or unmodulated subcarriers in order to help the detection and decoding.
~ N i 1 i f
i
However, if we compute the N - point IDFT of Xk , we shall obtain a complex - valued time series, which is not equivalent to N QAM - modulated subcarriers. Instead, we create N=2N information symbols by defining X X *, k=1,........,N-1
Rule
Water-Pouring Rule ( Shannon, 1949)
nn ( f ) / C ( f )
K
2
P(f)
W f
An FFT-Based Multicarrier System

There are mainly two methods to implement multicarrier system: 1.Digital filter bank 2.FFT,when N>32 The block diagram of a multicarrier system based on FFT . Due to the cyclic prefix, successive blocks (OFDM frames) of the transmitted information sequence do not interfere each other (time guard band).
* Because of the sidelobes (the first sidelobe is only 13db down from the the peak at the desired sub - carrier for DFT implementation), ICI problem are vulnerable unless a full CP is used and other types of digital filter banks that have the perfect reconstruction property associated with wave let based filters appear to be an attractive alternative.
k 0 N 1
n=0,1,....,N-1
where 1/ N is simply a scale factor. xn corresponds to the samples of the sum x(t ) of N subcarrier signals, at , its frequency response at the subcarrier freq. 2 k Ck C cn e j 2 nk / N , N n 0 X k Ck X k k , k 0,1,..., N 1
x x
N ,
xN 1, ..x0 ,.., xN 1 to each block of N signal samples
0, 1,
x ..., xN 1
where is the channel dispersion spans (samples). The CP samples are appended to the beginning of each block. * The received sequence rn is obtained by convolution of cn , 0 n , with xn , - n N-1, and the first samples of rn are discarded. Then the transmitted sequence is recovered by using N-point DFT for demodulation. * In the frequency domain, when the channel impulse response is
N k 0 Where T is the symbol duration, and the subcarrier f k /T, k=0,1,.....,N.
k
x(t )
1
X k e j 2 kt / T ,
N 1
0tT
The signal synthesis for multicarrier modulation based on IDFT is shown in the figure. * In practice, the signal samples xn are passed through a digital-to-analog (D/A) converter whose output, ideally , would be the signal waveform x (t ). The received signal r (t ) x(t ) c(t ) n(t ) * The channel time dispersion could cause ISI. To avoid the effect of ISI, the best way is to append a CP(cyclic prefix)
*For the i-th sub-channel capacity PSD
Pav C W log2 (1 ) WN 0
maximizing the capacity,the power distribution in frequency
K nn ( f ) / | C ( f ) |2 p( f ) 0
Multi-carrier system
(OFDM, MC-CDMA, MC-DSCDMA, OFDM-CDMA, VSFOFCDM)
Multi-Carrier System