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Transcript of RS-FH/CDMA
2. Reed Solomon Codes
3. RS\FH-CDMA Scheme
4. Research Work
5. Performance Analysis and Comparison
6. Conclusion TYPES OF CDMA Frequency-Hopping CDMA with
Reed–Solomon Code Sequences
Wireless Communications IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 55, NO. 11, NOVEMBER 2007 CODE DIVISION MULTIPLE ACCESS CDMA is a channel access method used by various radio communication technologies A multiple access method is a definition of how the radio spectrum is divided into channels and how the channels are allocated to the many users of the system. Users are spread across both frequency and time in the same channel.
A unique digital codes, rather than separate RF frequencies or channels are used to differentiate subscribers.
The codes are shared by both MS and the base station, and are called “Pseudo-noise code sequences”. Mao-Fu Lin, Cheng-Yuan Chang, Yu-Shing Liu, and Wing C. Kwong,- Senior IEEE Members Direct Sequence Spread Spectrum -DS-CDMA
Frequency Hopping Spread Spectrum-FH CDMA FH-CDMA A spread spectrum technology that enables many users to share the same channel by employing a unique hopping pattern to distinguish different users’ transmission. The carrier hops randomly from one frequency to another is called FH spread spectrum. A common modulation format for FH system is that of M-ary frequency shift keying (MFSK). The combination is referred to as FH/MFSK. Reed Solomon Codes Properties of RS Codes RS code is specified as RS(n,k) with m-bit Symbol.
n = no. of encoded symbols in a block
k = no. of original message symbols
n-k = 2t; no. of parity symbols been appended.
t = symbol-error correcting capability of the code
Useful for burst-error correction
The amount of power required ?
Properties of Reed-Solomon Codes - Useful for burst-error correction; ie, they are effective for channels with memory.
-Used efficiently on channels where the set of input symbols is large.
- The amount of power required to encode and decode RS code is related to t.
- A large t means a large no, of errors can be corrected but requires more computational power than a small value of t. Galois Field Architecture RS codes are based on finite field GF(p^s)
Generator Polynomial RS code is generated using special polynomial.
All valid codes are exactly divisible by Gen. polynomial a (alpha) are called the primitive elements of the field. C(x) = g(x). i(x) RS Encoder p(x) = i(x). x^n-k mod g(x) x(n-k).d(x)/g(x) = q(x) + r(x)/g(x) Easy to bit implement The whole block can be read into the encoder, & then output other side without alteration. Hard disks,
xDSL Applications RS\FH-CDMA Scheme N-time slots
L- Carrier Frequency Bands
Sk == LxN distinct FH pattern Divide L freq bands into sets of M orthogonal frequencies.
At most M orthogonal symbols
log2(M) bits/sym To increase data rate--> RS codes GF(p) p-1 = RS code sequences length
log 2 (p^d+1) b/sym
d= cross corelation , > 1 Symbol Interference level = d --> trade off
Table shows how every 6 data bits are mapped to 64 RS code sequences. Example:
p = 5, s = 1, d = 2.
The RS code sequences are of length p − 1 = 4
p^d+1 = 125, thus supporting
up to 125 symbols with log2 (125) = 6 bit/symbol. Sk = FH pattern of each user (Predefined)
S1 = (1, 0, 3, 1), S2 = (2, 4, 1, 1), S3 = (3, 0, 2, 2), S4 = (4, 4, 0, 2),
Data Bits = 000110, 011110, 100011, and 101100 X1 = (1, 2, 0, 4), X2 = (1, 1, 2, 4), X3 = (2, 2, 3, 0), X4 = (3, 2, 0, 3), Yk = Xk + pSk Sk- determines which freq bands are used.
Xk -Which freq in chosen band is transmitted. Conclusion A new modulation scheme for FH-CDMA by utilizing the
large cardinality of the RS code sequences was proposed. The performance of RS/FH-CDMA in a Rayleigh fading channel was analyzed.
Results shows that MFSK/ and RS/FHCDMA
provided a tradeoff between the performance and the
If the data rate is more important, one should use
RS/FH-CDMA; otherwise, MFSK/FH-CDMA provided a better performance but a lower data rate. Thank You Reed-Solomon codes are non-binary cyclic codes with symbols made up of m-bit sequences. Systematic Linear Block Codes RS codes achieve the largest possible code minimum distance for any linear code with the same encoder input and output block lengths. Generator Polynomial RS code is generated using special polynomial.
All valid codes are exactly divisible by Gen. polynomial C(x) = g(x). i(x) FH-CDMA System: MFSK/FH-CDMA: Performance Comparison BEP vs K simultaneous Users in Rayleigh Fading Channel
-RS/FH-CDMA supports the highest data rate (i.e., log2 p^3 = 12 bit/symbol)
-prime/FH-CDMA supports log2(p^2) = 8 bits/symbol.
-MFSK/FH-CDMA only supports log2 M = 4 bit/symbol Performance Comparison under same data rate condition performance gets worse as the no. of time slots reduces to 5 in MFSK-CDMA and 11 in prime/FH-CDMA but is still better then RS\FH-CDMA
In summary, the RS/FH-CDMA supports a higher data rate than the MFSK/FH-CDMA at the expense of worsening the NSE-Normalized Spectral efficiency