CSE 5345 – Fundamentals of Wireless Networks

Today Spread Spectrum Coding and Error Control

Spread Spectrum - Transmitter Input is fed into a channel encoder Produces analog signal with narrow bandwidth Signal is further modulated using sequence of digits Spreading code or spreading sequence Pseudonoise, or pseudo-random number Resulting in increased bandwidth of signal

Spread Spectrum - Receiver On receiving end, digit sequence is used to demodulate the spread spectrum signal Signal is fed into a channel decoder to recover data

Spread Spectrum

Spread Spectrum - Why Resistance to noise and multipath distortion Data hiding and encryption Concurrent transmission for several users

Frequency Hoping Spread Spectrum (FHSS) Transmission over seemingly random frequencies A number of channels allocated for the FH signal Width of each channel = bandwidth of input signal Signal hops from frequency to frequency At fixed intervals Transmitter operates in one channel at a time Bits are transmitted using some encoding scheme At each successive interval, a new carrier frequency is selected

Frequency Hoping Spread Spectrum Channel sequence dictated by spreading code Receiver hops in synchronization with transmitter Advantages Eavesdroppers hear only unintelligible blips Attempts to jam signal on one frequency succeed only at knocking out a few bits

Frequency Hoping Spread Spectrum

FHSS Performance Considerations Large number of frequencies used Resistant to interference and jamming Jammer must jam all frequencies With fixed power, this reduces the jamming power in any one frequency band

Direct Sequence Spread Spectrum (DSSS) Each bit in original signal is represented by multiple bits in the transmitted signal Spreading code spreads signal across a wider frequency band Spread is in direct proportion to number of bits used One technique combines digital information stream with the spreading code bit stream using exclusive-OR (Figure 7.6)

Direct Sequence Spread Spectrum (DSSS)

DSSS Using BPSK Multiply BPSK signal, sd(t) = A d(t) cos(2 fct) by c(t) [takes values +1, -1] to get s(t) = A d(t)c(t) cos(2 fct) A = amplitude of signal fc = carrier frequency d(t) = discrete function [+1, -1] At receiver, incoming signal multiplied by c(t) Since, c(t) x c(t) = 1, incoming signal is recovered

DSSS Using BPSK

Code-Division Multiple Access (CDMA) Basic Principles of CDMA D = rate of data signal Break each bit into k chips Chips are a user-specific fixed pattern Chip data rate of new channel = kD

CDMA Example If k=6 and code is a sequence of 1s and -1s For a ‘1’ bit, A sends code as chip pattern <c1, c2, c3, c4, c5, c6> For a ‘0’ bit, A sends complement of code <-c1, -c2, -c3, -c4, -c5, -c6> Receiver knows sender’s code and performs electronic decode function <d1, d2, d3, d4, d5, d6> = received chip pattern <c1, c2, c3, c4, c5, c6> = sender’s code

6: Wireless and Mobile Networks CDMA Encode/Decode channel output Zi,m d1 = -1 1 - Zi,m= di.cm Data bits d0 = 1 1 - 1 - 1 - sender slot 1 channel output slot 0 channel output code slot 1 slot 0 Di = S Zi,m.cm m=1 M Received input 1 - 1 - d0 = 1 d1 = -1 slot 1 channel output slot 0 channel output code receiver slot 1 slot 0 6: Wireless and Mobile Networks

[1 -1 1 1] [1 1 -1 1] User 1: 1 -1 1 1 User 2: -1 -1 1 -1 Channel: 0 -2 2 0 Receiver 1: [1 -1 1 1]*Channel=4=>1 Receiver2: [1 1 -1 1]*Channel=-4=>-1 A*[A1*b+A2*c+A3*d]

Coding and Error Control

Coping with Data Transmission Errors Error detection codes Detects the presence of an error Automatic repeat request (ARQ) protocols Block of data with error is discarded Transmitter retransmits that block of data Error correction codes, or forward correction codes (FEC) Designed to detect and correct errors

Error Detection Process Transmitter For a given frame, an error-detecting code (check bits) is calculated from data bits Check bits are appended to data bits Receiver Separates incoming frame into data bits and check bits Calculates check bits from received data bits Compares calculated check bits against received check bits Detected error occurs if mismatch

Error Detection Process

Parity Check Parity bit appended to a block of data Even parity Added bit ensures an even number of 1s Odd parity Added bit ensures an odd number of 1s Example, 7-bit character [1110001] Even parity [11100010] Odd parity [11100011]

Cyclic Redundancy Check (CRC) Transmitter For a k-bit block, transmitter generates an (n-k)-bit frame check sequence (FCS) Resulting frame of n bits is exactly divisible by predetermined number Receiver Divides incoming frame by predetermined number If no remainder, assumes no error Skip

CRC using Modulo 2 Arithmetic Exclusive-OR (XOR) operation Parameters: T = n-bit frame to be transmitted D = k-bit block of data; the first k bits of T F = (n – k)-bit FCS; the last (n – k) bits of T P = pattern of n–k+1 bits; this is the predetermined divisor Q = Quotient R = Remainder

CRC using Modulo 2 Arithmetic For T/P to have no remainder, start with Divide 2n-kD by P gives quotient and remainder Use remainder as FCS

CRC using Modulo 2 Arithmetic Does R cause T/P have no remainder? Substituting, No remainder, so T is exactly divisible by P

CRC using Polynomials All values expressed as polynomials Dummy variable X with binary coefficients

CRC using Polynomials Widely used versions of P(X) CRC–12 CRC–16 X12 + X11 + X3 + X2 + X + 1 CRC–16 X16 + X15 + X2 + 1 CRC – CCITT X16 + X12 + X5 + 1 CRC – 32 X32 + X26 + X23 + X22 + X16 + X12 + X11 + X10 + X8 + X7 + X5 + X4 + X2 + X + 1

CRC using Digital Logic Dividing circuit consisting of: XOR gates Up to n – k XOR gates Presence of a gate corresponds to the presence of a term in the divisor polynomial P(X) A shift register String of 1-bit storage devices Register contains n – k bits, equal to the length of the FCS

Digital Logic CRC

Wireless Transmission Errors Error detection requires retransmission Detection inadequate for wireless networks Error rate on wireless link can be high => a large number of retransmissions Long propagation delay Long transmission time (slow data rate) Wireless Channel is error prone Error Correction instead of only error detection  Coding

Block Error Correction Codes Transmitter Forward error correction (FEC) encoder maps each k-bit block into an n-bit block codeword Codeword is transmitted; analog for wireless transmission Receiver Incoming signal is demodulated Block passed through an FEC decoder

Forward Error Correction Process

FEC Decoder Outcomes No errors present Codeword produced by decoder matches original codeword Decoder detects and corrects bit errors Decoder detects but cannot correct bit errors; reports uncorrectable error Decoder detects no bit errors, though errors are present

Block Code Principles Hamming distance: for 2 n-bit binary sequences, the number of different bits E.g., v1=011011; v2=110001; d(v1, v2)=3 Redundancy – ratio of redundant bits to data bits Code rate – ratio of data bits to total bits (k/n)

Block Code Principles Coding gain the reduction in the required Eb/N0 to achieve a specified BER of an error-correcting coded system

Hamming Code Designed to correct single bit errors Family of (n, k) block error-correcting codes with parameters: Block length: n = 2m – 1 Number of data bits: k = 2m – m – 1 Number of check bits: n – k = m Minimum distance: dmin = 3 Single-error-correcting (SEC) code SEC double-error-detecting (SEC-DED) code Inserted at 2i position

Hamming Code Process Encoding: k data bits + (n -k) check bits Decoding: compares received (n -k) bits with calculated (n -k) bits using XOR Resulting (n -k) bits called syndrome word Syndrome range is between 0 and 2(n-k)-1 Each bit of syndrome indicates a match (0) or conflict (1) in that bit position

Hamming Code Process - Example Data: 00111001

Hamming Code Process - Example Bit 6 error