Direct-Sequence Spread-Spectrum
|
|
- Donald Bradford
- 6 years ago
- Views:
Transcription
1 Chapter 3 Direct-Sequence Spread-Spectrum In this chapter we consider direct-sequence spread-spectrum systems. Unlike frequency-hopping, a direct-sequence signal occupies the entire bandwidth continuously. he signal is obtained by starting with a narrowband signal and directly modulating a high bandwidth signal. As with frequency hopping direct-sequence has advantages when the channel contains a jamming like signal. he jamming could be intentional and hostile, self jamming (multipath), and multiuser jamming. In the remained of this chapter we examine the capabilities of direct-sequence is these three environments.. Introduction Below we show the transmitter and receiver for a direct-sequence system. he data sequence b t consists of a sequence of data bits of duration. he data sequence is multiplied with a binary spreading sequence a t which has N components called chips per data bit. b t s t a t Pcos ω c t Figure 3.: Block Diagram of Direct-Sequence Spread-Spectrum ransmitter b t b l p t l l b l a t a l p c t l c a l l c N Usually a i is a periodic sequence with period. In some cases for each period of the sequence a i one data bit is transmitted, i.e. c. When the sequence a i is periodic the spreading signal is a periodic waveform so 3-
2 3- CHAPR 3. DIRC-SQUNC SPRAD-SPCRUM that a t a t l for any integer l. In other cases c, that is, many data bits are transmitted before the sequence repeats. In this case it is useful to model a i as a sequence of independent, identically distributed binary random variables equally likely to be. In any case it is nearly always true that c N is an integer. his is usually called the processing gain. It is the factor by which the signal is spread. s t Pa t b t cos π f c t he transmitted signal has power P. Below we show a data signal and the result of multiplying by a spreading signal with 3 chips per bit. he sequence was generated by a linear feedback shift register such that â i mod â i 3 â i 5 where â denotes a, sequence. he actual sequence a is found via the usual transformation of,. he initial loading of the shift register is [ ]. he receiver consist of a mixer followed by a filter Data waveform b(t) time/ User waveform s(t) time/ Figure 3.: Waveforms b t and a t b t matched to the spreading code of the transmitter. Consider the case where N, that is there is exactly one period r t Filter t i Z i b i b i cos ω c t Figure 3.3: Direct-Sequence Spread-Spectrum Receiver of the spreading sequence per data bit. (It is easy to see how to modify the results for N. For N for each data bit we either transmit a t or a t depending on the sign of the data bit with appropriate delays. he matched filter has impulse response given by h t a t t he filter output is given by Z t cos π f cτ r τ h t τ dτ
3 . 3-3 t t cos π f cτ r τ a t τ dτ hus the filter does a running correlation of the received signal (mixed down to baseband) with the spreading sequence. hat is, at each time instance the filter output is the correlation of the received signal over the past seconds with the spreading signal a t. From the below figure we can visualize the output of the filter at time t as the integral of the product of the received signal with a shifted version of the spreading code. In this sense the matched filter provides a running correlation of the received signal over the past seconds with the spreading signal. Consider the filter output during the time interval t due to the transmitted signal alone, r t Pa t b t cos π f c t hen Z t P t a τ b τ a τ t P b a τ a τ t P b ˆR t P b R t t dτ t dτ t Pb a τ a τ t dτ where ˆR t t a τ a τ t t dτ a u a u t du a u a u t du t and R t t t a τ a τ a τ a τ t dτ t dτ he last step in each of the above two equations follows because of the periodicity of the spreading signal (one period of the spreading signal per data bit). We can write these correlation functions in terms of the spreading sequences as follows. For t k c s with s c. R t c s a N ka a N k a a N a k s a N k a a N ka a N a k k k c s a l k N a l s a l k N a l l l c s C k N sc k N
4 3-4 CHAPR 3. DIRC-SQUNC SPRAD-SPCRUM where C k N k l a l a l k k N N k l a l ka l N k Similarly, for k c t k c otherwise ˆR t c s a a k a a k a N ka N s a a k a a k a N ka N c s C k sc k Notice that both R t and ˆR t vary linearly with t for t k c k c for every k. r τ b b a k a k a N a N a a a k a τ t kc a k a k a N a N k c a τ t a a a N k a N k a N k a N a N t τ Figure 3.4: Received Signal Consider the spreading sequence a he aperiodic correlation function is k C k It is useful to state a few properties of the aperiodic autocorrelation function.. he partial or aperiodic autocorrelation functions are symmetric. C k C k. he full autocorrelation is the sum of two aperiodic or partial autocorrelation functions. θ k N C a l a l k k C k N k N l C k C k N N k he function θ k is called the autocorrelation function of the sequence a.
5 If we consider the spreading sequences to be a sequence of independent, identically distributed random variables then the following expectation with respect to the spreading sequences can be computed. Assume k and n. hen C k C n N k l N n a l a l k m k n N k k n N k n a m a m n For the sequence above the autocorrelation function has the following values. k θ k 7 he output of the filter with impulse response matched to the spreading sequence is shown below for a sequence of length 3. If two consecutive bits have the same sign (b b ) then the output of the filter during the interval [,] is given by Z t P b c s θ k sθ k On the other hand if b b then the output during the interval is given by Z t P b c s ˆθ k sˆθ k where the function ˆθ k is called the odd autocorrelation and is defined as ˆθ k N k a l a l k l N a l a l k C k C k N k N l N k he odd autocorrelation function differs from the standard autocorrelation function in that part of the terms in the summation have a negative sign. At the sampling time (t i ) the filter output due to the desired signal alone is given by Z i i i a τ a τ i dτ his result leads to the correlator implementation of the optimal (for AWGN) receiver. It is useful (for synchronization) to know the outputs of the matched filter at other times besides the time that we make a decision. he filter output is sampled at multiples of. he output at the sampling times is (s k ) Z i P c N b i Pb i b i. Direct-Sequence Spread-Spectrum with one Interference Consider a direct-sequence system with a jammer whose signal is an unmodulated tone at the same phase and frequency of the direct-sequence user. j t J cos ω c t he jamming signal has power J. he ratio J P is called the jammer-to-signal power ratio. he received signal is r t s t j t he receiver is similar to that for BPSK.
6 3-6 CHAPR 3. DIRC-SQUNC SPRAD-SPCRUM 4 Data waveform 3 Z(t) time/ Figure 3.5: Output of Matched Filter for a Sequence of ength 3 Demodulator r t PF t i b i b i Z i cos ω c t a t b t s t r t a t Pcos ω c t j t Figure 3.6: Block Diagram of Direct-Sequence Spread-Spectrum ransmitter
7 . 3-7 Figure 3.7: Distribution of Interference for n 7 Figure 3.8: Distribution of Interference for n 3 he decision statistic for bit b i is Z it i Z i i r t b i η i a t cos ω ct dt where η i is the output due to the jamming signal. he output due to the jamming signal can be written as (ignoring double frequency terms) η i i J a t dt i Since a t in a i p c t j c t i i j i N η i J c J N in j i N in a i j i N a i Random Sequence Model If we model the sequence a i as i.i.d. binary random variables then in j i N a i is a binomial distributed random variable with mean and variance N. hus η i is zero mean with variance J N. he signal-to-noise ratio, SNRout, at the output of the demodulator is then SNRout P J N Since the signal-to-noise ratio, SNR in, at the input to the receiver is the system is said to have a processing gain of N. SNR in P J rror Probability with one Interference he probability of error for the tone jammer (with perfect phase information) is P e P e P e P P J N N a i a i J c Figure 3.9: Distribution of Interference for n 7
8 3-8 CHAPR 3. DIRC-SQUNC SPRAD-SPCRUM Figure 3.: Distribution of Gaussian Interference Figure 3.: Comparison of Distributions where the sum extends over N values of the index i. For large N, a i N is approximately Gaussian with mean zero and variance (central limit theorem). he error probability can then be approximated by P e Q J c Q P J N Note that the jamming power is effectively reduced by a factor of N. Another way of expressing the error probability is in terms of an effective jamming noise power density. Since BPSK with spreading by a factor N has noise bandwidth of c the effective jamming noise spectral density N J is defined as N J Using this in the expression for error probability yields P e Q J c J c Notice that this is a factor of (3dB) worse than Gaussian noise of the same spectral density. he reason is that we have assumed the jammer has perfect phase information so that no power is wasted in the quadrature component of the signal. If the jammer had a random phase the performance would be better by 3dB and equivalent to the performance in Gaussian noise of the same power. N J 3. Direct-Sequence Spread-Spectrum with Multipath Interference Consider a direct-sequence system over a channel with multipath fading the received signal is modeled as r t α j s t τ j n t j where τ j is the delay of the j-th path, α j is the amplitude and n t is white Gaussian noise. Below we analyze the performance of two different receivers. he first receiver ignores the multipath interference and uses a filter matched to a single path to make a decision. he second receiver uses a bank of filters matched to the various paths and combines the filter outputs to make a decision. he can be implemented by a single filter and a tapped delay line. Because the structure of the receiver looks like a garden rake it is called the rake receiver. he rake receiver usually requires amplitude and phase estimation of the various paths and is thus more complex than a signly branch receiver. Assuming that the receiver is matched to the first path and τ the output of the matched filter is Z i Z i i i b i r t j a t cos ω ct dt I j η i
9 where I j α j i α j i i i s t τ j a t cos π f c t dt α j P cos π f c τ j i Pcos π f c t τ i b t τ j a t τ j a t cos π f c t dt i b t τ j a t τ j a t dt and η i is a Gaussian random variable with mean zero and variance N. Now assume that τ i. hen where and hus Z i b i i a t τ j a t dt i b i τ i a t τ j a t dt j α j P cos π f c τ j b i R τ j b i ˆR τ j I j α j P cos π f c τ j i τ j b i α R τ ˆR τ τ a t τ a t dt a t τ a t dt τ α j b i j ˆR τ j b i R τ j cos π f c τ j hus the channel experiences some intersymbol interference. If we model the intersymbol interference as Gaussian noise, the variance of the interference (with random delays and phases) can be determined. Now consider the case where the delays are uniformly distributed over the interval c c. In most cases the phase variable cos π f c τ j will be independent of τ j. his is true because f c τ j. hus when τ j varies only slightly, f c τ j will vary considerably. When computing averages then we can think of only slightly varying τ j without changing R τ j but causing π f c τ j to vary over many multiples of π. hus for each very small range of τ j, π f c τ j will vary over many multiples of π. hus when computing the expectation we can separate out the cos φ j cos π f c τ j randomness from the R τ j, ˆR τ j randomness. In fact, we will treat φ j and τ j as independent random variables. he output due to the desired signal then is given by Z b he conditional variance Var Z b of the the interference is determined as follows. et hen I j α α j ˆR τ j b i R τ j cos π f c τ j η i Var Z b j I j N I j α j N c τ j c ˆR τ j R τ j dτ j
10 3- CHAPR 3. DIRC-SQUNC SPRAD-SPCRUM he averaging above is with respect to the delays of the multipath signal. Substituting in for the definition of the partial correlation functions we obtain I j α N j c ˆR τ j τ j R τ j dτ j c α N j α j 3 N N k N k k c τ j k c ˆR τ j R τ j dτ j c s c s C k sc k c s C k N sc k N ds α j N 3 N c k s c s C k C k N c s s C k C k C k N C k N s C k C k N ds α j c 3 N 6 3 N C k C k N C k C k k C k N C k N C k C k N If we define the parameter r as r N k C C k C k N C k C k C k N C k N k C k N then the mean square interference is Var Z b r 3 c 6 3 N r 6N 3 N j j α j α j N N he signal-to-noise ratio is defined as the squared mean output divided by the variance and is given as SNR Z b Var Z b α r i α i 6N 3 N N For example the spreading sequence of length 7 has parameter r 8. he length 3 m-sequence has r 68 and the spreading sequence of length 7 has r 6. Consider the case of negligble background noise. he signal-to-noise ratios for these different spreading sequences are SNR α 6N3 N r i α i
11 3. 3- N SNR db α 7 5 log i α i α log i α i α log i α i In the homework it is shown that the signal-to-noise ratio averaged over all possible spreading sequences increases linearly in N. Notice that the signal-to-noise ratio decreases as the number of paths increase. his is because the receiver is treating all the paths except one as interference. he direct-sequence receiver reduces the effect of these interferring paths by a factor of N because of the processing gain. A receiver which makes uses of these extra paths is discussed next.. Performance with a Rake Receiver Now consider the case of a receiver that uses a filter matched to each delay. he usual method to combine the different filter outputs is by weighting each component by the strength of the path it is matched to. Below we show a block diagram of such a recevier. he received signal is first mixed to baseband by a pair of mixers with 9 degrees phase offset for the locally generated reference. We represent this by a complex mixing. he double lines correspond to complex signals. he baseband signal is then filtered with a filter matched to the baseband transmitted signal. he output of the baseband filter enters a tapped delay line. Different delays are weighted by different amounts. he magnitude of the weighting corresponds to the magnitude of a particular path while the phase compensates for any phase change so that the desired multipath component after the gain has zero phase or in other words a purely real part. Of course there will be some interference from other paths that contribute to the imaginary part but this will be ignored by the receiver. r t h t DAY IN exp jπ f c t β β Real[ ] DC Figure 3.: Rake Receiver
12 3- CHAPR 3. DIRC-SQUNC SPRAD-SPCRUM Figure 3.3: Matched Filter Output Figure 3.4: Rake Receiver Output Below we show the output of a matched filter for a baseband signal with three paths with delays, 3 and 8 with relative amplitudes,.7 and.3. he signal is spread by a factor of 3. he output of the rake which delays the signal by 8 and weights by, delays by 5 weights by.7 and adds these to an undelayed version weighted by.3. he receiver computes the following decision statistic for bit b where τ Z j j r t τ j In the absence of background thermal noise α Z j α j b l l l j he decision statistic Z due to the desired users is Z j α j Z j a t τ j cos ω c t τ j dt τ j τ j b t τ l a t τ l a t τ j dt cos ω c τ l τ j Z b o compute the variance of the interference we postulate the following model of the delays. he delays are random variables distributed over disjoint intervals of length c. Furthermore, the minimum separation between delays is also c. hat is min τ j τ l c. his is done so that the paths that the receiver is able to lock onto are in fact distinguishable. For example consider the case where τ j is uniform over the interval 4 l c 4 l c c and assume that 4 c c c. Furthermore assume that the delays are independent. hen the variance of the interference can be calculated as follows. First let I j l be the effect of the l-th multipath on Z j. hen I j l α l τ j τ j j α j b t τ l a t τ l a t τ j dt cos ω c τ j τ l For τ j τ l For τ l τ j I j l α l b R τ l τ j b ˆR τ l τ j cos ω c τ l τ j I j l α l b R τ l τ j b ˆR τ l τ j cos ω c τ l τ j he variance is where Var Z Var V j j l l j I j l α j V j
13 It is straightforward (but very lengthy) to show for random spreading codes that Var Z hus the signal-to-noise ratio is j α j α l l 3N l j l N N j If we define SNR α j α j j α j l l j α 3N l j l N N j α j l l j α l j l N j α j then SNR j α j α 3N N Notice that if α j is a constant then the signal-to-noise ratio does not decrease as the number of paths in the channel increases. his is in contrast to the single filter receiver in which the performance degrades the more paths there are in the channel. 4. Direct-Sequence Spread-Spectrum Multiple-Access (DS-SSMA) In this section we consider the performance a direct-sequence system with multiple-access interference (also know as code division multiple access (CDMA). ach user is given a code sequence. he receiver for a particular user demodulates the signal by match filtering the received signal with a filter that is matched to the transmitted signal of the desired user. We should point out that this is not the optimal receiver but is one that is currently being used in practical systems. In our analysis we would like to determine the average probability of error. he averaging is respect to the data bits that the other users are transmitting, the relative delays of the other users and the relative phase of the other users. here are numerous different modulation formats that can be used in a direct-sequence system including BPSK, QPSK, MSK. For our purposes we will just consider BPSK. b k t a k t s k t b k l p t l l a k l p c t l c l Pa k t b k t cos π f c t he received signal consist of the delayed versions of all of the users and additive white Gaussian noise. r t K s k t τ k n t k At receiver the received signal is first mixed down to baseband by multiplying the received signal by cos π f c t and then filtered with a filter matched to the spreading sequence of user. quivalently (except with
14 3-4 CHAPR 3. DIRC-SQUNC SPRAD-SPCRUM b t Delay τ b t b K t a t a t Pcos ω c t Delay τ Pcos ω c t Delay τ K + a K t Pcos ω c t Figure 3.5: Block Diagram of a Direct-Sequence System respect to generating timing information) the received signal after the mixer can be correlated with a local replica of the spreading sequence to produce a decision statistic. We will assume that the receiver is perfectly synchronized to the transmitted signal (both timing and phase) so that without loss of generality we can assume that τ. he filter for user is matched to the spreading code of user. he output of the filter for user contains the desired signal, interference from other users and noise. Below we show the matched filter output for a single user, two users and three users with spreading sequences of length 3. he matched filter output at the sampling time is given by Z i i r t a i t cos π f c t dt i i K k i s i t s k t τ k n t a t cos π f c t dt K s k t τ k a t cos π f c t dt η i k where η i is a Gaussian random variable with mean zero and variance N. Z i P i b i i a t b t K k cos φ k K a k t τ k b k t τ k cos φ k a t dt η i k i a i k t τ k b k t τ k a t dt η i
15 r t h t a t Z i t i b i b i cos ω c t Figure 3.6: Direct-Sequence Spread-Spectrum Receiver Figure 3.7: Matched filter output for a single user with N 3 where φ k π f c τ k and I k b i K k cos φ k I k η i i a i k t τ k b k t τ k a t dt he term due to other users can be written in terms of the crosscorrelation of the different users sequences. where the functions R k and ˆR k are given by τ a k t τ k b k t τ k a t dt k a k t τ k b k t τ k a t dt a k t τ k b k t τ k a t dt b k τ k τ k a k t τ k a t dt b k a k t τ k a t dt τ k b k R k τ k b k ˆR k τ k R k τ ˆR k τ τ a k t τ a t dt a k t τ a t dt τ hus I k cos φ k b k R k τ k b k ˆR k τ k he cross correlation functions R k and ˆR k can be written in terms of the aperiodic cross correlation of the Figure 3.8: Matched filter output for two users with N 3 with τ τ.
16 3-6 CHAPR 3. DIRC-SQUNC SPRAD-SPCRUM N k l a Figure 3.9: Matched filter output for three users with N 3 with τ 3 τ τ. a k t τ k b k t τ k b k a N k l a N k a N k a k a k a N k l N k l a b k a N k l a N k a N k a a t τ k t a a a l a l a l a N a N c c l c l c t Figure 3.: Received Signal spreading sequences given by C k l N l m a k m a m l l N N l m a m k la m N l otherwise For l τ c R k τ ˆR k τ C k l N c τ l c C k l N C k l N C k l c τ l c C k l C k l he variance of the interference (which has zero mean) can be determined for random phases φ k and random data b k and b k i as and delays τ k and spreading sequences a k Ik 3 6N 3 R k τ k ˆR k τ k N l N l R τ k ˆR τ k dτ l c R τ k ˆR τ k dτ l c l c C l k l c τ Ck l τ l c l c C k l C k l τ l c l c τ Ck l N l c τ Ck l N τ l c C k l N C k l N τ l c l c τ dτ N C l l k Ck l Ck l N Ck l N
17 C k l C k l C k l N C k l N he parameter r k defined below captures the effect of different spreading sequences on the signal-to-noise ratio. r k N C l l k Ck l Ck l N Ck l N C k l C k l C k l N C k l N N C l l k C k l C k l N N C k k l C l C k k l C l l N he last line follows from the identity N C k i l C k i l m l N N C k k l C i i l m l N he variance of the multiple-access term becomes I k r k 6N 3 he signal-to-noise ratio is SNR Z b Var Z b K k r k 6N 3 N If the output of the matched filter due to other users signals is modeled as a Gaussian random variable and we consider only random spreading sequences then SNR he error probability is then approximated by N K 3N P e Q SNR As an example consider the case of three users with sequence of length 3. he sequences for the different users are m-sequences derived from the following feedback shift register connections. i 3 User : â i â i 5 â with initial values â â â â 3 â spreading sequence is obtained after the usual conversion of to + and to -. a User : â i â a i â i. User 3: â 3 i â 3 a 3 3 i â i. i â i â i 3 i â i 3 3 â i 3 4 i â 4 he actual i. â i 5 with initial values â â â â 3 â 4 â i with initial values â â 3 â 3 â 3 3 â 3 4
18 3-8 CHAPR 3. DIRC-SQUNC SPRAD-SPCRUM With these sequences and initial states the signal-to-noise ratio (in the absence of background noise) is calculated to be SNR 7 73dB. If we change the initial values to â â â â 3 â 4 â â â â 3 â 4 â 3 â 3 â 3 â 3 3 â 3 4 then the signal-to noise ratio becomes SNR 5 47dB. (hese are the initial states that maximize and minimize the signal-to-noise ratio). On the other hand for random sequences the signal-to-noise ratio is 6.67dB. hus by choosing the appropriate starting points of the spreading sequences (even with a given feedback connection) we can affect the signal-to-noise ratio. However for large N the difficulty in finding the optimal starting states become computationally intractable. 5. Optimal Multiuser Detection In this section we consider the problem of optimally detecting the data sequences transmitted by K users to minimize the probability of chosing the wrong set of sequences. he setup is the same as the previous section. r t K k P k a k t τ k b k t τ k cos π f c t τ k n t where each user could possible have different received power P k and delay τ k. Assume that the data sequence of user K is finite and of length J. Assume also that the users are labeled such that τ τ τ K. A critical assumption that we will make is that each user employs rectangular pulse shapes. his effectively limits the effect of a single data bit to a time interval of duration. hus we will assume that b k t J b k m p t m m Another critical assumption is that the receiver knows exactly the delays of all the users as well as the spreading signals and received powers. Consider the data sequence b b b b K b b b K b b b K b J b J b K J Now consider reindexing the data bits according to the above ordering. We will let the index l designate which data bit from l to l JK. he l data bit corresponds to data bit of user. he l data bit corresponds to data bit of user. In general if l mk k where m J then data bit l corresponds to the m-th data bit of the k-th user. he received signal can be written as where r t JK l P l c l t b l n t c l t P k a k t τ k p t m τ k cos π f c t τ k We now define the following correlation values x l n c l t c n t dt Note the following about the correlations.. x l n x n l
19 x l l j j his is due to the fact that the data pulses are rectangular pulses of duration. Now the goal is to minimize the probability of choosing the wrong sequence b. o do this we need to find the sequence b to minimize r t K JK c l t b l dt l quivalently the receiver should choose the data sequence b to maximize where Λ JK b l r t c l t dt l JK JK b l y l l l JK l JK b l x l nb n n y l r t c l t dt JK c l t c n t dt n he conclusion from the above equation is that the optimal receiver computes the vector y y y JK and uses that as a sufficient statistic in order to compute the optimal decision rule. he vector y can be obtained from a bank of K matched filters, matched to the individual spreading signals of different users. Now we can simplify the metric computation as follows. Λ Λ Λ Λ JK l JK l JK b l y l b l y l b l y l l JK b l y l l JK l JK l JK b l x l l b l x l l b l x l l l JK b l l x l l JK JK l JK l l n JK l JK l n n l l b l x l nb n b l x l nb n b l x l l jb l j j K b l x l l jb l j j where we have assumed that x l m if m or l m K. he form for Λ is essentially the same as the form for the metric for MS with intersymbol interference. Now it is clear we can apply (as in the ISI case) dynamic programming (Viterbi Algorithm) to determine the optimal sequence b. We define the state to be the last K data bits σ l b l K b l K λ l σ l σ l y l b l b l x l l b l x l l jb l j j Λ JK λ l σ l σ l b y x b l he complexity of the optimal detector is proportional to the number of states in the Viterbi algorithm. For binary signaling this is K. If the pulses were not time limited to duration but of longer duration the memory of the channel would grow and the number of states would also grow.
20 3- CHAPR 3. DIRC-SQUNC SPRAD-SPCRUM 6. Problems. Show that for random spreading sequences the average aperiodic correlation functions has the following averages. C k C n N k l N n a l a l k m k n N k k n N k n a m a m n. Derive the mean square value of the interference at the output of a matched filter due to a multipath signal with delay distributed uniformly on c c in a direct-sequence spread-spectrum system with N chips per bit and random spreading sequences. Compare to the mean square interference if the delay is uniformly distributed on. 3. Derive the mean square value of the multiple-access interference with random spreading sequences. Use this to determine the signal-to-noise ratio for random sequences. 4. Derive the mean square value of the multiple-access interference for k 3 and N 3 with the sequence shown below. Sequence one derived via the shift register with x i x i 3 x i 5. Sequence two derived via the shift register with x i x i x i x i 3 x i 5. Sequence three derived via the shift register with x i x i x i 3 x i 4 x i 5. Verify that these sequences (of length 3) are not cyclic shifts of each other. Assume they all start in state (). 5. A direct-sequence spread-spectrum system transmits a binary modulated signal s t using a spreading sequence a t. he data sequence is a sequence of M bits b M b b b b M where b t s t M l M b l p t l Pa t b t a t NM a m p c t m c m NM he spreading sequence is periodic with period N and c N, thus there is exactly one period of the spreading sequence per data bit. he received signal is r t s t αs t τ n t where τ is a delay known to the receiver and α is a known constant. Determine an optimal receiver that has small complexity (not exponential in M). he optimal receiver if only one data bit (the one-shot problem) is transmitted (M ) is a filter matched to one period of a t αa t τ. However, this receiver can also be used when multiple bits are transmitted. he receiver samples the matched filter appropriately and makes a decision about the individual data bits at each sampling time. Find the average value of the desired signal output and the variance of the interference from multipath (if any) for this receiver. Assume random spreading sequences. Find an expression for the bit error probability with this receiver.
21 Derive the signal-to-noise ratio for each user in a direct-sequence spread-spectrum system that has K 3 users and N 3 with the sequences shown below. here is no fading but only white Gaussian background noise. Sequence one derived via the shift register with â i â i 3 â i 5. Starting state=(). a a Sequence two derived via the shift register with â i â i â i â i 3 â i 5. Starting state=(). a a Sequence three derived via the shift register with â i â i â i 3 â i 4 â i 5. Starting state=(). Compare the results to the signal-to-noise ratio for random spreading codes. 7. Derive the signal-to-noise ratio for the rake receiver for random spreading sequences in multipath fading. Assume that τ l is uniformly distributed on the interval 4 l c 4 l c c. First show the following equality for the model discussed in the notes. Second show that I j l I j l V j V j Use the above to derive the signal-to-noise ratio α l 3N j j l l α j α j 4 j l N 3N l j l j otherwise α l l l j 3N j j α j α j 4 j j N 3N j j SNR j α j j α j α l l l j 3N j l N N 8. Consider a direct-sequence spread spectrum (DSSS) system with N chips per bit and random spreading codes. Assume a pulsed jammer with power J transmitting Gaussian noise part of the time and not transmitting the other part of the time. et ρ be the fraction of time the jammer is on and ρ be the fraction of time the jammer is off. When the jammer is on the power is J ρ so that the average power is J. Assume the jammer is on (or off) for a whole bit interval. Assume the receiver can coherently demodulate the received signal. (a) Determine the average error probability as a function of ρ. (b) Determine the worst case error probability (maximum over ρ. (c) Compare to a BPSK system with Rayleigh fading. 9. Consider a direct-sequence spread-spectrum system with N 3 chips per bit. Assume the spreading code is from a maximal-length shift register sequence with feedback connection as follows. he sequence is derived via the shift register with feedback x i x i 3 x i 5 and starting state=(). (a) Plot the output of the matched filter as a function of time for a sequence of 5 bits (= ) Now consider a second transmitter with a sequence derived as follows. Sequence two derived via the shift register with x i x i x i x i 3 x i 5. Starting state=(). (b) Determine the output of the matched filter (matched to sequence one) but due to a signal using sequence two with the same sequence of data as in part (a).
Digital Band-pass Modulation PROF. MICHAEL TSAI 2011/11/10
Digital Band-pass Modulation PROF. MICHAEL TSAI 211/11/1 Band-pass Signal Representation a t g t General form: 2πf c t + φ t g t = a t cos 2πf c t + φ t Envelope Phase Envelope is always non-negative,
More informationReview of Doppler Spread The response to exp[2πift] is ĥ(f, t) exp[2πift]. ĥ(f, t) = β j exp[ 2πifτ j (t)] = exp[2πid j t 2πifτ o j ]
Review of Doppler Spread The response to exp[2πift] is ĥ(f, t) exp[2πift]. ĥ(f, t) = β exp[ 2πifτ (t)] = exp[2πid t 2πifτ o ] Define D = max D min D ; The fading at f is ĥ(f, t) = 1 T coh = 2D exp[2πi(d
More informationPerformance of Coherent Binary Phase-Shift Keying (BPSK) with Costas-Loop Tracking in the Presence of Interference
TMO Progress Report 4-139 November 15, 1999 Performance of Coherent Binary Phase-Shift Keying (BPSK) with Costas-Loop Tracking in the Presence of Interference M. K. Simon 1 The bit-error probability performance
More informationBASICS OF DETECTION AND ESTIMATION THEORY
BASICS OF DETECTION AND ESTIMATION THEORY 83050E/158 In this chapter we discuss how the transmitted symbols are detected optimally from a noisy received signal (observation). Based on these results, optimal
More informationThe Performance of Quaternary Amplitude Modulation with Quaternary Spreading in the Presence of Interfering Signals
Clemson University TigerPrints All Theses Theses 1-015 The Performance of Quaternary Amplitude Modulation with Quaternary Spreading in the Presence of Interfering Signals Allison Manhard Clemson University,
More informationAdvanced 3 G and 4 G Wireless Communication Prof. Aditya K Jagannathan Department of Electrical Engineering Indian Institute of Technology, Kanpur
Advanced 3 G and 4 G Wireless Communication Prof. Aditya K Jagannathan Department of Electrical Engineering Indian Institute of Technology, Kanpur Lecture - 19 Multi-User CDMA Uplink and Asynchronous CDMA
More informationWireless Communication Technologies 16:332:559 (Advanced Topics in Communications) Lecture #17 and #18 (April 1, April 3, 2002)
Wireless Communication echnologies Lecture 7 & 8 Wireless Communication echnologies 6:33:559 (Advanced opics in Communications) Lecture #7 and #8 (April, April 3, ) Instructor rof. arayan Mandayam Summarized
More informationPerformance Analysis of Spread Spectrum CDMA systems
1 Performance Analysis of Spread Spectrum CDMA systems 16:33:546 Wireless Communication Technologies Spring 5 Instructor: Dr. Narayan Mandayam Summary by Liang Xiao lxiao@winlab.rutgers.edu WINLAB, Department
More informationFlat Rayleigh fading. Assume a single tap model with G 0,m = G m. Assume G m is circ. symmetric Gaussian with E[ G m 2 ]=1.
Flat Rayleigh fading Assume a single tap model with G 0,m = G m. Assume G m is circ. symmetric Gaussian with E[ G m 2 ]=1. The magnitude is Rayleigh with f Gm ( g ) =2 g exp{ g 2 } ; g 0 f( g ) g R(G m
More informationANALYSIS OF A PARTIAL DECORRELATOR IN A MULTI-CELL DS/CDMA SYSTEM
ANAYSIS OF A PARTIA DECORREATOR IN A MUTI-CE DS/CDMA SYSTEM Mohammad Saquib ECE Department, SU Baton Rouge, A 70803-590 e-mail: saquib@winlab.rutgers.edu Roy Yates WINAB, Rutgers University Piscataway
More informationMulti User Detection I
January 12, 2005 Outline Overview Multiple Access Communication Motivation: What is MU Detection? Overview of DS/CDMA systems Concept and Codes used in CDMA CDMA Channels Models Synchronous and Asynchronous
More informationMaximum Likelihood Sequence Detection
1 The Channel... 1.1 Delay Spread... 1. Channel Model... 1.3 Matched Filter as Receiver Front End... 4 Detection... 5.1 Terms... 5. Maximum Lielihood Detection of a Single Symbol... 6.3 Maximum Lielihood
More informationE303: Communication Systems
E303: Communication Systems Professor A. Manikas Chair of Communications and Array Processing Imperial College London An Overview of Fundamentals: PN-codes/signals & Spread Spectrum (Part B) Prof. A. Manikas
More informationEE5713 : Advanced Digital Communications
EE5713 : Advanced Digital Communications Week 12, 13: Inter Symbol Interference (ISI) Nyquist Criteria for ISI Pulse Shaping and Raised-Cosine Filter Eye Pattern Equalization (On Board) 20-May-15 Muhammad
More informationLecture 7: Wireless Channels and Diversity Advanced Digital Communications (EQ2410) 1
Wireless : Wireless Advanced Digital Communications (EQ2410) 1 Thursday, Feb. 11, 2016 10:00-12:00, B24 1 Textbook: U. Madhow, Fundamentals of Digital Communications, 2008 1 / 15 Wireless Lecture 1-6 Equalization
More informationCHAPTER 14. Based on the info about the scattering function we know that the multipath spread is T m =1ms, and the Doppler spread is B d =0.2 Hz.
CHAPTER 4 Problem 4. : Based on the info about the scattering function we know that the multipath spread is T m =ms, and the Doppler spread is B d =. Hz. (a) (i) T m = 3 sec (ii) B d =. Hz (iii) ( t) c
More informationAnalog Electronics 2 ICS905
Analog Electronics 2 ICS905 G. Rodriguez-Guisantes Dépt. COMELEC http://perso.telecom-paristech.fr/ rodrigez/ens/cycle_master/ November 2016 2/ 67 Schedule Radio channel characteristics ; Analysis and
More informationSignal Design for Band-Limited Channels
Wireless Information Transmission System Lab. Signal Design for Band-Limited Channels Institute of Communications Engineering National Sun Yat-sen University Introduction We consider the problem of signal
More informationDesign of MMSE Multiuser Detectors using Random Matrix Techniques
Design of MMSE Multiuser Detectors using Random Matrix Techniques Linbo Li and Antonia M Tulino and Sergio Verdú Department of Electrical Engineering Princeton University Princeton, New Jersey 08544 Email:
More information2016 Spring: The Final Exam of Digital Communications
2016 Spring: The Final Exam of Digital Communications The total number of points is 131. 1. Image of Transmitter Transmitter L 1 θ v 1 As shown in the figure above, a car is receiving a signal from a remote
More informationCopyright license. Exchanging Information with the Stars. The goal. Some challenges
Copyright license Exchanging Information with the Stars David G Messerschmitt Department of Electrical Engineering and Computer Sciences University of California at Berkeley messer@eecs.berkeley.edu Talk
More information8 PAM BER/SER Monte Carlo Simulation
xercise.1 8 PAM BR/SR Monte Carlo Simulation - Simulate a 8 level PAM communication system and calculate bit and symbol error ratios (BR/SR). - Plot the calculated and simulated SR and BR curves. - Plot
More informationSquare Root Raised Cosine Filter
Wireless Information Transmission System Lab. Square Root Raised Cosine Filter Institute of Communications Engineering National Sun Yat-sen University Introduction We consider the problem of signal design
More informationEs e j4φ +4N n. 16 KE s /N 0. σ 2ˆφ4 1 γ s. p(φ e )= exp 1 ( 2πσ φ b cos N 2 φ e 0
Problem 6.15 : he received signal-plus-noise vector at the output of the matched filter may be represented as (see (5-2-63) for example) : r n = E s e j(θn φ) + N n where θ n =0,π/2,π,3π/2 for QPSK, and
More informationLecture 12. Block Diagram
Lecture 12 Goals Be able to encode using a linear block code Be able to decode a linear block code received over a binary symmetric channel or an additive white Gaussian channel XII-1 Block Diagram Data
More informationMultiuser Detection. Summary for EECS Graduate Seminar in Communications. Benjamin Vigoda
Multiuser Detection Summary for 6.975 EECS Graduate Seminar in Communications Benjamin Vigoda The multiuser detection problem applies when we are sending data on the uplink channel from a handset to a
More informationthat efficiently utilizes the total available channel bandwidth W.
Signal Design for Band-Limited Channels Wireless Information Transmission System Lab. Institute of Communications Engineering g National Sun Yat-sen University Introduction We consider the problem of signal
More informationLECTURE 16 AND 17. Digital signaling on frequency selective fading channels. Notes Prepared by: Abhishek Sood
ECE559:WIRELESS COMMUNICATION TECHNOLOGIES LECTURE 16 AND 17 Digital signaling on frequency selective fading channels 1 OUTLINE Notes Prepared by: Abhishek Sood In section 2 we discuss the receiver design
More informationCommunication Theory Summary of Important Definitions and Results
Signal and system theory Convolution of signals x(t) h(t) = y(t): Fourier Transform: Communication Theory Summary of Important Definitions and Results X(ω) = X(ω) = y(t) = X(ω) = j x(t) e jωt dt, 0 Properties
More informationECE6604 PERSONAL & MOBILE COMMUNICATIONS. Week 3. Flat Fading Channels Envelope Distribution Autocorrelation of a Random Process
1 ECE6604 PERSONAL & MOBILE COMMUNICATIONS Week 3 Flat Fading Channels Envelope Distribution Autocorrelation of a Random Process 2 Multipath-Fading Mechanism local scatterers mobile subscriber base station
More informationADAPTIVE DETECTION FOR A PERMUTATION-BASED MULTIPLE-ACCESS SYSTEM ON TIME-VARYING MULTIPATH CHANNELS WITH UNKNOWN DELAYS AND COEFFICIENTS
ADAPTIVE DETECTION FOR A PERMUTATION-BASED MULTIPLE-ACCESS SYSTEM ON TIME-VARYING MULTIPATH CHANNELS WITH UNKNOWN DELAYS AND COEFFICIENTS Martial COULON and Daniel ROVIRAS University of Toulouse INP-ENSEEIHT
More informationTracking of Spread Spectrum Signals
Chapter 7 Tracking of Spread Spectrum Signals 7. Introduction As discussed in the last chapter, there are two parts to the synchronization process. The first stage is often termed acquisition and typically
More informationWeiyao Lin. Shanghai Jiao Tong University. Chapter 5: Digital Transmission through Baseband slchannels Textbook: Ch
Principles of Communications Weiyao Lin Shanghai Jiao Tong University Chapter 5: Digital Transmission through Baseband slchannels Textbook: Ch 10.1-10.5 2009/2010 Meixia Tao @ SJTU 1 Topics to be Covered
More informationEE6604 Personal & Mobile Communications. Week 13. Multi-antenna Techniques
EE6604 Personal & Mobile Communications Week 13 Multi-antenna Techniques 1 Diversity Methods Diversity combats fading by providing the receiver with multiple uncorrelated replicas of the same information
More informationComputation of Bit-Error Rate of Coherent and Non-Coherent Detection M-Ary PSK With Gray Code in BFWA Systems
Computation of Bit-Error Rate of Coherent and Non-Coherent Detection M-Ary PSK With Gray Code in BFWA Systems Department of Electrical Engineering, College of Engineering, Basrah University Basrah Iraq,
More informationEstimation of the Capacity of Multipath Infrared Channels
Estimation of the Capacity of Multipath Infrared Channels Jeffrey B. Carruthers Department of Electrical and Computer Engineering Boston University jbc@bu.edu Sachin Padma Department of Electrical and
More informationComparative Performance of Three DSSS/Rake Modems Over Mobile UWB Dense Multipath Channels
MTR 6B5 MITRE TECHNICAL REPORT Comparative Performance of Three DSSS/Rake Modems Over Mobile UWB Dense Multipath Channels June 5 Phillip A. Bello Sponsor: Contract No.: FA871-5-C-1 Dept. No.: E53 Project
More informationUpper Bounds for the Average Error Probability of a Time-Hopping Wideband System
Upper Bounds for the Average Error Probability of a Time-Hopping Wideband System Aravind Kailas UMTS Systems Performance Team QUALCOMM Inc San Diego, CA 911 Email: akailas@qualcommcom John A Gubner Department
More informationData-aided and blind synchronization
PHYDYAS Review Meeting 2009-03-02 Data-aided and blind synchronization Mario Tanda Università di Napoli Federico II Dipartimento di Ingegneria Biomedica, Elettronicae delle Telecomunicazioni Via Claudio
More informationPower Spectral Density of Digital Modulation Schemes
Digital Communication, Continuation Course Power Spectral Density of Digital Modulation Schemes Mikael Olofsson Emil Björnson Department of Electrical Engineering ISY) Linköping University, SE-581 83 Linköping,
More information5. Pilot Aided Modulations. In flat fading, if we have a good channel estimate of the complex gain gt, ( ) then we can perform coherent detection.
5. Pilot Aided Modulations In flat fading, if we have a good channel estimate of the complex gain gt, ( ) then we can perform coherent detection. Obtaining a good estimate is difficult. As we have seen,
More informationParameter Estimation
1 / 44 Parameter Estimation Saravanan Vijayakumaran sarva@ee.iitb.ac.in Department of Electrical Engineering Indian Institute of Technology Bombay October 25, 2012 Motivation System Model used to Derive
More informationThese outputs can be written in a more convenient form: with y(i) = Hc m (i) n(i) y(i) = (y(i); ; y K (i)) T ; c m (i) = (c m (i); ; c m K(i)) T and n
Binary Codes for synchronous DS-CDMA Stefan Bruck, Ulrich Sorger Institute for Network- and Signal Theory Darmstadt University of Technology Merckstr. 25, 6428 Darmstadt, Germany Tel.: 49 65 629, Fax:
More informationSOLUTIONS TO ECE 6603 ASSIGNMENT NO. 6
SOLUTIONS TO ECE 6603 ASSIGNMENT NO. 6 PROBLEM 6.. Consider a real-valued channel of the form r = a h + a h + n, which is a special case of the MIMO channel considered in class but with only two inputs.
More informationData Detection for Controlled ISI. h(nt) = 1 for n=0,1 and zero otherwise.
Data Detection for Controlled ISI *Symbol by symbol suboptimum detection For the duobinary signal pulse h(nt) = 1 for n=0,1 and zero otherwise. The samples at the output of the receiving filter(demodulator)
More informationShallow Water Fluctuations and Communications
Shallow Water Fluctuations and Communications H.C. Song Marine Physical Laboratory Scripps Institution of oceanography La Jolla, CA 92093-0238 phone: (858) 534-0954 fax: (858) 534-7641 email: hcsong@mpl.ucsd.edu
More informationDetermining the Optimal Decision Delay Parameter for a Linear Equalizer
International Journal of Automation and Computing 1 (2005) 20-24 Determining the Optimal Decision Delay Parameter for a Linear Equalizer Eng Siong Chng School of Computer Engineering, Nanyang Technological
More informations o (t) = S(f)H(f; t)e j2πft df,
Sample Problems for Midterm. The sample problems for the fourth and fifth quizzes as well as Example on Slide 8-37 and Example on Slides 8-39 4) will also be a key part of the second midterm.. For a causal)
More informationThis examination consists of 11 pages. Please check that you have a complete copy. Time: 2.5 hrs INSTRUCTIONS
THE UNIVERSITY OF BRITISH COLUMBIA Department of Electrical and Computer Engineering EECE 564 Detection and Estimation of Signals in Noise Final Examination 6 December 2006 This examination consists of
More informationOptimisation of Pseudolite Pulsing Scheme for Participative & Non-Participative Receivers
Optimisation of Pseudolite Pulsing Scheme for Participative & Non-Participative Receivers Jean-Baptiste Gigant A Thesis submitted for the Degree of Master Degree Institute for Communications and Navigation
More informationEE4512 Analog and Digital Communications Chapter 4. Chapter 4 Receiver Design
Chapter 4 Receiver Design Chapter 4 Receiver Design Probability of Bit Error Pages 124-149 149 Probability of Bit Error The low pass filtered and sampled PAM signal results in an expression for the probability
More informationω 0 = 2π/T 0 is called the fundamental angular frequency and ω 2 = 2ω 0 is called the
he ime-frequency Concept []. Review of Fourier Series Consider the following set of time functions {3A sin t, A sin t}. We can represent these functions in different ways by plotting the amplitude versus
More informationRADIO SYSTEMS ETIN15. Lecture no: Equalization. Ove Edfors, Department of Electrical and Information Technology
RADIO SYSTEMS ETIN15 Lecture no: 8 Equalization Ove Edfors, Department of Electrical and Information Technology Ove.Edfors@eit.lth.se Contents Inter-symbol interference Linear equalizers Decision-feedback
More informationPrinciples of Communications Lecture 8: Baseband Communication Systems. Chih-Wei Liu 劉志尉 National Chiao Tung University
Principles of Communications Lecture 8: Baseband Communication Systems Chih-Wei Liu 劉志尉 National Chiao Tung University cwliu@twins.ee.nctu.edu.tw Outlines Introduction Line codes Effects of filtering Pulse
More informationWireless Information Transmission System Lab. Channel Estimation. Institute of Communications Engineering. National Sun Yat-sen University
Wireless Information Transmission System Lab. Channel Estimation Institute of Communications Engineering National Sun Yat-sen University Table of Contents Introduction to Channel Estimation Generic Pilot
More informationThis examination consists of 10 pages. Please check that you have a complete copy. Time: 2.5 hrs INSTRUCTIONS
THE UNIVERSITY OF BRITISH COLUMBIA Department of Electrical and Computer Engineering EECE 564 Detection and Estimation of Signals in Noise Final Examination 08 December 2009 This examination consists of
More informationEE6604 Personal & Mobile Communications. Week 15. OFDM on AWGN and ISI Channels
EE6604 Personal & Mobile Communications Week 15 OFDM on AWGN and ISI Channels 1 { x k } x 0 x 1 x x x N- 2 N- 1 IDFT X X X X 0 1 N- 2 N- 1 { X n } insert guard { g X n } g X I n { } D/A ~ si ( t) X g X
More informationSNR i = 2E b 6N 3. Where
Correlation Properties Of Binary Sequences Generated By The Logistic Map-Application To DS-CDMA *ZOUHAIR BEN JEMAA, **SAFYA BELGHITH *EPFL DSC LANOS ELE 5, 05 LAUSANNE **LABORATOIRE SYSCOM ENIT, 002 TUNIS
More informationA First Course in Digital Communications
A First Course in Digital Communications Ha H. Nguyen and E. Shwedyk February 9 A First Course in Digital Communications 1/46 Introduction There are benefits to be gained when M-ary (M = 4 signaling methods
More informationFBMC/OQAM transceivers for 5G mobile communication systems. François Rottenberg
FBMC/OQAM transceivers for 5G mobile communication systems François Rottenberg Modulation Wikipedia definition: Process of varying one or more properties of a periodic waveform, called the carrier signal,
More informationFigure 1.1 (a) Model of a communication system, and (b) signal processing functions.
. Introduction to Signals and Operations Model of a Communication System [] Figure. (a) Model of a communication system, and (b) signal processing functions. Classification of Signals. Continuous-time
More informationOptimized Impulses for Multicarrier Offset-QAM
Optimized Impulses for ulticarrier Offset-QA Stephan Pfletschinger, Joachim Speidel Institut für Nachrichtenübertragung Universität Stuttgart, Pfaffenwaldring 47, D-7469 Stuttgart, Germany Abstract The
More informationMulticarrier transmission DMT/OFDM
W. Henkel, International University Bremen 1 Multicarrier transmission DMT/OFDM DMT: Discrete Multitone (wireline, baseband) OFDM: Orthogonal Frequency Division Multiplex (wireless, with carrier, passband)
More informationInterleave Division Multiple Access. Li Ping, Department of Electronic Engineering City University of Hong Kong
Interleave Division Multiple Access Li Ping, Department of Electronic Engineering City University of Hong Kong 1 Outline! Introduction! IDMA! Chip-by-chip multiuser detection! Analysis and optimization!
More informationDigital Communications
Digital Communications Chapter 9 Digital Communications Through Band-Limited Channels Po-Ning Chen, Professor Institute of Communications Engineering National Chiao-Tung University, Taiwan Digital Communications:
More informationDigital Baseband Systems. Reference: Digital Communications John G. Proakis
Digital Baseband Systems Reference: Digital Communications John G. Proais Baseband Pulse Transmission Baseband digital signals - signals whose spectrum extend down to or near zero frequency. Model of the
More informationApproximate Minimum Bit-Error Rate Multiuser Detection
Approximate Minimum Bit-Error Rate Multiuser Detection Chen-Chu Yeh, Renato R. opes, and John R. Barry School of Electrical and Computer Engineering Georgia Institute of Technology, Atlanta, Georgia 30332-0250
More informationPrinciples of Communications
Principles of Communications Chapter V: Representation and Transmission of Baseband Digital Signal Yongchao Wang Email: ychwang@mail.xidian.edu.cn Xidian University State Key Lab. on ISN November 18, 2012
More informationECE 564/645 - Digital Communications, Spring 2018 Homework #2 Due: March 19 (In Lecture)
ECE 564/645 - Digital Communications, Spring 018 Homework # Due: March 19 (In Lecture) 1. Consider a binary communication system over a 1-dimensional vector channel where message m 1 is sent by signaling
More informationLIKELIHOOD RECEIVER FOR FH-MFSK MOBILE RADIO*
LIKELIHOOD RECEIVER FOR FH-MFSK MOBILE RADIO* Item Type text; Proceedings Authors Viswanathan, R.; S.C. Gupta Publisher International Foundation for Telemetering Journal International Telemetering Conference
More informationStochastic Processes. M. Sami Fadali Professor of Electrical Engineering University of Nevada, Reno
Stochastic Processes M. Sami Fadali Professor of Electrical Engineering University of Nevada, Reno 1 Outline Stochastic (random) processes. Autocorrelation. Crosscorrelation. Spectral density function.
More informationEE456 Digital Communications
EE456 Digital Communications Professor Ha Nguyen September 5 EE456 Digital Communications Block Diagram of Binary Communication Systems m ( t { b k } b k = s( t b = s ( t k m ˆ ( t { bˆ } k r( t Bits in
More informationENSC327 Communications Systems 2: Fourier Representations. Jie Liang School of Engineering Science Simon Fraser University
ENSC327 Communications Systems 2: Fourier Representations Jie Liang School of Engineering Science Simon Fraser University 1 Outline Chap 2.1 2.5: Signal Classifications Fourier Transform Dirac Delta Function
More informationSemi-Blind ML Synchronization for UWB Systems
Semi-Blind ML Synchronization for UWB Systems Stefan Franz, Cecilia Carbonelli, Urbashi Mitra Communication Sciences Institute, University of Southern California 3740 McClintock Avenue, Los Angeles, CA,
More informationProjects in Wireless Communication Lecture 1
Projects in Wireless Communication Lecture 1 Fredrik Tufvesson/Fredrik Rusek Department of Electrical and Information Technology Lund University, Sweden Lund, Sept 2018 Outline Introduction to the course
More informationExample: Bipolar NRZ (non-return-to-zero) signaling
Baseand Data Transmission Data are sent without using a carrier signal Example: Bipolar NRZ (non-return-to-zero signaling is represented y is represented y T A -A T : it duration is represented y BT. Passand
More informationA Family of Nyquist Filters Based on Generalized Raised-Cosine Spectra
Proc. Biennial Symp. Commun. (Kingston, Ont.), pp. 3-35, June 99 A Family of Nyquist Filters Based on Generalized Raised-Cosine Spectra Nader Sheikholeslami Peter Kabal Department of Electrical Engineering
More informationRandom Matrices and Wireless Communications
Random Matrices and Wireless Communications Jamie Evans Centre for Ultra-Broadband Information Networks (CUBIN) Department of Electrical and Electronic Engineering University of Melbourne 3.5 1 3 0.8 2.5
More informationDigital Modulation 1
Digital Modulation 1 Lecture Notes Ingmar Land and Bernard H. Fleury Navigation and Communications () Department of Electronic Systems Aalborg University, DK Version: February 5, 27 i Contents I Basic
More informationGEORGIA INSTITUTE OF TECHNOLOGY SCHOOL OF ELECTRICAL AND COMPUTER ENGINEERING Final Examination - Fall 2015 EE 4601: Communication Systems
GEORGIA INSTITUTE OF TECHNOLOGY SCHOOL OF ELECTRICAL AND COMPUTER ENGINEERING Final Examination - Fall 2015 EE 4601: Communication Systems Aids Allowed: 2 8 1/2 X11 crib sheets, calculator DATE: Tuesday
More informationDigital Communications
Digital Communications Chapter 5 Carrier and Symbol Synchronization Po-Ning Chen, Professor Institute of Communications Engineering National Chiao-Tung University, Taiwan Digital Communications Ver 218.7.26
More informationEffects of Non-Ideal Pre-Distorter High Power Amplifiers in WCDMA Using Multi-User Detectors
Effects of Non-Ideal Pre-Distorter High Power Amplifiers in WCDMA Using Multi-User Detectors Downloaded from ijeeeiustacir at 3:11 IRST on Sunday January th 19 S Ghavami and B Abolhassani Abstract: Wide
More informationInteractions of Information Theory and Estimation in Single- and Multi-user Communications
Interactions of Information Theory and Estimation in Single- and Multi-user Communications Dongning Guo Department of Electrical Engineering Princeton University March 8, 2004 p 1 Dongning Guo Communications
More informationECS455: Chapter 4 Multiple Access
ECS455: Chapter 4 Multiple Access 4.4 m-sequence Binary Random Sequence X -4 X -3 X -2 X - X -0 X X 2 X 3 X 4 Coin-flipping sequence H H T H H T H T T Bernoullitrials/sequence 0 0 0 0 Binary (indp.) random
More informationCS6956: Wireless and Mobile Networks Lecture Notes: 2/4/2015
CS6956: Wireless and Mobile Networks Lecture Notes: 2/4/2015 [Most of the material for this lecture has been taken from the Wireless Communications & Networks book by Stallings (2 nd edition).] Effective
More informationEE Introduction to Digital Communications Homework 8 Solutions
EE 2 - Introduction to Digital Communications Homework 8 Solutions May 7, 2008. (a) he error probability is P e = Q( SNR). 0 0 0 2 0 4 0 6 P e 0 8 0 0 0 2 0 4 0 6 0 5 0 5 20 25 30 35 40 SNR (db) (b) SNR
More informationCommunications and Signal Processing Spring 2017 MSE Exam
Communications and Signal Processing Spring 2017 MSE Exam Please obtain your Test ID from the following table. You must write your Test ID and name on each of the pages of this exam. A page with missing
More informationLECTURE 18. Lecture outline Gaussian channels: parallel colored noise inter-symbol interference general case: multiple inputs and outputs
LECTURE 18 Last time: White Gaussian noise Bandlimited WGN Additive White Gaussian Noise (AWGN) channel Capacity of AWGN channel Application: DS-CDMA systems Spreading Coding theorem Lecture outline Gaussian
More informationMMSE Decision Feedback Equalization of Pulse Position Modulated Signals
SE Decision Feedback Equalization of Pulse Position odulated Signals AG Klein and CR Johnson, Jr School of Electrical and Computer Engineering Cornell University, Ithaca, NY 4853 email: agk5@cornelledu
More informationConsider a 2-D constellation, suppose that basis signals =cosine and sine. Each constellation symbol corresponds to a vector with two real components
TUTORIAL ON DIGITAL MODULATIONS Part 3: 4-PSK [2--26] Roberto Garello, Politecnico di Torino Free download (for personal use only) at: www.tlc.polito.it/garello Quadrature modulation Consider a 2-D constellation,
More informationAdaptive Bit-Interleaved Coded OFDM over Time-Varying Channels
Adaptive Bit-Interleaved Coded OFDM over Time-Varying Channels Jin Soo Choi, Chang Kyung Sung, Sung Hyun Moon, and Inkyu Lee School of Electrical Engineering Korea University Seoul, Korea Email:jinsoo@wireless.korea.ac.kr,
More informationUCSD ECE153 Handout #40 Prof. Young-Han Kim Thursday, May 29, Homework Set #8 Due: Thursday, June 5, 2011
UCSD ECE53 Handout #40 Prof. Young-Han Kim Thursday, May 9, 04 Homework Set #8 Due: Thursday, June 5, 0. Discrete-time Wiener process. Let Z n, n 0 be a discrete time white Gaussian noise (WGN) process,
More informationCell throughput analysis of the Proportional Fair scheduler in the single cell environment
Cell throughput analysis of the Proportional Fair scheduler in the single cell environment Jin-Ghoo Choi and Seawoong Bahk IEEE Trans on Vehicular Tech, Mar 2007 *** Presented by: Anh H. Nguyen February
More informationDigital Signal Processing
Digital Signal Processing 23 (2013 635 645 Contents lists available at SciVerse ScienceDirect Digital Signal Processing www.elsevier.com/locate/dsp Stochastic signaling in the presence of channel state
More informationPRE-RAKE DIVERSITY WITH GENERALIZED ORTHOGONAL CODES AND IMPERFECT CHANNEL CONDITIONS FOR FDD/DS-CDMA SYSTEMS
VOL. 4, NO. 7, SEPTEMBER 9 ISSN 89-668 6-9 Asian Research Publishing Networ (ARPN). All rights reserved. PRE-RAKE DIVERSITY WITH GENERALIZED ORTHOGONAL CODES AND IMPERFECT CHANNEL CONDITIONS FOR FDD/DS-CDMA
More informationSummary II: Modulation and Demodulation
Summary II: Modulation and Demodulation Instructor : Jun Chen Department of Electrical and Computer Engineering, McMaster University Room: ITB A1, ext. 0163 Email: junchen@mail.ece.mcmaster.ca Website:
More informationRalf Koetter, Andrew C. Singer, and Michael Tüchler
Ralf Koetter, Andrew C. Singer, and Michael Tüchler Capitalizing on the tremendous performance gains of turbo codes and the turbo decoding algorithm, turbo equalization is an iterative equalization and
More informationSIGNAL PROCESSING FOR TRANSMIT-REFERENCE UWB. Hieu Q. Dang and Alle-Jan van der Veen. TU Delft, Fac. EEMCS, Mekelweg 4, 2628 CD Delft, The Netherlands
SIGNAL ROCESSING FOR TRANSMIT-REFERENCE UWB Hieu Q Dang and Alle-Jan van der Veen TU Delft, Fac EEMCS, Mekelweg 4, 2628 CD Delft, The Netherlands Transmit-reference (TR) is known as a realistic but low
More informationOnamethodtoimprove correlation properties of orthogonal polyphase spreading sequences
Regular paper Onamethodtoimprove correlation properties of orthogonal polyphase spreading sequences Beata J. Wysocki and Tadeusz A. Wysocki Abstract In this paper, we propose a simple but efficient method
More informationMitigation of Multipath-induced Errors in Satellite Navigation
Mitigation of Multipath-induced Errors in Satellite Navigation Master Thesis Ioana Gulie Aalborg University Department of Electronic Systems Fredrik Bajers Vej 7B 922 Aalborg, Denmark Astrium GmbH Department
More information