Wireless Personal Communications 25: 117–136, 2003. © 2003 Kluwer Academic Publishers. Printed in the Netherlands.
Performance of MMSE Receiver Based CDMA System with Higher Order Modulation Formats in a Fading Channel ALI F. ALMUTAIRI 1, HANIPH A. LATCHMAN 1 , TAN F. WONG 1, MINKYU LEE 1 and SCOTT L. MILLER 2 1 Department of Electrical and Computer Engineering, University of Florida, Gainesville, FL 32611-6130, U.S.A. E-mail:
[email protected] 2 Department of Electrical Engineering, Texas A&M University, College Station, TX 77843-3128, U.S.A.
Abstract. This paper studies the effect of using higher order modulation formats on the performance of minimum mean-squared error (MMSE) receiver based direct-sequence (DS) code-division multiple access (CDMA) systems at different loading levels in additive white Gaussian noise (AWGN) and slow fading channels. The performance of BPSK, QPSK, and 16QAM modulation formats are compared and analytical and simulation results are presented in terms of the bit error rates (BER) for these different modulation formats. A comparison of the rejection of the near-far effects for each modulation scheme is also presented. The main contribution of this paper is in showing that user capacity may be increased by using higher order modulation schemes to cause the MMSE receiver to operate away from the interference limiting region. In particular it is shown that under high loading levels, 16QAM outperforms QPSK and BPSK for identical bandwidth and information rate, while at moderate loading levels, QPSK represents the best option. A combination of pilot symbol assisted modulation (PSAM) and linear prediction are used to estimate the fading process. A general structure of the MMSE receiver capable of demodulating a wide range of digital modulation formats in this type of environment is presented. Keywords: CDMA, MMSE, modulation, QAM.
1. Introduction The MMSE receiver, shown in Figure 1 and which has been described in detail in [3, 10, 11], is known for its low complexity and ease of implementation. While BPSK is often used as the underlying modulation format with the MMSE receiver, in this paper we study the use of higher level modulations to achieve higher bandwidth efficiency. One of the main objectives of cellular systems designers is to increase the user capacity for a given quality of service and available bandwidth and in this work we propose to use higher order modulations to achieve this goal. To understand the advantages of the MMSE receiver, we need to describe briefly how it works. The received signal which consists of the desired user’s signal, multiple access interference (MAI), and Gaussian noise is fed at the chip rate into the equalizer until the N-tap delay line becomes full (see Figure 1). After one symbol time, the equalizer content are correlated with the tap weights, a, and the result of this correlation is used to make a decision about which symbol was sent. These tap weights are updated every symbol interval to minimize the mean square error between the output of the filter and the desired output. In practice, the filter is trained for a reasonable period of time by a known training symbol sequence to reach a tap weight vector that is close to the optimum weights. After the training Corresponding author.
118 Ali F. Almutairi et al.
Figure 1. The MMSE receiver structure.
period, the receiver switches to decision feedback mode. It has been shown in [4] that the decision directed mode proves to be troublesome in a fading channel. In deep fades, incorrect decisions being fed back to the receiver cause the MMSE receiver to lose track of the desired signal. A modified MMSE receiver structure to overcome this problem was described in [4] for a BPSK modulation format. In [2], different tracking techniques of the desired user fading process and a general MMSE receiver structure for a fading channel were presented. In the literature, BPSK and sometimes QPSK are used as modulation formats for the MMSE receiver. As noted in [3], if BPSK is used, the MMSE receiver becomes interference limited when the system load is close to the processing gain. This threshold is reached because of the imperfect cancellation of the Multiple Access Interference (MAI) due to the lack of dimensions in the system. One way to improve the performance of the system is to introduce more dimensions while keeping the bandwidth the same to help in suppressing the MAI. To achieve that, one can choose a higher order modulation format like MPSK or 16-QAM to increase the processing gain (the number of chips per symbols). The justification for increasing the processing gain of the system by employing higher order modulation is presented in the following example. In an unspread system, for the same bit rate, using QPSK will result in using half the bandwidth required of a BPSK system, while using a 16-QAM will result in using one fourth of the bandwidth required by the BPSK system. In a CDMA system, to utilize the total available bandwidth when higher order modulation formats are used, the spreading gain of the QPSK system should be twice that of the BPSK system and the spreading gain of the 16-QAM system should be 4 times that spreading gain of the BPSK system. Consequently, throughout this paper, we have used random sequences with spreading gains of 31 for the BPSK system, 62 for the QPSK system, and 124 for the 16-QAM system, as examples to illustrate the proposed technique. By adopting a higher order modulation and increasing the processing gain, the MMSE receiver is effectively moved out of the interference limited region, and it can then suppress more interference than the original system. Since the receiver now is operating in the interference resistant region, one can increase the transmitted power to obtain a higher SINR for acceptable performance. Using a higher order modulation allows us to increase the spreading
MMSE Receiver Based CDMA System with Higher Order Modulation Formats 119 gain and hence move the MMSE receiver back to the interference-resistant operation region. However the power efficiency of the modulation decreases when a higher order modulation is employed. Therefore an optimal design will necessarily involve a tradeoff between the interference rejection capability and power efficiency of the modulation. This constraint implies that higher order modulations are expected to be beneficial in a moderately to heavily loaded system but not in a lightly loaded one. These observations are verified and quantified in this paper. Milstein and Shamain studied the performance of QPSK and 16-QAM modulation formats in a multipath and narrowband Gaussian interference (NGI) environment, in [16] and [17], for single user and two user systems. They showed that when the multipaths cause significant intersymbol interference (ISI), with or without NGI, the 16-QAM system outperforms the QPSK system. In this paper, our focus will be on the improvement of the system performance in terms of BER and user capacity, in the presence of MAI when higher order modulations are used. In addition, we investigate the performance of the CDMA system in a fading environment with optimum or adaptive implementation of the MMSE receiver for different system loading conditions. Furthermore, we investigate the case when the desired user’s fading is not exactly known to the receiver. The use of multi-level modulation formats, like 16-QAM, leads to some interesting research problems. As with unspread systems, any time a multilevel modulation format is used in a fading channel, it becomes necessary to carefully track the phase and amplitude of the desired user’s fading process in order for the receiver to demodulate the desired user’s signal successfully. Channel tracking through the use of pilot symbol assisted modulation (PSAM) in single user systems has been proposed by several authors [5, 7, 8, 15], as a method to estimate the fading process and mitigate its effects at the receiver. In PSAM, pilot symbols are inserted periodically into the data stream and channel estimates are obtained using Gaussian interpolation [15], Wiener filtering interpolation [5], or sinc interpolation [8]. It should be noted that there is always a delay associated with the use of PSAM since the demodulator has to receive a certain number of pilot symbols to estimate the fading process. This estimation technique cannot be applied directly to the MMSE receiver since this receiver updates its tap weights every symbol based on the demodulation of the previous symbol. Linear prediction has also been used to obtain estimates of a fading process for a single user system in [6] and for multiuser systems in [4] and [2]. As described in [4], linear prediction of the desired user’s fading is performed by using the outputs of the MMSE filter from past symbol intervals. This technique can lose track of the fading process due to a burst of decision errors, as pointed out in [6] and [2]. In [2], we have shown that a combination of PSAM and linear prediction can effectively track the fading process of the desired user. The use of pilot symbols has been proven to be beneficial in preventing the MMSE receiver from feeding back unreliable decisions when it is operating in its decision directed mode while the desired user signal is going into a deep fade. In this paper, we used this technique to estimate the desired user fading process. The rest of the paper is organized as follows. Section 2 describes the system model. Sections 3 and 4 present analytical and simulation performance results for systems in additive white Gaussian noise (AWGN) and fading channels, respectively. Section 5 discusses practical implementation considerations such as adaptive MMSE receiver operation and modulation order selection. Finally some concluding remarks are made in Section 6.
120 Ali F. Almutairi et al. 2. System Model In this section, an MMSE receiver based CDMA system is described. There are K active users in the system and each user is assumed to have a unique spreading waveform cj (t). It is assumed that all users transmit asynchronously over the same channel with carrier frequency wo . The modulated signal of the j th user can be written as sj (t) = Re{ 2pj dj (t)cj (t)ej wo t } (1) = Re{gj (t)ej wo t } , where gj (t) is the complex envelope of sj (t), pj is the transmitted power, and dj (t) is a complex baseband signalling format with symbol interval Ts . The waveform cj (t) is assumed to be in the bipolar form with chip interval Tc . Therefore, the processing gain N is equal to Ts /Tc . The bandpass received signal at the receiver is given by K αj (t)ej θj (t )gj (t − τj )ej wo t + n(t) . (2) r(t) = Re j =1
The variables τj , αj , θj are respectively, the propagation delay, amplitude and phase of the fading process for the j th user. The process n(t) is an AWGN process with a spectral density of No /2, and the fading amplitude is Rayleigh-distributed while the fading phase is uniformlydistributed. It is assumed that the desired user is user 1 and the receiver has knowledge of its propagation delay. Without loss of generality, τ1 can be set to zero. After converting the received signal to complex baseband, the signal is passed through a filter matched to the chip pulse shape, which is√assumed to be a rectangular pulse of duration Tc . The matched filter has a scale factor of 2p1 Tc associated with it. Based on these assumptions, The equalizer contents of the MMSE receiver are given by K pj j θ1 (m) c1 + αj (m)ej θj (m) [dj (m)
fj (l, δ) r(m) = d1 (m)α1 (m)e p 1 (3) j =2 gj (l, δ)] + n(m) , + dj (m − 1)
where the vector n(m) consists of elements that are independent zero-mean complex Gaussian random variables whose real and imaginary parts have variances given by (2EsN/No ) where Es is the average energy per symbol. In the above equation, τj = lj Tc + δj where lj is an integer fj and
gj are defined as follows and 0 ≤ δj < Tc . The vectors
δ δ
(4) fj (N − l) fj (l, δ) = fj (N − l − 1) + 1 − Tc Tc δ δ (5) gj (N − l),
gj (l, δ) = gj (N − l − 1) + 1 − Tc Tc where c(l) fj (l) = (c(l) j + j )/2
(6)
c(l) gj (l) = (c(l) j − j )/2
(7)
MMSE Receiver Based CDMA System with Higher Order Modulation Formats 121 T c(l) j = (cj,N−l , cj,N−l+1 , . . . , cj,N−1 , cj,0 , cj,1 , . . . , cj,N−l−1 )
(8)
T
c(l) j = (−cj,N−l , −cj,N−l+1 , . . . , −cj,N−1 , −cj,0 , cj,1 , . . . , cj,N−l−1 ) .
(9)
The variable r(m) can be written in the form r(m) = d1 (m)α1 (m)ej θ1 (m) c1 + r˜ (m).
(10)
We define the following terms to be used in the next section. The autocorrelation matrix, R, of the equalizer contents is defined as R = E r(m)r(m)H . The autocorrelation matrix ˜ = E r˜ (m)˜r(m)H and of the MAI and noise part of the equalizer contents is given as R the correlationbetween the desired user response and the received signal is given by Pi = E di∗ (m)r(m) . 3. Performance in an AWGN Channel In this section, we modify the model presented in Section 2 to study the performance of the CDMA system using different modulation formats in an AWGN channel. This can be done by setting the amplitude and phase of the fading process to 1 and zero respectively, in Equation (10). In addition, assume that hik = 1, user √ 1 is the desired user and the integrator in front of the MMSE receiver has a scale factor of 2p1 Tc associated with it. Based on these assumptions, the received vector, r(m), can be written as (11) r(m) = d1 (m)c1 + r˜ (m). ∗ Since E d1 d1 = 1, the correlation vector P and the autocorrelation matrix R can be written as follows (dropping the dependence on m for convenience): (12) P = E d1∗ r = c1 ˜ R = E |d1 |2 c1 cT1 + R (13) ˜ = PPH + R, ˜ = E r˜ r˜ H . where R The tap MMSE weight vector, a, may also be expressed in terms of P and R by a = R−1 P.
(14)
The output of the filter can be written as z = aH r = d1 PH R−1 P + PH R−1 r˜ ˜ = d1 PH R−1 P + n.
(15)
Now we need to find the value of PH R−1 P and the variance of n˜ which represents the contribution of the MAI and the white noise at the output of the MMSE filter. Using the matrix-inversion lemma, we can find the inverse of R as follows: ˜ −1 + R ˜ −1 P(1 + PH R ˜ −1 P)−1 PH R ˜ −1 R−1 = R ˜ −1 H ˜ −1 ˜ −1 + R PP R . = R ˜ −1 P 1 + PH R
(16)
122 Ali F. Almutairi et al. If we multiply both sides of Equation (16) from the left by PH and on the right by P and simplify the result we will get PH R−1 P =
˜ −1 P PH R . ˜ −1 P 1 + PH R
(17)
The variance of the term n˜ can be written as ˜ −1 P = E[n˜ n˜ H ] = PH R−1 RR
˜ −1 P PH R . ˜ −1 P]2 [1 + PH R
Then the output of the MMSE filter given in Equation (15) can be written as ˜ −1 P PH R z = d1 ˜ −1 P 1 + PH R ˜ −1 P PH R 1 + NI 0, ˜ −1 P]2 2 [1 + PH R ˜ −1 P PH R 1 . + j NQ 0, ˜ −1 P]2 2 [1 + PH R
(18)
(19)
Having the output of the filter z in this form, it is straightforward to see that the probability of symbol error is given by [9] 3 (20) pe16QAM ≈ 3pˆ 1 − pˆ , 4 where
H ˜ −1 P P R , pˆ ≈ Q 5
where the Q-function is defined as 2 ∞ u 1 du . exp − Q(x) = √ 2 2π x
(21)
(22)
Equation (20) implicitly depends on codes, delays, and transmitted powers of the interfering ˜ To obtain an average value for the symbol error rate (SER), one user, through the matrix R. would average Equation (20) over these quantities. The (SER) can be related to the minimum mean squared error, Jmin , by writing Jmin as Jmin = 1 − PH R−1 P.
(23)
Substituting Equation (17) into Equation (23), we get Jmin =
1 ˜ −1 P 1 + PH R
(24)
MMSE Receiver Based CDMA System with Higher Order Modulation Formats 123 so that pˆ can be written as 1 − Jmin . pˆ ≈ Q 5Jmin
(25)
The symbol error rate for 16-QAM in terms of Jmin is obtained by substituting Equation (25) into Equation (20). It is straightforward to show that for BPSK and QPSK we have ˜ −1 P 2PH R (26) peBPSK ≈ Q peQPSK ≈ 2Q
˜ −1 P . PH R
(27)
The probabilities of symbol errors for BPSK and QPSK in terms of Jmin are given as 2(1 − Jmin ) peBPSK ≈ Q Jmin peQPSK ≈ 2Q
1 − Jmin Jmin
(28)
.
(29)
For the single user case, these results reduce to the well known results for an AWGN channel shown in many digital communications books such as [9] and [13]. Assuming that the system is using Gray coding, the bit error rate (BER) is given in terms of the SER by BER ≈
SER , log2 M
(30)
where M is the number of points in the constellation. For BPSK, QPSK, and 16-QAM, M equals 2, 4, and 16, respectively. The justification for the Gaussian approximation that is used throughout this paper is based on the central limit theorem by noting that the output of the filter is a sum of random variables with different probability density functions (pdfs). Therefore, the sum of these random variables at the output of the filter can be considered a Gaussian random variable. This approximation is widely used in evaluating the performance of conventional receivers [14] and is even more accurate with the MMSE receiver since we have less interference at the output of the filter and more Gaussian noise [11]. Poor and Verdu in [12] studied the behavior of the output of the MMSE receiver and found that the output is approximately Gaussian in many cases. Figures 2–4 show the performance of the MMSE receiver with BPSK, QPSK, and 16-QAM in a Gaussian channel for 1-, 20-, and 50-user CDMA systems. The semi-analytical results are based on the SER equations given in Equations (20), (26), and (27). The processing gains are 31, 62, 124 for BPSK, QPSK, and 16-QAM, respectively. These processing gains were chosen to ensure the full use of the available bandwidth by these systems. We will use these values of processing gains for the modulation formats considered in the rest of the paper. For a single user system, the bit error rate is the same for BPSK and QPSK and lower than Eb . When the load of the system increases to 20, the QPSK-based that of 16-QAM for a given N o
124 Ali F. Almutairi et al.
Figure 2. Semi-analytical performance of BPSK, QPSK, and 16-QAM in a Gaussian channel with one user.
CDMA systems outperforms the BPSK and the 16-QAM systems. The rate of improvement Eb increases. On the other hand, the 16-QAM system is faster for QPSK than for BPSK as N o Eb = 12 dB the 16-QAM BER becomes lower starts about 1 dB worse than BPSK but at N o than that of BPSK. With the load further increased to 50 users, both BPSK and QPSK reach a point at which the bit error rate will become flat as in ENbo increases. This basically means we can increase the load of the system by increasing the processing gain without increasing the bandwidth or decreasing the information rate by simply going to a higher order modulation. Therefore, there is a tradeoff between the information rate and higher load for multilevel modulations. We can explain the behavior of the MMSE in receiver as follows: When the CDMA system is using BPSK, at some loading point, the MMSE receiver will not have enough dimension, provided by the processing gain, to suppress all the interfering users. At this point, the MMSE receiver becomes interference limited, like the conventional matched filter receiver, and the performance cannot be improved by simply increasing the transmitted power. One way to overcome this is to increase the processing gain. To do so while keeping the bandwidth and information rate the same, one could choose a higher order modulation. In our case, QPSK would be the choice for a moderately-loaded system and 16-QAM would be the choice for a highly-loaded system. In addition, Figure 3 compares an LMS based MMSE receiver system performance for 20 users with the semi-analytical results. The figure shows a very good agreement between the simulation and the analytical BER for the different modulation schemes.
MMSE Receiver Based CDMA System with Higher Order Modulation Formats 125
Figure 3. Semi-analytical and simulation performances of BPSK, QPSK, and 16-QAM in a Gaussian channel with 20 users.
Figure 4. Semi-analytical performance of BPSK, QPSK, and 16-QAM in a Gaussian channel with 50 users.
126 Ali F. Almutairi et al. 4. Performance in a Fading Channel with Optimum Implementation of the MMSE Receiver In this section, we will extend the work of the previous section by investigating the performance of the three modulation formats, namely, BPSK, QPSK, and 16-QAM, in a fading channel. These different modulation formats are compared based on their BER performance at different loading conditions of the MMSE based CDMA system. We assume that the optimum MMSE filter is used and hence all the users’ fading processes are assumed to be known to the receiver. In the next section, the performance of the system when an adaptive MMSE filter implementation is used, will be investigated in detail. Assuming that the desired user’s phase is known exactly and that the received signal is phase corrected before being fed into the MMSE receiver, the input to the MMSE receiver can be written as ˆ
y(m) = e−j θ1,m r(m),
(31)
where θˆ1,m is the estimated phase of the desired user’s fading and here we assumed θˆ1,m = θ1,m . Substituting Equation (11) into Equation (31), the input to the MMSE receiver, y(m), can be written as y(m) = d1 (m)α1,mc1 +
K pj j =2
p1
αj,m ej θj,m [dj (m)
fj (l, δ)
gj (l, δ)] + n(m)e + dj (m − 1)
−j θˆ1,m
(32)
= d1 (m)α1,mc1 + y˜ where θj,m = θj,m − θˆ1,m . Next, the real and imaginary parts of the variable y(m) are taken and processed to find the I-channel and Q-channel desired user data. To find the desired user signal, we need to calculate the optimum tap weights for the I and Q channels. It is straightforward to show that the optimum tap weights for the I and Q channel filters are the same. Let the autocorrelation matrices for the I and Q channels received vectors, y1 and y2 , at the input of the be 1R1 and R2 and the steering vectors be P1 and P2 , respectively. MMSE filters ∗ We have E Re[d1 ]Re[d1 ] = 2 . In addition, the correlation vector P1 , the autocorrelation matrix R1 , and the tap weights vector a1 can be written as follows (dropping the dependence on m for convenience): P1 = E[Re[d1∗ ]y1 ] =
1 α1,m c1 = P2 4
1 2 ˜1 α c1 cH + R 2 1,m 1 ˜ 1 = R2 = PPH + R
R1 =
a1 = a2 = R1 −1 P1 = a,
(33)
(34)
(35)
MMSE Receiver Based CDMA System with Higher Order Modulation Formats 127 ˜ 1 = 1 R. ˜ The output of the where R˜1 = E[y˜1 y˜1 H ]. Note that since y˜ is circular symmetric R 2 filters can be written as z1 = aH y1 = Re[d1 ]P1 H R1 −1 P1 + P1 H R1 −1 y˜ 1
(36)
−1
= Re[d1 ]P1 R1 P1 + n˜ 1 . H
Now we need to find the value of P1 H R1 −1 P1 and the variance of n˜ 1 . Using the matrixinversion lemma, we can find the inverse of R1 as follows ˜ −1 2R . (37) R1 −1 = ˜ −1 P1 1 + P1 H R It can be shown that the variance of the term n˜ 1 is ˜ −1 P1 2P1 H R . (38) E[n˜ 1 n˜ H 1 ] = ˜ −1 P1 ]2 [1 + P1 H R With the gaussian assumption as before, the output of the modified MMSE receiver ˜ −1 P1 2P1 H R z = d1 −1 1 + 2P1 H R˜1 P1 ˜ −1 P1 2P1 H R (39) + NI 0, ˜ −1 P1 ]2 [1 + P1 H R ˜ −1 P1 2P1 H R . + j NQ 0, ˜ −1 P1 ]2 [1 + P1 H R Having the output of the filter z in this form, it is straightforward to show that the probability of symbol error for 16QAM conditioned in α1 is given by [9] 3 (40) pe/α1 = 3pˆe/α1 1 − pˆ e/α1 4 H ˜ −1 2 H ˜ −1 P P α c c R R 1 1 1 1 1 1 1 = Q . (41) pˆ e/α1 = Q 5 5 Averaging pˆ e/α1 over the probability density function (pdf) of the desired user’s fading amplitude, α1 , gives the expression for Pˆ as ∞ 2 H ˜ −1 α c c R 1 1 1 dα , (42) fα,m (α)Q pˆ ≈ 5 0 where fα,m (α) = 2α exp (−α 2 ) is the probability density function (pdf) of the desired user fading amplitude. A closed form solution for this integral can be obtained by performing the integration and changing variables, to get: c1 H R ˜ −1 c1 1 1 . 1− (43) pˆ = ˜ −1 c1 2 10 + c1 H R 1
128 Ali F. Almutairi et al.
Figure 5. The performance of BPSK, QPSK, and 16-QAM in a fading channel with 3 users with optimum MMSE receiver implementation.
The probability of symbol error for the 16-QAM is given by 3 p16QAM = 3pˆ 1 − pˆ . 4
(44)
For BPSK and QPSK modulation, the average symbol error rates can be derived in the same manner and they are given, respectively, by c1 H R ˜ −1 c1 1 1 (45) pBPSK = 1 − H ˜ −1 c1 2 2 + c1 R 1
pQPSK
c1 H R ˜ −1 c1 1 =1− . H ˜ −1 c1 4 + c1 R
(46)
1
Assuming that the system is using Gray coding, the bit error rate (BER) is given by BER ≈
SER . log2 M
(47)
These equations implicitly depend on the interfering user codes, delays, transmitted powers, ˜ To obtain an average value for SER or BER, one and fading amplitudes through the matrix R. would average over these quantities. To show the improvements of the systems employing higher order modulation formats, Figures 5–7 illustrate the performance, in terms of BER, of MMSE receiver based systems
MMSE Receiver Based CDMA System with Higher Order Modulation Formats 129
Figure 6. The theoretical performance of BPSK, QPSK, and 16-QAM in a fading channel with 30 users with optimum MMSE receiver implementation.
Figure 7. The theoretical performance of QPSK , and 16-QAM in a fading channel with 60 users with optimum MMSE receiver implementation.
130 Ali F. Almutairi et al. with BPSK, QPSK, and 16-QAM modulation formats in a fading channel. These figures are based on the semi-analytical results obtained previously. The received powers were modeled as a lognormal with zero mean and 1.5 dB standard deviation. The BER performance of the Eb is shown in Figure 5 for the different modulation formats. 3-user system as a function of N o The theoretical and simulation based performances are in agreement. The performance of the 16-QAM degrades by 3 dB compared to that of the QPSK and BPSK performance, which have the same performance for such loading. When the load of the system increases to 30 users, as shown in Figure 6, the performance of the system that is based on BPSK degrades rapidly. In this case, an error floor is introduced and the performance of the system cannot Eb Eb . The 16-QAM system outperforms the QPSK system for N be improved by increasing N o o greater than 18 dB. When the system loading is further increased to 60 users as shown in Figure 7, the QPSK based system loses its ability to suppress the new level of interference and an error floor results, while the 16-QAM system still operates effectively.
5. Performance in a Fading Channel with an Adaptive Implementation of the MMSE Receiver In the previous section an optimum implementation of the MMSE receiver was assumed when we investigated the performance of the system in a fading channel. The optimum receiver is impractical and hard to construct because it assumes that the powers, the fading processes, the time delays, and the spreading sequences of all users are known. An adaptive MMSE receiver based on the LMS algorithm can be used as a practical alternative to implement the MMSE receiver. In addition the desired user’s fading process is estimated to provide the receiver with the phase and amplitude references to demodulate the desired user’s signal. The estimation of the desired user’s fading process is accomplished through the use of a technique based on linear prediction and pilot symbols described in detail in [1] and [2]. The modified MMSE receiver structure, which are used to demodulate the desired user’s signal, is shown in Figure 8. Figures 9–11 are respectively the BER performance of MMSE receiver base systems with BPSK, QPSK, or 16-QAM modulation formats in a slowly fading channel for 3-, 30-, and 60-user CDMA systems. In generating these figures, the following simulation environment was chosen. The mobile operated in the 900 MHz band, with a speed of 5 mph. The bit rate was 9600 bps, and a pilot symbol was sent every 10th symbol. This corresponds to fd Ts of 0.0028, 0.0014, 0.007 for 16-QAM, QPSK, and BPSK, respectively. The received powers were modeled as a lognormal distribution with zero mean and 1.5 dB standard deviation. The receiver structure shown in Figure 8 has been used. The BER performance of the 3-user system as a function of Eb /No is shown in Figure 9 for the three different modulation formats. As expected, the CDMA system with BPSK modulation outperforms the other systems. In this case there is no advantage of using higher order modulations since using higher order modulations will require more transmitted power to achieve the same BER. When the load of the system increases to 30 users, as shown in Figure 10, the performance of the BPSK-based system degrades rapidly. In this case, an error floor is introduced and the performance of the system cannot be improved by increasing Eb /No . When the system loading is further increased to 60 users as shown in Figure 11, the QPSK based system loses its ability to suppress the new level of interference and an error floor results. The 16 QAM-based system can still suppress the MAI in this case.
MMSE Receiver Based CDMA System with Higher Order Modulation Formats 131
Figure 8. The modified MMSE structure.
Figure 9. The performance of BPSK, QPSK, and 16-QAM in a slow fading channel with 3 users, fading estimated.
132 Ali F. Almutairi et al.
Figure 10. The performance of BPSK, QPSK, and 16-QAM in a slow fading channel with 30 users, fading estimated.
Figure 11. The performance QPSK (known fading), and 16-QAM (known and estimated fading) in a slow fading channel with 60 users.
MMSE Receiver Based CDMA System with Higher Order Modulation Formats 133 6. Conclusion In this paper, we have studied the performance of an MMSE receiver based CDMA system in AWGN and fading channels with BPSK, QPSK, and 16QAM modulation formats. It has been found that for the same bandwidth and information rate, the QPSK and 16QAM-based systems outperform the BPSK-based system when the load of the system is high. This performance improvement is made possible by increasing the processing gain and hence the ability of the MMSE receiver to suppress the multiple access interference. In this context, for MMSE receiver based CDMA system, one should look at higher order modulations as a mean to increase the bandwidth efficiency not only by transmitting more bits in the available bandwidth but also by allowing more users to use the bandwidth.
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Ali F. Almutairi, “Design Issues for Minimum Mean Square Error (MMSE) Receiver-Based CDMA Systems”, Ph.D. Thesis, University of Florida, May 2000. Ali F. Almutairi, Scott L. Miller and Haniph L. Latchman, “Tracking of Multilevel Modulation Formats for DS/CDMA System in a Slowly Fading Channel”, DIMACS Series in Discrete Mathimatics and Theoretical Computer Science, Vol. 52, pp. 19–29, 1999. B. Predrag, B. Rapajic and S. Vucetic, “Adaptive Receiver Structures for Asynchronous CDMA Systems”, IEEE Journal on Selected Areas in Communications, Vol. 12, No. 4, pp. 685–697, 1994. Afonso N. Barbosa and Scott L. Miller, “Adaptive Detection of DS/CDMA Signals in Fading Channels”, IEEE Transactions on Communications, Vol. 46, pp. 115–124, 1998. James K. Caves, “An Analysis of Pilot Symbol Assisted Modulation for Rayleigh Fading Channels”, IEEE Trans. on Veh. Technol., Vol. 40, pp. 686–693, 1991. Pooi Yuen Kam and Cho Huak Teh, “Reception of PSK Signals over Fading Channels via Quadrature Amplitude Estimation”, IEEE Transactions on Communications, Vol. 31, pp. 1024–1027, 1983. James K. Caves, “Pilot Symbol Assisted Modulation and Differential Detection in Fading and Delay Spread”, IEEE Transactions on Communications, Vol. 43, pp. 2206–2212, 1995. Y.S. Kim, C.J. KIM, G.Y. Jeong, Y.J. Bang, H.K. Park and S.S. Choi, “New Rayleigh Fading Channel Estimator Based on PSAM Channel Sounding Technigue”, in Proc. of IEEE Int. Conf. on Commun. ICC’97, Montreal, Canada, June 1997, pp. 1518–1520. Israel Korn, Digital Communications, Van Nostrand Rienhold Company Inc, 1985. Upamanyu Madhow and Michael L. Honig, “MMSE Interference Suppression for Direct-sequence Spreadspectrum CDMA”, IEEE Transactions on Communications, Vol. 42, pp. 3178–3188, 1994. Scott L. Miller, “An Adaptive Direct-sequence Code-division Multiple-access Receiver for Multiuser Interference Rejection”, IEEE Transactions on Communications, Vol. 43, pp. 1746–1755, 1995. H. Vincent Poor and Sergio Verdú, “Probability of Error in MMSE Multiuser Detection”, IEEE Transactions on Information Theory, Vol. 43, pp. 858–871, 1997. Joan G. Proakis, Digital Communications, McGraw-Hill, 1995. Michael B. Pursley, “Performance Evaluation for Phase-coded Spread-spectrum Multiple-access Communication – Part I: System Analysis, IEEE Transactions on Communications, Vol. 25, pp. 795–799, 1977. S. Sampei and Terumi Sunaga, “Rayleigh Fading Compensation for QAM in Land Mobile Radio Communications”, IEEE Trans. on Veh. Technol., Vol. 42, pp. 137–147, 1993. P.K. Shamain and L.B. Milstein, “Using Higher Order Constellations with Minimum Mean Square Error (MMSE) Receiver for Severe Multipath CDMA Channel”, Personal, Indoor, and Mobile Radio Communications, pp. 1035–1038, 1998. Prasad Shamain and Laurence B. Milstein, “Minimum Mean Square Error (MMSE) Receiver Employing 16QAM in CDMA Channel with Narrowband Gaussian Interference”, in Proceeding of 1999 IEEE Military Communications Conference, 1999.
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Ali F. Almutairi received the B.S. degree in electrical engineering from the University of South Florida 1993, Tampa, Florida, in 1993. In December 1003, he has been awarded a full scholarship from Kuwait University to pursue his graduate studies. He received M.S. and Ph.D. degrees in electrical engineering from the University of Florida, Gainesville, Florida, in 1995 and 2000, respectively. At the present, he is an assistant professor at Electrical Engineering Department, Kuwait University and director of the Wireless Communication Networks Laboratory. His current research interests include CDMA system, multiuser detection, cellular networks performance issues, coding and modulation. Dr. Almutairi is a member of IEEE and other professional societies and served as a reviewer for many technical papers.
Dr. Haniph A. Latchman is a Rhodes Scholar and received his Ph.D. from Oxford University in 1986 and his Bachelor of Science degree (First Class Honors) from the University of The West Indies-Trinidad and Tobago, in 1981. Dr. Latchman joined the University of Florida in 1987 where he teaches graduate and undergraduate courses and conducts research in the areas of control systems, communications and computer networks and is Director of the Laboratory for Information Systems and Telecommunications (LIST). Dr. Latchman has received numerous teaching and research awards, including the University of Florida Teacher of the Year Award, two University-wide Teaching Improvement Program Awards, College of Engineering Teacher of the Year Awards, the IEEE 2000 Undergraduate Teaching Award, the Boeing Summer Faculty Fellowship in 2000 and a 2001 Fulbright Fellowship. He is a Senior Member of the IEEE and has published over 100 technical journal articles and conference proceedings and given numerous conference presentations in the areas of his research in multivariable and computer control systems, and communications and internetworking. He has also directed sponsored research grants totaling some $3.5M and he is the author of the books Computer Communication Networks and the Internet, published by McGraw Hill and Linear Control
MMSE Receiver Based CDMA System with Higher Order Modulation Formats 135 Systems – A First Course, published by John Wiley. Dr. Latchman is also an Associate Editor for the IEEE Transactions on Education and served as Guest Editor for Special Issues of the International Journal of Nonlinear and Robust Control, the IEEE Communications Magazine and the International Journal on Communication Systems.
Tan F. Wong received the B.Sc. degree (1st class honors) in electronic engineering from the Chinese University of Hong Kong in 1991, and the M.S.E.E. and Ph.D. degrees in electrical engineering from Purdue University in 1992 and 1997, respectively. He was a research engineer working on the high speed wireless networks project in the Department of Electronics at Macquarie University, Sydney, Australia. He also served as a post-doctoral research associate in the School of Electrical and Computer Engineering at Purdue University. He is currently an assistant professor of electrical and computer engineering at the University of Florida. His research interests include spread-spectrum communication systems, multiuser communications, and wireless cellular networks.
Minkyu Lee received the M.S. degree in electrical and computer engineering from University of Florida in 1999. He is currently working toward the Ph.D. degree in electrical and computer engineering at University of Florida. His research interests are in the area of power line home network to support the Qos and to design then next generation protocol.
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Scott Miller (S ’87–M ’88–SM ’97) was born in Los Angeles California in 1963. He received the B.S., M.S., and Ph.D. degrees in electrical engineering from the University of California at San Diego (UCSD) in 1985, 1986, and 1988 respectively. He then joined the Department of Electrical and Computer Engineering at the University of Florida, where he was an Assistant Professor from 1988 through 1993 and an Associate Professor from 1993 through 1998. In August 1998 he joined the Electrical Engineering Department at Texas A&M University where he is currently a Professor. He has also held visiting positions at Motorola Inc., University of Utah and UCSD. His current research interests are in the area of wireless communications with a special emphasis on CDMA systems. He has taught courses at both the graduate and undergraduate level on such topics as signals and systems, engineering mathematics, digital and analog communications, probability and random processes, coding, information theory, spread spectrum, detection and estimation theory, wireless communications, queueing theory and communication networks. He has published over 75 refereed journal and conference papers on a variety of topics in the area of digital communication theory. He is a senior member of the IEEE and an Editor for the IEEE Transactions on Communications. His hobbies include tennis, swimming and cycling.
