dB.)
receiver in weak interference. Figure 2.3 shows the BER vs. for ten equicorrelated users ( ). The single-user receiver suffers from MAI and perform poorly in most cases. The linear receivers perform similarly to the ML receiver when the number of users is small.
§ 2.3 Interference Cancellation Methods
The interference cancellation scheme first estimates interference from other users and then can-cels it from the received signal. Let be the interference cancelled signal for User. We then have
(2.15)
(a) (b) (c)
(d) (e) (f)
yj yj
yj
yj
yj
yj
gj gj gj
gj gj gj
aj aj
aj aj aj
aj
− aj
−
aj
−
aj
−
aj
−
Figure 2.4: Interference estimate functions. (a) Soft-decision function (b) Hard-decision func-tion (c) Null-zone funcfunc-tion (d) Hyperbolic tangent funcfunc-tion (e) Unit-clipper funcfunc-tion (f) Modi-fied unit-clipper function.
where represents the interference estimate of
. The number of interference cancelled in (2.15) depends on the algorithm used. For description simplicity, we assume a two-stage cancellation scheme such that
, where is a decision function. Commonly used decision functions are summarized in Fig. 2.4. Note that channel gains are assumed to be known. The second stage output is obtained by
(2.16)
The decision functions in Fig. 2.4 are further described below.
(a) Soft-decision function: (b) Hard-decision function:
sgn
Matched filter bank
Figure 2.5: Block diagram for an SIC receiver.
(c) Null-zone function:
(d) Hyperbolic tangent function:
represents the power of interference and noise for theth user.
(e) Unit-clipper function:
(f) Modified unit-clipper function:
In the following, we describe the basic types of interference cancellation schemes, namely, SIC and PIC.
First stage Second stage y1
y2
y3
ˆ ( )1
s n
ˆ ( )2
s n
ˆ ( )3
s n
z1
z2
z3 2
,
C1
1 ,
C2
1 ,
C3
2 ,
C3 3 ,
C1
3 ,
C2
Respreading Matched
Filter
Matched Filter
Matched Filter
Respreading
Respreading
Matched Filter
Matched Filter
Matched Filter
ˆ1
b
ˆ2
b
ˆ3
b ( )
r n
Figure 2.6: Block diagram for a general two-stage partial SPIC receiver.
§ 2.3.1 Successive Interference Cancellation
The SIC cancels one user interference from the received signal at a time. Since only one inter-ference needs to be estimated and subtracted in each stage, the strongest user signal is then the best candidate. It’s structure is depicted in Figure 2.5. Assume that the received signal powers are ranked as
, and the interference cancelled signal for userat theth stage is obtained as
(2.17) where
, for allis the initial receive signal. The SIC output at theth stage is then
(2.18)
Although the SIC is simple to apply, there are some drawbacks listed below.
Since the user is detected successively, the subsequent users will experience less interfer-ence. To make all users have similar performance, transmission power for each user will be different. A proper power profile may not be easy to obtain. In addition, the power ordering operation requires additional computational complexity.
The interference resulted from the erroneous cancellation will propagate to all the users at following stages. This introduces the error propagation effect.
First stage Second stage
1 1
a C
2 2
a C
3 3
a C Respreading
Matched Filter
Matched Filter
Matched Filter
Respreading
Respreading
Matched Filter
Matched Filter
Matched Filter
(2)
ˆ1
b
(2 )
ˆ2
b
( 2)
ˆ3
b
(1)
ˆ1
b
(1)
ˆ2
b
(1)
ˆ3
b
ˆ ( )1
s n ( )
r n
y1
y2
y3
ˆ ( )2
s n
ˆ ( )3
s n
Figure 2.7: Block diagram for a two-stage coupled partial HPIC receiver.
A SIC scheme needs at least stages for a -user environment. This will greatly in-crease the detection delay especially when the user number is large.
§ 2.3.2 Parallel Interference Cancellation
The PIC cancels interference from all other users at the same time. In contrast to SIC, the PIC has lower detection delay and does not have the power assignment problem. It has been shown that the PIC has superior performance over the SIC in an power balanced scenario. Conventional PIC receivers permit a full cancellation of the MAI. One problem associated with this full PIC is that the MAI estimate may not be reliable in the earlier canceling stages. This makes the PIC less effective when the number of users is large. As a remedy, the partial PIC detector has been proposed in which partial cancellation factors (PCFs) are introduced to control the interference cancellation level. As shown in 2.6, a complete partial PIC requires PCFs for one stage where is the number of users; the computational complexity is high. Simplified partial PICs have been proposed, in which only PCFs are needed. Two structures are commonly used for simplified partial PICs; we call them the coupled and decoupled structures. In the coupled structure, each user output is influenced by all PCFs [62] as seen in Figure 2.7, while in the decoupled structure each user output is only influenced by a specific PCF as shown
First stage Second stage
Figure 2.8: Block diagram for a two-stage decoupled partial SPIC receiver.
in Figure 2.8. The partial HPICs mentioned in Chapter 1 all use the coupled structure. A MSE criterion, as shown below, has been proposed to optimize PCFs [57].
!
where" is the error probability for theth user. As we can see, each PCF can be determined independently. From (2.19), we can observe that when the data bits are all correctly detected, the optimal PCFs will approach unity. On the other hand, when the data bits are all erroneously detected, ("
), the optimal PCFs will approach zero. This is intuitively appealing.
Although simple, the optimal PCFs in (2.19) are not accurate for short codes. Thus, its real-world application is limited.
The optimal PCF obtained by theoretical calculation may not be efficient when the channel is time-varying. There exist an adaptive partial HPIC that can overcome this problem [62]. This adaptive HPIC is blind in the sense that no training sequence is required. Due to its simplicity
r(n)
e(n) ˆ( ) +
r n x1(n)
1( )n χ
2( )n χ
K( )n χ ˆ1
b
ˆ2
b
ˆK
b LMS weight
update equation
1( ) w n
2( ) w n
K( ) w n Matched
Filter
x2(n)
xK(n)
x1(n)
x2(n)
xK(n)
First stage Second stage
Matched Filter
Matched Filter
Figure 2.9: LMS algorithm for two-stage adaptive blind partial HPIC receivers.
and robustness, the LMS algorithm was used as the adaptive algorithm. A typical block diagram for a two-stage HPIC is shown in Fig. 2.9. The weights are trained using the LMS algorithm which minimizes a MMSE criterion defined as (for theth stage)
#
(2.20)
where is the optimal weight vector at theth stage, and
#
$
(2.21)
The weight after trained, $
, acts as each user’ PCF. Note that this is a system identifi-cation problem. The LMS update equation for the th stage (with stages of interference cancellation) is formulated as
%
(2.22)
%
5 10 15 20 25 30 10−2
10−1 100
User number
BER
Conv. receiver LMMSE SIC Full HPIC Full SPIC Partial HPIC (C
k=0.6) partial SPIC (C
k=0.3)
Figure 2.10: BER performance comparison for different multiuser receivers (,
dB, and power balanced).
where
is the input vector. The interference estimate for theth user in the-stage is given by
$
(2.23)
Then the-stage output from the adaptive blind partial HPIC can be obtained
(2.24)
Note that the adaptive blind partial HPIC is different from the work in [17], since this scheme does not require the training sequence. The optimal weights are optimized in one bit interval;
its adaptation is on the chip-level.
As to the partial SPIC, both the coupled and decoupled structures have been studied. In this dissertation, we focus on the decoupled structure which is shown in Figure 2.8. The reason to consider this structure is that the PCF optimization is simpler and its performance is comparable
Table 2.1: Required information for different multiuser receivers.
SU ML MBER DEC LMMSE AMMSE IC
Desired user’s signature
Desired user’s timing
User amplitude
noise variance
Others’ signature
Others’ timing
Training data
SU : Single-user receiver
ML : Maximum-likelihood receiver MBER : Minimum BER receiver DEC : Decorrelator
LMMSE : Linear mean square error receiver AMMSE : Adaptive LMMSE
IC : Interference cancellation receiver
to other structures. We have carried out simulations to compare performance of various two-stage PIC with LMMSE receivers. The result is shown in Figure 2.10 (,dB, and power balance is assumed). The LMMSE performs the best among all multiuser receivers.
The SIC has only minor advantage over the single-user receiver. This is because in the power balanced scenario, the power ranking does not have advantages. The full HPIC performs better than SIC. Note that the full SPIC perform poorly when the user number increases. Partial PICs with optimal PCFs perform much better and the partial SPIC performs similarly to the LMMSE receiver. In Table 2.1 we summarize requirement information for various MUD methods.