6.5 Simulation Results
6.5.3 Comparison of Code Assignment Strategies
Figures 6.3(a) and 6.3(b) show the received Eb/N0 and the call admission rate of the RM, CM, and IA+CF code assignment strategies with various effective traffic loads.
We have following observations. First, comparing to RM, the IA+CF method has better received Eb/N0 when 0.75 ≤ ρ ≤ 2.25. However for ρ ≥ 2.5, IA+CF has lower received Eb/N0 due to the increasing MAI by accommodating more users than RM. Second, comparing to CF, the IA+CF method has better Eb/N0 at the cost of a slightly lower call admission rate. For ρ = 2, the Eb/N0 improvement of the IA+CF method over the CF method is 1.9 dB, while the call admission of IA+CF is 1.6% lower than CF. The reason why the call admission rate for the IA+CF method is slightly lower than that of the CF method can be explained as follows. The CF method can make the tree structure of the allocated codes more compact, gather more larger code resources for higher-rate users, thereby increasing the admission rate. The IA+CF method aims to avoid MAI first before executing the CF principle. Third, one can
−200 −15 −10 −5 0 5 10 15 20 50
100 150 200 250 300 350 400
Fig. 6.2: An illustration example of approximating MAI by Gaussian distributed random variable.
The time- and frequency-domain spreading factors of the reference and single interfering users are SF = 16 and M = 8, respectively.
also find that for 1 ≤ ρ ≤ 2.25 the IA+CF method has highest received Eb/N0, the RM method ranks second, and the CF method has the lowest Eb/N0. Fourth, as the traffic load increases, the difference between the IA+CF and CF methods, in terms of both the received Eb/N0 and call admission rate, becomes smaller. For example, the difference of Eb/N0 between the two methods decreases from 1.9 dB to 0.1 dB as ρ changes from 2 to 5.5; the call admission rate appears to be the same at ρ = 5.5.
This is because when there are more active users in the system, the IA+CF method can not easily find a good code with low interference for a new coming user. In this situation, the IA+CF method picks a code according to the CF principle.
6.6 Chapter Summary
In this chapter, we have proposed a novel interference avoidance code assignment strategy for multi-rate MC-DS-CDMA with TF-domain spreading. We analyze the error rate performance and defined new performance metric MAI coefficient to estimate the quantity of MAI imposed on each code channel. By simulations and analysis, we demonstrate that the proposed interference avoidance code assignment method can effectively reduce the MAI for multi-rate users in an MC-DS-CDMA system with time- and frequency-domain spreading, while maintaining the high call admission rate.
0.75 16 1.5 2 2.5 3 3.5 4 4.5 5 5.5 7
8 9 10 11 12
Effective traffic load (ρ) Average E b/N 0 (dB)
IA+CF
RM
CF
(a) Average received Eb/N0 (dB)
0.75 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5
40 50 60 70 80 90 100
Effective traffic load (ρ)
Average call admission rate (%)
CF IA+CF
RM
(b) Average admission rate
Fig. 6.3: Comparison of the average received Eb/N0 and call admission rate against the effective traffic load for the RM, CF, and the IA+CF code assignment strategies, where the code pattern is [ 1 1 2 8 ], Eb/N0 = 12 dB at the transmitter, and the required received Eb/N0= 5 dB.
Chapter 7
Joint Subcarrier Power Allocation and Interference Avoidance Code Assignment
for Downlink MC-DS-CDMA
In this chapter, we cooperate a subcarrier power allocation and the interference avoid-ance code assignment in Chapter 6 to solve the challenging problem how to max-imally benefit from a particular subcarrier power allocation, while simultaneously controlling the MAI at an acceptable level and maintaining a high call admission rate in the downlink multi-rate multi-carrier direct sequence code division multiple access (MC-DS-CDMA) system with time- and frequency-domain (TF-domain) spreading.
To achieve this goal, a subcarrier power allocation is first proposed to optimize the received signal power. By analyzing the error rate performance in the presence of the subcarrier power allocation, we can define the same MAI coefficient as that in Chapter 6. This means the interference code assignment method proposed in Chap-ter 6 can also be applied together with the subcarrier power allocation. Thus, in the proposed joint scheme, the interference avoidance code assignment plays the role to eliminate MAI and the subcarrier power allocation is to optimize the received signal power.
7.1 System Model
7.1.1 Transmitted Signal
The transmitter structure in the MC-DS-CDMA system with time- and frequency-domain spreading is shown in Fig. 5.1. A serial-to-parallel converter is applied to reduce the subcarrier data rate by converting data streams with bit duration Tb,k(X) into U reduced-rate parallel substreams with new bit duration Tk(X) = UTb,k(X) for user k in group X ∈ {Ao, Bo, Co}. Each substream experiences a frequency flat (or non-dispersive) fading. Then, for each substream, a spreading code g(X)k (t) is used to spread data signal in the time domain. After being copied to M subcarriers, the data in each substream is multiplied by a frequency domain spreading code {c(X)k [j]}. In this case, the frequency-domain spreading gain is M. The user group X is defined as follows. Let go(t) and co[j] be the time domain spreading code and the frequency do-main spreading code of the reference user, respectively. Following [44], we categorize the interfering users into three groups:
1. group Ao: 1
where Pk,i,j(X), {fi,j} and {ϕ(X)k,i,j} represent the transmitted power, the j-th subcarrier frequency and the initial phase in the i-th substream, respectively. The waveform of
the i-th substream b(X)k,i (t) = P∞
h=−∞b(X)k,i [h]PT(X)
k (t − hTk(X)) contains a rectangular pulses of duration Tk(X), where b(X)k,i [h] = ±1 with equal probability. The time domain spreading code gk(X)(t) = P∞
`=−∞gk(X)[`]PTc(t − `Tc) represents the chip sequence of the rectangular pulses of duration Tc, where gk(X)[`] = ±1 with equal probability. Note that the time domain spreading factor of user k in the group X is G(X)k = Tk(X)/Tc.
7.1.2 Received Signal
The receiver structure of the MC-DS-CDMA using time-domain and frequency-domain spreading codes is shown in Fig. 5.2. Recall that each substream experiences the flat Rayleigh fading. Then, the received signal of the reference user (denoted by ro) in the synchronous transmission can be expressed as:
ro(t) =
where Po,i,j and αo,i,j are the reference user’s transmission power and the channel amplitude for the i-th subcarrier of the j-th substream; KX is the number of users in the group X; and n(t) is the white Gaussian noise with double-sided power spectrum density of N0/2. In (7.2), φo,i,j = ϕo,i,j + ψo,i,j is uniformly distributed in [0, 2π), where ψo,i,j is the channel’s phase of the i-th subcarrier in the j-th substream.
Without loss of generality, let the bit of interest be bo,s[0], i.e. the first bit in the s-th substream from the reference user. After time domain despreading, the output signal for the reference user in the v-th subcarrier of the s-th substream can
be expressed as: where To is the bit duration of the reference user; βo,s,v is the weights for a certain combining scheme; Ik,s,v(X) denotes the MAI induced from user k of group X to the v-th subcarrier of the s-th substream of the reference user; and ns,v is the white Gaussian noise with zero mean and variance of |βo,s,v2 |2NT0o. The MAI terms Ik,s,v(X) in (7.3) can be Then combining M subcarriers, the decision variable of bo,s[0] for the reference user becomes
In (7.5), we face the problem to simultaneously maximize the desired signal’s power and eliminate the MAI. One should note that as a user maximizes its received signal power by a particular subcarrier power allocation, it may result in excessive MAI to other users. The MAI occrus when user k adjusts Pk,s,v(X) according to α(X)k,s,v. It
is difficult to please each user just by this particular subcarrier power allocation. One of the goals in this chapter is to find a method to improve the desired signal quality and control MAI.