Multi-Carrier and Spread Spectrum Systems: From OFDM and MC ...

RF Issues 1994.7.2.1 Effects of Non-linear Distortions in DS-CDMA and MC-CDMAThe fact that multi-carrier CDMA transmission is more sensitive to HPA non-linearitiesthan single-carrier CDMA transmission is valid in the single-user case, i.e. in the uplinktransmitter. However, for the downlink the situation is different. The downlink transmittedsignal is the sum of all active user signals, where the spread signal for both transmissionschemes (single-carrier or multi-carrier) will have a high PAPR [23]. Therefore, for thedownlink both systems may have quite similar behavior. To justify this, we additionallyconsider a single-carrier DS-CDMA system, where the transmitter consists of a spreader,transmit filter, and the HPA. The receiver is made out of the receive filter and the despreader,i.e. detector. The transmit and receive filters are chosen such that the channel isfree of inter-chip interference when the HPA is linear. For instance, raised cosine filterswith the roll-off factor α, equally split between the transmitter and receiver side, can beconsidered.For both systems, conventional correlative detection is used. As disturbance, we consideronly the effects of HPAs in the presence of additive white Gaussian noise. In orderto compensate for the effects of the HPA non-linearities, an automatic gain control (AGC)with phase compensation is used in both systems. This is equivalent to a complex-valuedone tape equalizer. Both schemes use BPSK modulation. The processing gain for MC-CDMA is P G,MC = 64 and for DS-CDMA P G,DS = 63. The total number of users is K.The non-linear HPA can be modeled as a memory-less device [77]. Let x(t) = r(t)e −jϕ(t) be the HPA complex-valued input signal with amplitude r(t) and phase ϕ(t).Thecorresponding output signal can be written asy(t) = R(t) e −jφ(t) , (4.87)where R(t) = f(r(t))describes the AM/AM conversion representing the non-linear functionbetween the input and the output amplitudes. The AM/PM distortion (t) = g(r(t),ϕ(t)) produces additional phase modulation. In the following, we consider two types ofHPAs, namely a TWTA and a SSPA, which are commonly used in the literature [77].The non-linear distortions of HPAs depend strongly on the output back-off (OBO):OBO = P satP out, (4.88)where P sat = A 2 sat represents the saturation power and P out = E{|y(t)| 2 } is the meanpower of the transmitted signal y(t). Small values of the OBO cause the amplifier operationpoint to be near saturation. In this case a good HPA efficiency is achieved, but asa consequence the HPA output signal is highly distorted.HPA modelsTraveling Wave Tube Amplifier (TWTA)For this type of amplifier the AM/AM and AM/PM conversions are [77]R n (t) =2r n(t)1 + rn 2(t) ,φ(t) = ϕ(t) + π/3r2 n (t)1 + rn 2 , (4.89)(t)