Analysis of MIMO with Zero Forcing Successive Interference Cancellation Equalizer

Analysis of MIMO with Zero Forcing Successive Interference Cancellation Equalizer

Ashwinder Singp, Navtej Singh Sandhu2 , Jaspinder Singp ,

1. ech Student1 Guru Nanak Dev University, Amritsar, M.Tech Student2 Guru Nanak Dev University Amritsar, M.Tech Student3 Guru Nanak Dev University Amritsar

   Abstract This paper contain some advance d applic ation of MIMO systems and some main notes in their i mple mentations, which star te d by MIMO wi th ZF techni que that investigate the effec ts of phase noise in centr alized and distri bute d narr owband MIMO systems, and discuss the fe asibility of phase and fre quenc y sync hronizati on pr oble m. An e qualizer, called successive interference cancellation zero-forcing equalizer (SIC-ZFE) is pr oposed. The pr oposed equalizer pr ovi des ISI-free c ommunicati ons over the IS I MIMO channels without a long guar d peri od. The simulate d results wi th the 2 ×2 MIMO syste m wi th zero forcing e qualizer showe d matchi ng results as obtaine d in for a 1 ×1 system for BPS K modul ation in Rayleigh channel. In this paper , we will try to i mpr ove the bit error r ate perfor mance by tr ying out Successive Interference Cancellati on (SIC). We will assume that the c hannel is a flat fading Rayleigh multi path c hannel and the modulation is BPSK. Simulati on results show that e ve n with only one selected antenna at the recei ver , perfor mances in terms of B ER still satisfactory. Ne ver theless, when more ante nnas are selected, better B ER val ues are achie ve d thanks to recei ve di versity.

   Key Words —– MIMO, Successive Interference cancellation, Zero Forcing, Simulati on, Alg orithm.

   1. IN TR OD UCTION

      Multiple antennas communications are a new trend for high speed wireless communications. Algorithms for mu ltip le antennas systems, like V-BLAST [1] and space- time block codes [2,3] , were proposed. These algorithms work we ll with flat fading channels but, with the increasing channel bandwidth, consideration in selective fading becomes viable. Migrating to selective fading channel imp lies that the space-time rece iver will need to eliminate the inter-symbol interference (ISI), and at the

      same time resolve the inter-block interference (IBI) problem. IBI can be avoided by inserting a long guard period between each block of transmitted signals [4-6]. However, this guard period is a kind of transmission redundancy, which consumes the system bandwidth. This bandwidth consumption proble m will be even more severe for the channel with high dispersion.

      Recently, a pro mising system known as Space-lime Modulated Codes (STMC) is proposed by Xia [7]. STMC is a special type of the space time block codes for selective fading MIMO channel. The STMC systems resolve the IBI proble m with a rela xed guard period require ment. Hence, it avoids the degradation of system throughput suffered by most of the block b ased transmission system.

      Based on FIR-ZFE, we p roposed a new equalize r, called Successive Interference Z2m-Forc ing Equalizer (SICZFE), which inherited a ll the advantages of FIR- ZFE. The SIC-ZFE improves the performance of the FIR-ZFE system by introducing the successive interference cancellat ion technique within each signal vector. As a result, even if there a re any detection errors, it will only affect the current signal vector. Therefore, the GSIC-ZFE is free fro m error p ropagation problem when compared to the DFE technique considered in [7]. Rather than the traditional ele ment- by-ele ment interference cancellation mechanism, a successive interference cancellation process is proposed in SIC-ZFE for reducing the computational comple xity. Consider a STM C system with K sub-channels. If we only detect and cancel one element in each interference cancellation, K iterations will be required for detecting the whole signal vector. Thanks to the nice parallel equalization structure of FIR-ZFE. It is possible to choose any number of elements to be equalized in iteration of interference cancellation. For e xa mp le, if K ele ments are detected and canceled in each iterat ion, the number of iterations will be reduced to [K/K]a, n d hence the computational comple xity will be reduced by

      approximately K times. Simulat ion results showed that significant imp rovement over FIR-ZFE can be obtained, even if only two iterations of interference cancellation are performed for each signal vector.

   2. 2×2 MIMO channel

      In a 2×2 MIM O channel, probable usage of the available to transmit antennas. Consider that we have a

      transmission sequence, for exa mp le . In norma l transmission, we will be sending in the first time slot, in the second time slot, and so on. However, as we now have 2 transmit antennas, we may group the symbols into groups of two. In the first time slot, send and fro m the first and second antenna. In second time slot, send and fro m the first and second antenna, send and in the third time slot and so on. Notice that as we are grouping two symbols and sending them in one time slot, we need only n/2 time slots to complete the transmission data rate is doubled. This forms the simple e xp lanation of a probable MIMO transmission scheme with 2 transmit antennas and 2 rece ive antennas.

      Figure 1: To Transmit to Receive (2×2) MIMO channel

   3. Ze ro forcing equalizer for 2×2 MIMO channel

      Let us now try to understand the math for e xtracting the two symbols which interfered with each other. In the first time slot, the received signal on the first receive antenna

      is (1)

      The received signal on the second receive antenna is

      (2)

      fro m transmit antenna to receive antenna, is the channel fro m transmit antenna to

      receive antenna, is the channel from transmit antenna to receive antenna, , are the

      transmitted symbol.

      The equation can be represented in matrix notation as

      (3)

      Equivalently, To solve for , The Zero Forcing (ZF) linear detector for meet ing this constraint . is given by,

      (4)

   4. Zer o Forcing wi th Successive Interference Cancellation (ZF-S IC)

      Using [9]the Zero Forc ing (ZF) equalizat ion approach described above, the receiver can obtain an estimate of the two transmitted symbols , i.e.

      (5)

      Take one of the estimated symbols (for e xa mp le ) and subtract its effect from the received vector and

      (6)

      (7)

      The above equation is same as equation obtained for receive diversity case. Optima l way of co mb ining the informat ion fro m mu ltiple copies of the received symbols in receive diversity case is to apply Maxima l Ratio Co mb ining (M RC).

      where[8]

      , are the received symbol on the first and second antenna respectively, is the channel fro m transmit antenna to receive antenna , is the channel

      (7) This forms the simp le e xp lanation for Zero Forc ing Equalizer with Successive Interference Cancellation (ZF-SIC) approach.

      Figure 2: S IC-ZFE Algorithm

   5. SIMULATION

      In this section first Generate random b inary sequence of

      +1s and -1s. Group them into pair of t wo symbols and send two symbols in one time slot then Multiply the symbols with the channel and then add white Gaussian noise. Equalize the rece ived symbols with Ze ro Forc ing criterion and Take the symbol fro m the second spatial dimension, subtract fro m the received symbol. Perform Maxima l Ratio Co mbin ing for equalizing the new received symbol then Perform hard decision decoding and count the bit errors. Repeat for mult iple values of and plot the simulat ion and theoretical results.

      Figure 3 : BER plot fo BPS K in 2×2 MIMO channel with Zero Forcing S uccessive Interference Cancellation equalization

      Co mpared to Zero Forcing equalization alone case, addition of successive interference cancellat ion results in around 2.2dB of imp rovement for BER of . he improve ment is brought in because decoding of the informat ion fro m the first spatial dimension ) has a lower error probability that the symbol transmitted fro m the second dimension. However, the assumption is that is decoded correctly may not be true in general.

   6. CONCLUSIONS

An equalizer for on the SIC and the linear ZFE is proposed. In each iteration, the proposed equalizer detects and cancels a group of ele ments of the source vector in a receive signal. This SIC process allows the FIR equalizers designed by SIC-ZFE algorith m to be further optimized without error propagation proble m. Simu lation results showed that significant BER performance gain can be obtained by the proposed SIC- ZFE even if only two interference cancellat ion iterations are applied to each input signal vector when compared to that of FIR-ZFE.

REFERENCES

1. G.G. Ra leigh and J.M. Cioffi, Spatio-te mporal coding for wire less communication,

   IEEE Trans. on Communications, vo1.46, 110.3, pp.357-366, 1988.

2. S.M. A la mouti, A simp le transmit diversity technique

   for wireless communicat ions,

   IEEE Trans. on Selected Areas in Communications, vol. 16, no.8, pp.1451-1458, 1988.

3. A Scaglione, P. Stoica, S. Ba rbarossa, G.B.Giannakis and H Sa mpath,

   Optima l designs for space-time linear precoders and decoders, IEEE Trans. on Signal Processing, ~01.501, 10.5,p p.1051-1064, May 2002.

4. V.Pohl, V.Jungnicke l, E.Jorswieck and V.von Helmo lt, Ze ro forc ing equalizing filte r for MIM O channels with intersymbol interference, Proc. IEEEPIMRC, vo1.3, pp.1037-1041,2002.

5. HSa mpath, P.Stoica and A.Pau lra j, Generalized linear precoder and decoder design for MlMO channels using the weighted MMSE criterion,

   lEEE Trans. on Communication, vo1.49,no.12, pp.2198- 2206, Dec. 2001.

6. X.G. Xia, G. Wang and P. Fan, Space-Time

   Modulated Codes for Me mory Channels: Capacity and Information Rates. Zero-Fo rcing Dec ision

   Feedback Equalize r, P mc . IEEE Sensor Array and

   Multichannel Signal

   Processing Workshop, pp.183-187,2000.

7. DIG-COMM-BARRY-LEE-M ESSERSCHMITT Digital Co mmunication: Third Edit ion, by John R. Ba rry,

   Edwa rd A. Lee, Dav id G. Messerschmitt

8. WIRELESS-TSE, VISWANATH Fundamentals of Wireless Co mmunicat ion, Dav id Tse, Pra mod Viswanath