Analysis Of The Frequency Offset Effect On The Performance Of Zadoff-Chu Sequence Based Random Access Signals

In wireless cellular communication systems,random access signals are typically used by devices in the cellular network for initial network access or short message transmission.In4G systems(e.g.,LTE),a set of cyclically-shifted Zadoff-Chu(ZC)sequences generated from the same original ZC.sequence are used as the random access signals as they are orthogonal to each other due to the ideal or perfect cross-correlation property of a ZC sequence.In addition to being used as the multiple access signals,these ZC sequences are also employed as the timing signals by the access point to obtain the timing of each access device due to(again)the ideal autocorrelation property.However,the ideal cross-correlation/autocorrelation property of the ZC sequences is derived under the assumption of no frequency offset between the transmitter and the receiver.Unfortunately,the frequency offset does have a profound impact on the cross-correlation/autocorrelation property of a ZC sequence and hence on the orthogonality property of the sequences created from a ZC sequence with the same root as well.Consequently,the properties of ZC sequences as multiple access signals and timing signals are affected.Moreover,in practical wireless communication scenarios,the frequency offset between transceivers is inevitable,which includes the accumulated frequency uncertainties at the access device transmitter and the access point receiver depending on the accuracy of the oscillator as well as the Doppler effect resulting from the mobility of the access device.This dissertation studies the frequency offset effect on ZC sequences as random access signals,particularly the interference and timing characteristics,and aims to provide some theoretical and technical insights to the design and selection of a ZC sequence set when applied to practical communication systems.The main contents and contributions are listed as follows:(1)The mathematical model of the random access signal transceiver is studied.And then a closed-form expression of the correlation between two cyclic-shifted ZC sequences with frequency offset is derived.It is shown that ZC sequence's perfect correlation is no longer true in practical applications when a frequency offset is present between the transmitter and the receiver.That is,the ideal correlation property is lost under non-zero frequency offset,which may impair the overall performance of the random access signals formed from these sequences.(2)The effect of frequency offset on the interference characteristics among multiple ZC sequences in an orthogonal ZC sequence set is studied.A frequency offset damages the orthogonality of a ZC sequence set,hence causing non-zero cross-correlation between the sequences in the set.This translates to interference between the random access signals.The concept of the critical frequency offset associated with a ZC sequence pair and the spectrum of a ZC sequence set are introduced.And then inter-sequence interference properties are evaluated,including the average and upper bound of the inter-sequence interference of a given sequence set.This dissertation shows that the sensitivity of ZC sequence set to the interference caused by frequency offset is completely governed by its critical frequency offset spectrum,especially the lower end components of the spectrum.Therefore,a ZC sequence set can be altered to suit diverse frequency offset scenarios by reshaping the set spectrum with removing the smallest critical frequency offsets that dominate the interference in order to achieve the promised detection performance.(3)The effect of the frequency offset on the timing property of an individual ZC sequence is studied.The timing error rate is first derived under a given frequency offset and a time uncertainty range.A key mathematical concept,the timing spectrum,is then developed,which relates the frequency effect on a ZC sequence timing performance directly to the root parameter of a ZC sequence and the time uncertainty at a receiver.This dissertation demonstrates how the time uncertainty and the selection of the root parameter can jointly affect the sensitivity of a ZC sequence's timing performance to a frequency offset.It also shows how a timing spectrum fully characterizes a ZC sequence's timing behavior and how a ZC sequence's fundamental limitation(i.e.,the irreducible timing error floor)is precisely predicted from the timing spectrum in the presence of a frequency offset.The analytical results point out that there will be no timing error floor when the smallest critical frequency offset does not exist in the timing spectrum.(4)The design and selection of the ZC sequence root and ZC sequence set generated from the root are studied.In high frequency offset scenario,the correlation of ZC sequence is severely affected,which greatly degrades the detection and timing performance.According to the analyses of frequency offset effect,this dissertation develops a method to select the ZC sequence root and ZC sequence set under a given time uncertainty range to achieve the promised performance.The timing spectrum of the selected root does not contain the smallest critical frequency offset(s)to avoid the irreducible timing error floor.The carefully designed and planned spectrum of the ZC sequence set generated from the selected root also does not include the smallest critical frequency offset(s)to reduce the inter-sequence interference.